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>
779 <title>Data types and type synonyms</title>
781 <sect3 id="nullary-types">
782 <title>Data types with no constructors</title>
784 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
785 a data type with no constructors. For example:</para>
789 data T a -- T :: * -> *
792 <para>Syntactically, the declaration lacks the "= constrs" part. The
793 type can be parameterised over types of any kind, but if the kind is
794 not <literal>*</literal> then an explicit kind annotation must be used
795 (see <xref linkend="sec-kinding">).</para>
797 <para>Such data types have only one value, namely bottom.
798 Nevertheless, they can be useful when defining "phantom types".</para>
801 <sect3 id="infix-tycons">
802 <title>Infix type constructors</title>
805 GHC allows type constructors to be operators, and to be written infix, very much
806 like expressions. More specifically:
809 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
810 The lexical syntax is the same as that for data constructors.
813 Types can be written infix. For example <literal>Int :*: Bool</literal>.
817 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
818 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
821 Fixities may be declared for type constructors just as for data constructors. However,
822 one cannot distinguish between the two in a fixity declaration; a fixity declaration
823 sets the fixity for a data constructor and the corresponding type constructor. For example:
827 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
828 and similarly for <literal>:*:</literal>.
829 <literal>Int `a` Bool</literal>.
832 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
835 Data type and type-synonym declarations can be written infix. E.g.
837 data a :*: b = Foo a b
838 type a :+: b = Either a b
842 The only thing that differs between operators in types and operators in expressions is that
843 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
844 are not allowed in types. Reason: the uniform thing to do would be to make them type
845 variables, but that's not very useful. A less uniform but more useful thing would be to
846 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
847 lists. So for now we just exclude them.
854 <sect3 id="type-synonyms">
855 <title>Liberalised type synonyms</title>
858 Type synonmys are like macros at the type level, and
859 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
860 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
862 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
863 in a type synonym, thus:
865 type Discard a = forall b. Show b => a -> b -> (a, String)
870 g :: Discard Int -> (Int,Bool) -- A rank-2 type
877 You can write an unboxed tuple in a type synonym:
879 type Pr = (# Int, Int #)
887 You can apply a type synonym to a forall type:
889 type Foo a = a -> a -> Bool
891 f :: Foo (forall b. b->b)
893 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
895 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
900 You can apply a type synonym to a partially applied type synonym:
902 type Generic i o = forall x. i x -> o x
907 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
909 foo :: forall x. x -> [x]
917 GHC currently does kind checking before expanding synonyms (though even that
921 After expanding type synonyms, GHC does validity checking on types, looking for
922 the following mal-formedness which isn't detected simply by kind checking:
925 Type constructor applied to a type involving for-alls.
928 Unboxed tuple on left of an arrow.
931 Partially-applied type synonym.
935 this will be rejected:
937 type Pr = (# Int, Int #)
942 because GHC does not allow unboxed tuples on the left of a function arrow.
947 <sect3 id="existential-quantification">
948 <title>Existentially quantified data constructors
952 The idea of using existential quantification in data type declarations
953 was suggested by Laufer (I believe, thought doubtless someone will
954 correct me), and implemented in Hope+. It's been in Lennart
955 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
956 proved very useful. Here's the idea. Consider the declaration:
962 data Foo = forall a. MkFoo a (a -> Bool)
969 The data type <literal>Foo</literal> has two constructors with types:
975 MkFoo :: forall a. a -> (a -> Bool) -> Foo
982 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
983 does not appear in the data type itself, which is plain <literal>Foo</literal>.
984 For example, the following expression is fine:
990 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
996 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
997 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
998 isUpper</function> packages a character with a compatible function. These
999 two things are each of type <literal>Foo</literal> and can be put in a list.
1003 What can we do with a value of type <literal>Foo</literal>?. In particular,
1004 what happens when we pattern-match on <function>MkFoo</function>?
1010 f (MkFoo val fn) = ???
1016 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1017 are compatible, the only (useful) thing we can do with them is to
1018 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1025 f (MkFoo val fn) = fn val
1031 What this allows us to do is to package heterogenous values
1032 together with a bunch of functions that manipulate them, and then treat
1033 that collection of packages in a uniform manner. You can express
1034 quite a bit of object-oriented-like programming this way.
1037 <sect4 id="existential">
1038 <title>Why existential?
1042 What has this to do with <emphasis>existential</emphasis> quantification?
1043 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1049 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1055 But Haskell programmers can safely think of the ordinary
1056 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1057 adding a new existential quantification construct.
1063 <title>Type classes</title>
1066 An easy extension (implemented in <Command>hbc</Command>) is to allow
1067 arbitrary contexts before the constructor. For example:
1073 data Baz = forall a. Eq a => Baz1 a a
1074 | forall b. Show b => Baz2 b (b -> b)
1080 The two constructors have the types you'd expect:
1086 Baz1 :: forall a. Eq a => a -> a -> Baz
1087 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1093 But when pattern matching on <function>Baz1</function> the matched values can be compared
1094 for equality, and when pattern matching on <function>Baz2</function> the first matched
1095 value can be converted to a string (as well as applying the function to it).
1096 So this program is legal:
1103 f (Baz1 p q) | p == q = "Yes"
1105 f (Baz2 v fn) = show (fn v)
1111 Operationally, in a dictionary-passing implementation, the
1112 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1113 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1114 extract it on pattern matching.
1118 Notice the way that the syntax fits smoothly with that used for
1119 universal quantification earlier.
1125 <title>Restrictions</title>
1128 There are several restrictions on the ways in which existentially-quantified
1129 constructors can be use.
1138 When pattern matching, each pattern match introduces a new,
1139 distinct, type for each existential type variable. These types cannot
1140 be unified with any other type, nor can they escape from the scope of
1141 the pattern match. For example, these fragments are incorrect:
1149 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1150 is the result of <function>f1</function>. One way to see why this is wrong is to
1151 ask what type <function>f1</function> has:
1155 f1 :: Foo -> a -- Weird!
1159 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1164 f1 :: forall a. Foo -> a -- Wrong!
1168 The original program is just plain wrong. Here's another sort of error
1172 f2 (Baz1 a b) (Baz1 p q) = a==q
1176 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1177 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1178 from the two <function>Baz1</function> constructors.
1186 You can't pattern-match on an existentially quantified
1187 constructor in a <literal>let</literal> or <literal>where</literal> group of
1188 bindings. So this is illegal:
1192 f3 x = a==b where { Baz1 a b = x }
1195 Instead, use a <literal>case</literal> expression:
1198 f3 x = case x of Baz1 a b -> a==b
1201 In general, you can only pattern-match
1202 on an existentially-quantified constructor in a <literal>case</literal> expression or
1203 in the patterns of a function definition.
1205 The reason for this restriction is really an implementation one.
1206 Type-checking binding groups is already a nightmare without
1207 existentials complicating the picture. Also an existential pattern
1208 binding at the top level of a module doesn't make sense, because it's
1209 not clear how to prevent the existentially-quantified type "escaping".
1210 So for now, there's a simple-to-state restriction. We'll see how
1218 You can't use existential quantification for <literal>newtype</literal>
1219 declarations. So this is illegal:
1223 newtype T = forall a. Ord a => MkT a
1227 Reason: a value of type <literal>T</literal> must be represented as a pair
1228 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1229 That contradicts the idea that <literal>newtype</literal> should have no
1230 concrete representation. You can get just the same efficiency and effect
1231 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1232 overloading involved, then there is more of a case for allowing
1233 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1234 because the <literal>data</literal> version does carry an implementation cost,
1235 but single-field existentially quantified constructors aren't much
1236 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1237 stands, unless there are convincing reasons to change it.
1245 You can't use <literal>deriving</literal> to define instances of a
1246 data type with existentially quantified data constructors.
1248 Reason: in most cases it would not make sense. For example:#
1251 data T = forall a. MkT [a] deriving( Eq )
1254 To derive <literal>Eq</literal> in the standard way we would need to have equality
1255 between the single component of two <function>MkT</function> constructors:
1259 (MkT a) == (MkT b) = ???
1262 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1263 It's just about possible to imagine examples in which the derived instance
1264 would make sense, but it seems altogether simpler simply to prohibit such
1265 declarations. Define your own instances!
1280 <sect2 id="multi-param-type-classes">
1281 <title>Class declarations</title>
1284 This section documents GHC's implementation of multi-parameter type
1285 classes. There's lots of background in the paper <ULink
1286 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1287 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
1288 Jones, Erik Meijer).
1291 There are the following constraints on class declarations:
1296 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1300 class Collection c a where
1301 union :: c a -> c a -> c a
1312 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1313 of "acyclic" involves only the superclass relationships. For example,
1319 op :: D b => a -> b -> b
1322 class C a => D a where { ... }
1326 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1327 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1328 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1335 <emphasis>There are no restrictions on the context in a class declaration
1336 (which introduces superclasses), except that the class hierarchy must
1337 be acyclic</emphasis>. So these class declarations are OK:
1341 class Functor (m k) => FiniteMap m k where
1344 class (Monad m, Monad (t m)) => Transform t m where
1345 lift :: m a -> (t m) a
1355 <emphasis>All of the class type variables must be reachable (in the sense
1356 mentioned in <xref linkend="type-restrictions">)
1357 from the free varibles of each method type
1358 </emphasis>. For example:
1362 class Coll s a where
1364 insert :: s -> a -> s
1368 is not OK, because the type of <literal>empty</literal> doesn't mention
1369 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1370 types, and has the same motivation.
1372 Sometimes, offending class declarations exhibit misunderstandings. For
1373 example, <literal>Coll</literal> might be rewritten
1377 class Coll s a where
1379 insert :: s a -> a -> s a
1383 which makes the connection between the type of a collection of
1384 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1385 Occasionally this really doesn't work, in which case you can split the
1393 class CollE s => Coll s a where
1394 insert :: s -> a -> s
1404 <sect3 id="class-method-types">
1405 <title>Class method types</title>
1407 Haskell 98 prohibits class method types to mention constraints on the
1408 class type variable, thus:
1411 fromList :: [a] -> s a
1412 elem :: Eq a => a -> s a -> Bool
1414 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1415 contains the constraint <literal>Eq a</literal>, constrains only the
1416 class type variable (in this case <literal>a</literal>).
1419 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1426 <sect2 id="type-restrictions">
1427 <title>Type signatures</title>
1429 <sect3><title>The context of a type signature</title>
1431 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
1432 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
1435 f :: Eq (m a) => [m a] -> [m a]
1438 This choice recovers principal types, a property that Haskell 1.4 does not have.
1441 GHC imposes the following restrictions on the constraints in a type signature.
1445 forall tv1..tvn (c1, ...,cn) => type
1448 (Here, we write the "foralls" explicitly, although the Haskell source
1449 language omits them; in Haskell 1.4, all the free type variables of an
1450 explicit source-language type signature are universally quantified,
1451 except for the class type variables in a class declaration. However,
1452 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
1461 <emphasis>Each universally quantified type variable
1462 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1464 A type variable is "reachable" if it it is functionally dependent
1465 (see <xref linkend="functional-dependencies">)
1466 on the type variables free in <literal>type</literal>.
1467 The reason for this is that a value with a type that does not obey
1468 this restriction could not be used without introducing
1470 Here, for example, is an illegal type:
1474 forall a. Eq a => Int
1478 When a value with this type was used, the constraint <literal>Eq tv</literal>
1479 would be introduced where <literal>tv</literal> is a fresh type variable, and
1480 (in the dictionary-translation implementation) the value would be
1481 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1482 can never know which instance of <literal>Eq</literal> to use because we never
1483 get any more information about <literal>tv</literal>.
1490 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1491 universally quantified type variables <literal>tvi</literal></emphasis>.
1493 For example, this type is OK because <literal>C a b</literal> mentions the
1494 universally quantified type variable <literal>b</literal>:
1498 forall a. C a b => burble
1502 The next type is illegal because the constraint <literal>Eq b</literal> does not
1503 mention <literal>a</literal>:
1507 forall a. Eq b => burble
1511 The reason for this restriction is milder than the other one. The
1512 excluded types are never useful or necessary (because the offending
1513 context doesn't need to be witnessed at this point; it can be floated
1514 out). Furthermore, floating them out increases sharing. Lastly,
1515 excluding them is a conservative choice; it leaves a patch of
1516 territory free in case we need it later.
1527 <title>For-all hoisting</title>
1529 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms">) at the right hand
1530 end of an arrow, thus:
1532 type Discard a = forall b. a -> b -> a
1534 g :: Int -> Discard Int
1537 Simply expanding the type synonym would give
1539 g :: Int -> (forall b. Int -> b -> Int)
1541 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1543 g :: forall b. Int -> Int -> b -> Int
1545 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1546 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1547 performs the transformation:</emphasis>
1549 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1551 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1553 (In fact, GHC tries to retain as much synonym information as possible for use in
1554 error messages, but that is a usability issue.) This rule applies, of course, whether
1555 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1556 valid way to write <literal>g</literal>'s type signature:
1558 g :: Int -> Int -> forall b. b -> Int
1562 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1565 type Foo a = (?x::Int) => Bool -> a
1570 g :: (?x::Int) => Bool -> Bool -> Int
1578 <sect2 id="instance-decls">
1579 <title>Instance declarations</title>
1582 <title>Overlapping instances</title>
1584 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1589 instance context1 => C type1 where ...
1590 instance context2 => C type2 where ...
1594 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1596 However, if you give the command line option
1597 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1598 option</primary></indexterm> then overlapping instance declarations are permitted.
1599 However, GHC arranges never to commit to using an instance declaration
1600 if another instance declaration also applies, either now or later.
1606 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1612 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1613 (but not identical to <literal>type1</literal>), or vice versa.
1617 Notice that these rules
1622 make it clear which instance decl to use
1623 (pick the most specific one that matches)
1630 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1631 Reason: you can pick which instance decl
1632 "matches" based on the type.
1637 However the rules are over-conservative. Two instance declarations can overlap,
1638 but it can still be clear in particular situations which to use. For example:
1640 instance C (Int,a) where ...
1641 instance C (a,Bool) where ...
1643 These are rejected by GHC's rules, but it is clear what to do when trying
1644 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1645 cannot apply. Yell if this restriction bites you.
1648 GHC is also conservative about committing to an overlapping instance. For example:
1650 class C a where { op :: a -> a }
1651 instance C [Int] where ...
1652 instance C a => C [a] where ...
1654 f :: C b => [b] -> [b]
1657 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1658 GHC does not commit to the second instance declaration, because in a paricular
1659 call of f, b might be instantiate to Int, so the first instance declaration
1660 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1661 GHC will instead silently pick the second instance, without complaining about
1662 the problem of subsequent instantiations.
1665 Regrettably, GHC doesn't guarantee to detect overlapping instance
1666 declarations if they appear in different modules. GHC can "see" the
1667 instance declarations in the transitive closure of all the modules
1668 imported by the one being compiled, so it can "see" all instance decls
1669 when it is compiling <literal>Main</literal>. However, it currently chooses not
1670 to look at ones that can't possibly be of use in the module currently
1671 being compiled, in the interests of efficiency. (Perhaps we should
1672 change that decision, at least for <literal>Main</literal>.)
1677 <title>Type synonyms in the instance head</title>
1680 <emphasis>Unlike Haskell 1.4, instance heads may use type
1681 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1682 As always, using a type synonym is just shorthand for
1683 writing the RHS of the type synonym definition. For example:
1687 type Point = (Int,Int)
1688 instance C Point where ...
1689 instance C [Point] where ...
1693 is legal. However, if you added
1697 instance C (Int,Int) where ...
1701 as well, then the compiler will complain about the overlapping
1702 (actually, identical) instance declarations. As always, type synonyms
1703 must be fully applied. You cannot, for example, write:
1708 instance Monad P where ...
1712 This design decision is independent of all the others, and easily
1713 reversed, but it makes sense to me.
1718 <sect3 id="undecidable-instances">
1719 <title>Undecidable instances</title>
1721 <para>An instance declaration must normally obey the following rules:
1723 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1724 an instance declaration <emphasis>must not</emphasis> be a type variable.
1725 For example, these are OK:
1728 instance C Int a where ...
1730 instance D (Int, Int) where ...
1732 instance E [[a]] where ...
1736 instance F a where ...
1738 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1739 For example, this is OK:
1741 instance Stateful (ST s) (MutVar s) where ...
1748 <para>All of the types in the <emphasis>context</emphasis> of
1749 an instance declaration <emphasis>must</emphasis> be type variables.
1752 instance C a b => Eq (a,b) where ...
1756 instance C Int b => Foo b where ...
1762 These restrictions ensure that
1763 context reduction terminates: each reduction step removes one type
1764 constructor. For example, the following would make the type checker
1765 loop if it wasn't excluded:
1767 instance C a => C a where ...
1769 There are two situations in which the rule is a bit of a pain. First,
1770 if one allows overlapping instance declarations then it's quite
1771 convenient to have a "default instance" declaration that applies if
1772 something more specific does not:
1781 Second, sometimes you might want to use the following to get the
1782 effect of a "class synonym":
1786 class (C1 a, C2 a, C3 a) => C a where { }
1788 instance (C1 a, C2 a, C3 a) => C a where { }
1792 This allows you to write shorter signatures:
1804 f :: (C1 a, C2 a, C3 a) => ...
1808 Voluminous correspondence on the Haskell mailing list has convinced me
1809 that it's worth experimenting with more liberal rules. If you use
1810 the experimental flag <option>-fallow-undecidable-instances</option>
1811 <indexterm><primary>-fallow-undecidable-instances
1812 option</primary></indexterm>, you can use arbitrary
1813 types in both an instance context and instance head. Termination is ensured by having a
1814 fixed-depth recursion stack. If you exceed the stack depth you get a
1815 sort of backtrace, and the opportunity to increase the stack depth
1816 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1819 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1820 allowing these idioms interesting idioms.
1827 <sect2 id="implicit-parameters">
1828 <title>Implicit parameters</title>
1830 <para> Implicit paramters are implemented as described in
1831 "Implicit parameters: dynamic scoping with static types",
1832 J Lewis, MB Shields, E Meijer, J Launchbury,
1833 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1836 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1838 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1839 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1840 context. In Haskell, all variables are statically bound. Dynamic
1841 binding of variables is a notion that goes back to Lisp, but was later
1842 discarded in more modern incarnations, such as Scheme. Dynamic binding
1843 can be very confusing in an untyped language, and unfortunately, typed
1844 languages, in particular Hindley-Milner typed languages like Haskell,
1845 only support static scoping of variables.
1848 However, by a simple extension to the type class system of Haskell, we
1849 can support dynamic binding. Basically, we express the use of a
1850 dynamically bound variable as a constraint on the type. These
1851 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1852 function uses a dynamically-bound variable <literal>?x</literal>
1853 of type <literal>t'</literal>". For
1854 example, the following expresses the type of a sort function,
1855 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1857 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1859 The dynamic binding constraints are just a new form of predicate in the type class system.
1862 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1863 where <literal>x</literal> is
1864 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1865 Use of this construct also introduces a new
1866 dynamic-binding constraint in the type of the expression.
1867 For example, the following definition
1868 shows how we can define an implicitly parameterized sort function in
1869 terms of an explicitly parameterized <literal>sortBy</literal> function:
1871 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1873 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1879 <title>Implicit-parameter type constraints</title>
1881 Dynamic binding constraints behave just like other type class
1882 constraints in that they are automatically propagated. Thus, when a
1883 function is used, its implicit parameters are inherited by the
1884 function that called it. For example, our <literal>sort</literal> function might be used
1885 to pick out the least value in a list:
1887 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1888 least xs = fst (sort xs)
1890 Without lifting a finger, the <literal>?cmp</literal> parameter is
1891 propagated to become a parameter of <literal>least</literal> as well. With explicit
1892 parameters, the default is that parameters must always be explicit
1893 propagated. With implicit parameters, the default is to always
1897 An implicit-parameter type constraint differs from other type class constraints in the
1898 following way: All uses of a particular implicit parameter must have
1899 the same type. This means that the type of <literal>(?x, ?x)</literal>
1900 is <literal>(?x::a) => (a,a)</literal>, and not
1901 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1905 <para> You can't have an implicit parameter in the context of a class or instance
1906 declaration. For example, both these declarations are illegal:
1908 class (?x::Int) => C a where ...
1909 instance (?x::a) => Foo [a] where ...
1911 Reason: exactly which implicit parameter you pick up depends on exactly where
1912 you invoke a function. But the ``invocation'' of instance declarations is done
1913 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1914 Easiest thing is to outlaw the offending types.</para>
1916 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1918 f :: (?x :: [a]) => Int -> Int
1921 g :: (Read a, Show a) => String -> String
1924 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1925 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1926 quite unambiguous, and fixes the type <literal>a</literal>.
1931 <title>Implicit-parameter bindings</title>
1934 An implicit parameter is <emphasis>bound</emphasis> using the standard
1935 <literal>let</literal> or <literal>where</literal> binding forms.
1936 For example, we define the <literal>min</literal> function by binding
1937 <literal>cmp</literal>.
1940 min = let ?cmp = (<=) in least
1944 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1945 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1946 (including in a list comprehension, or do-notation, or pattern guards),
1947 or a <literal>where</literal> clause.
1948 Note the following points:
1951 An implicit-parameter binding group must be a
1952 collection of simple bindings to implicit-style variables (no
1953 function-style bindings, and no type signatures); these bindings are
1954 neither polymorphic or recursive.
1957 You may not mix implicit-parameter bindings with ordinary bindings in a
1958 single <literal>let</literal>
1959 expression; use two nested <literal>let</literal>s instead.
1960 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1964 You may put multiple implicit-parameter bindings in a
1965 single binding group; but they are <emphasis>not</emphasis> treated
1966 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1967 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1968 parameter. The bindings are not nested, and may be re-ordered without changing
1969 the meaning of the program.
1970 For example, consider:
1972 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1974 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1975 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
1977 f :: (?x::Int) => Int -> Int
1986 <sect2 id="linear-implicit-parameters">
1987 <title>Linear implicit parameters</title>
1989 Linear implicit parameters are an idea developed by Koen Claessen,
1990 Mark Shields, and Simon PJ. They address the long-standing
1991 problem that monads seem over-kill for certain sorts of problem, notably:
1994 <listitem> <para> distributing a supply of unique names </para> </listitem>
1995 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1996 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2000 Linear implicit parameters are just like ordinary implicit parameters,
2001 except that they are "linear" -- that is, they cannot be copied, and
2002 must be explicitly "split" instead. Linear implicit parameters are
2003 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2004 (The '/' in the '%' suggests the split!)
2009 import GHC.Exts( Splittable )
2011 data NameSupply = ...
2013 splitNS :: NameSupply -> (NameSupply, NameSupply)
2014 newName :: NameSupply -> Name
2016 instance Splittable NameSupply where
2020 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2021 f env (Lam x e) = Lam x' (f env e)
2024 env' = extend env x x'
2025 ...more equations for f...
2027 Notice that the implicit parameter %ns is consumed
2029 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2030 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2034 So the translation done by the type checker makes
2035 the parameter explicit:
2037 f :: NameSupply -> Env -> Expr -> Expr
2038 f ns env (Lam x e) = Lam x' (f ns1 env e)
2040 (ns1,ns2) = splitNS ns
2042 env = extend env x x'
2044 Notice the call to 'split' introduced by the type checker.
2045 How did it know to use 'splitNS'? Because what it really did
2046 was to introduce a call to the overloaded function 'split',
2047 defined by the class <literal>Splittable</literal>:
2049 class Splittable a where
2052 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2053 split for name supplies. But we can simply write
2059 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2061 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2062 <literal>GHC.Exts</literal>.
2067 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2068 are entirely distinct implicit parameters: you
2069 can use them together and they won't intefere with each other. </para>
2072 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2074 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2075 in the context of a class or instance declaration. </para></listitem>
2079 <sect3><title>Warnings</title>
2082 The monomorphism restriction is even more important than usual.
2083 Consider the example above:
2085 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2086 f env (Lam x e) = Lam x' (f env e)
2089 env' = extend env x x'
2091 If we replaced the two occurrences of x' by (newName %ns), which is
2092 usually a harmless thing to do, we get:
2094 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2095 f env (Lam x e) = Lam (newName %ns) (f env e)
2097 env' = extend env x (newName %ns)
2099 But now the name supply is consumed in <emphasis>three</emphasis> places
2100 (the two calls to newName,and the recursive call to f), so
2101 the result is utterly different. Urk! We don't even have
2105 Well, this is an experimental change. With implicit
2106 parameters we have already lost beta reduction anyway, and
2107 (as John Launchbury puts it) we can't sensibly reason about
2108 Haskell programs without knowing their typing.
2113 <sect3><title>Recursive functions</title>
2114 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2117 foo :: %x::T => Int -> [Int]
2119 foo n = %x : foo (n-1)
2121 where T is some type in class Splittable.</para>
2123 Do you get a list of all the same T's or all different T's
2124 (assuming that split gives two distinct T's back)?
2126 If you supply the type signature, taking advantage of polymorphic
2127 recursion, you get what you'd probably expect. Here's the
2128 translated term, where the implicit param is made explicit:
2131 foo x n = let (x1,x2) = split x
2132 in x1 : foo x2 (n-1)
2134 But if you don't supply a type signature, GHC uses the Hindley
2135 Milner trick of using a single monomorphic instance of the function
2136 for the recursive calls. That is what makes Hindley Milner type inference
2137 work. So the translation becomes
2141 foom n = x : foom (n-1)
2145 Result: 'x' is not split, and you get a list of identical T's. So the
2146 semantics of the program depends on whether or not foo has a type signature.
2149 You may say that this is a good reason to dislike linear implicit parameters
2150 and you'd be right. That is why they are an experimental feature.
2156 <sect2 id="functional-dependencies">
2157 <title>Functional dependencies
2160 <para> Functional dependencies are implemented as described by Mark Jones
2161 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2162 In Proceedings of the 9th European Symposium on Programming,
2163 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2167 Functional dependencies are introduced by a vertical bar in the syntax of a
2168 class declaration; e.g.
2170 class (Monad m) => MonadState s m | m -> s where ...
2172 class Foo a b c | a b -> c where ...
2174 There should be more documentation, but there isn't (yet). Yell if you need it.
2180 <sect2 id="sec-kinding">
2181 <title>Explicitly-kinded quantification</title>
2184 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2185 to give the kind explicitly as (machine-checked) documentation,
2186 just as it is nice to give a type signature for a function. On some occasions,
2187 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2188 John Hughes had to define the data type:
2190 data Set cxt a = Set [a]
2191 | Unused (cxt a -> ())
2193 The only use for the <literal>Unused</literal> constructor was to force the correct
2194 kind for the type variable <literal>cxt</literal>.
2197 GHC now instead allows you to specify the kind of a type variable directly, wherever
2198 a type variable is explicitly bound. Namely:
2200 <listitem><para><literal>data</literal> declarations:
2202 data Set (cxt :: * -> *) a = Set [a]
2203 </Screen></para></listitem>
2204 <listitem><para><literal>type</literal> declarations:
2206 type T (f :: * -> *) = f Int
2207 </Screen></para></listitem>
2208 <listitem><para><literal>class</literal> declarations:
2210 class (Eq a) => C (f :: * -> *) a where ...
2211 </Screen></para></listitem>
2212 <listitem><para><literal>forall</literal>'s in type signatures:
2214 f :: forall (cxt :: * -> *). Set cxt Int
2215 </Screen></para></listitem>
2220 The parentheses are required. Some of the spaces are required too, to
2221 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2222 will get a parse error, because "<literal>::*->*</literal>" is a
2223 single lexeme in Haskell.
2227 As part of the same extension, you can put kind annotations in types
2230 f :: (Int :: *) -> Int
2231 g :: forall a. a -> (a :: *)
2235 atype ::= '(' ctype '::' kind ')
2237 The parentheses are required.
2242 <sect2 id="universal-quantification">
2243 <title>Arbitrary-rank polymorphism
2247 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2248 allows us to say exactly what this means. For example:
2256 g :: forall b. (b -> b)
2258 The two are treated identically.
2262 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2263 explicit universal quantification in
2265 For example, all the following types are legal:
2267 f1 :: forall a b. a -> b -> a
2268 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2270 f2 :: (forall a. a->a) -> Int -> Int
2271 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2273 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2275 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2276 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2277 The <literal>forall</literal> makes explicit the universal quantification that
2278 is implicitly added by Haskell.
2281 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2282 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2283 shows, the polymorphic type on the left of the function arrow can be overloaded.
2286 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
2287 they have rank-2 types on the left of a function arrow.
2290 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2291 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2292 that restriction has now been lifted.)
2293 In particular, a forall-type (also called a "type scheme"),
2294 including an operational type class context, is legal:
2296 <listitem> <para> On the left of a function arrow </para> </listitem>
2297 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
2298 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2299 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
2300 field type signatures.</para> </listitem>
2301 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2302 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
2304 There is one place you cannot put a <literal>forall</literal>:
2305 you cannot instantiate a type variable with a forall-type. So you cannot
2306 make a forall-type the argument of a type constructor. So these types are illegal:
2308 x1 :: [forall a. a->a]
2309 x2 :: (forall a. a->a, Int)
2310 x3 :: Maybe (forall a. a->a)
2312 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2313 a type variable any more!
2322 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2323 the types of the constructor arguments. Here are several examples:
2329 data T a = T1 (forall b. b -> b -> b) a
2331 data MonadT m = MkMonad { return :: forall a. a -> m a,
2332 bind :: forall a b. m a -> (a -> m b) -> m b
2335 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2341 The constructors have rank-2 types:
2347 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2348 MkMonad :: forall m. (forall a. a -> m a)
2349 -> (forall a b. m a -> (a -> m b) -> m b)
2351 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2357 Notice that you don't need to use a <literal>forall</literal> if there's an
2358 explicit context. For example in the first argument of the
2359 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2360 prefixed to the argument type. The implicit <literal>forall</literal>
2361 quantifies all type variables that are not already in scope, and are
2362 mentioned in the type quantified over.
2366 As for type signatures, implicit quantification happens for non-overloaded
2367 types too. So if you write this:
2370 data T a = MkT (Either a b) (b -> b)
2373 it's just as if you had written this:
2376 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2379 That is, since the type variable <literal>b</literal> isn't in scope, it's
2380 implicitly universally quantified. (Arguably, it would be better
2381 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2382 where that is what is wanted. Feedback welcomed.)
2386 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2387 the constructor to suitable values, just as usual. For example,
2398 a3 = MkSwizzle reverse
2401 a4 = let r x = Just x
2408 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2409 mkTs f x y = [T1 f x, T1 f y]
2415 The type of the argument can, as usual, be more general than the type
2416 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2417 does not need the <literal>Ord</literal> constraint.)
2421 When you use pattern matching, the bound variables may now have
2422 polymorphic types. For example:
2428 f :: T a -> a -> (a, Char)
2429 f (T1 w k) x = (w k x, w 'c' 'd')
2431 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2432 g (MkSwizzle s) xs f = s (map f (s xs))
2434 h :: MonadT m -> [m a] -> m [a]
2435 h m [] = return m []
2436 h m (x:xs) = bind m x $ \y ->
2437 bind m (h m xs) $ \ys ->
2444 In the function <function>h</function> we use the record selectors <literal>return</literal>
2445 and <literal>bind</literal> to extract the polymorphic bind and return functions
2446 from the <literal>MonadT</literal> data structure, rather than using pattern
2452 <title>Type inference</title>
2455 In general, type inference for arbitrary-rank types is undecideable.
2456 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2457 to get a decidable algorithm by requiring some help from the programmer.
2458 We do not yet have a formal specification of "some help" but the rule is this:
2461 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2462 provides an explicit polymorphic type for x, or GHC's type inference will assume
2463 that x's type has no foralls in it</emphasis>.
2466 What does it mean to "provide" an explicit type for x? You can do that by
2467 giving a type signature for x directly, using a pattern type signature
2468 (<xref linkend="scoped-type-variables">), thus:
2470 \ f :: (forall a. a->a) -> (f True, f 'c')
2472 Alternatively, you can give a type signature to the enclosing
2473 context, which GHC can "push down" to find the type for the variable:
2475 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2477 Here the type signature on the expression can be pushed inwards
2478 to give a type signature for f. Similarly, and more commonly,
2479 one can give a type signature for the function itself:
2481 h :: (forall a. a->a) -> (Bool,Char)
2482 h f = (f True, f 'c')
2484 You don't need to give a type signature if the lambda bound variable
2485 is a constructor argument. Here is an example we saw earlier:
2487 f :: T a -> a -> (a, Char)
2488 f (T1 w k) x = (w k x, w 'c' 'd')
2490 Here we do not need to give a type signature to <literal>w</literal>, because
2491 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2498 <sect3 id="implicit-quant">
2499 <title>Implicit quantification</title>
2502 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2503 user-written types, if and only if there is no explicit <literal>forall</literal>,
2504 GHC finds all the type variables mentioned in the type that are not already
2505 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2509 f :: forall a. a -> a
2516 h :: forall b. a -> b -> b
2522 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2525 f :: (a -> a) -> Int
2527 f :: forall a. (a -> a) -> Int
2529 f :: (forall a. a -> a) -> Int
2532 g :: (Ord a => a -> a) -> Int
2533 -- MEANS the illegal type
2534 g :: forall a. (Ord a => a -> a) -> Int
2536 g :: (forall a. Ord a => a -> a) -> Int
2538 The latter produces an illegal type, which you might think is silly,
2539 but at least the rule is simple. If you want the latter type, you
2540 can write your for-alls explicitly. Indeed, doing so is strongly advised
2549 <sect2 id="scoped-type-variables">
2550 <title>Scoped type variables
2554 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2555 variable</emphasis>. For example
2561 f (xs::[a]) = ys ++ ys
2570 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2571 This brings the type variable <literal>a</literal> into scope; it scopes over
2572 all the patterns and right hand sides for this equation for <function>f</function>.
2573 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2577 Pattern type signatures are completely orthogonal to ordinary, separate
2578 type signatures. The two can be used independently or together.
2579 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2580 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2581 implicitly universally quantified. (If there are no type variables in
2582 scope, all type variables mentioned in the signature are universally
2583 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2584 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2585 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2586 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2587 it becomes possible to do so.
2591 Scoped type variables are implemented in both GHC and Hugs. Where the
2592 implementations differ from the specification below, those differences
2597 So much for the basic idea. Here are the details.
2601 <title>What a pattern type signature means</title>
2603 A type variable brought into scope by a pattern type signature is simply
2604 the name for a type. The restriction they express is that all occurrences
2605 of the same name mean the same type. For example:
2607 f :: [Int] -> Int -> Int
2608 f (xs::[a]) (y::a) = (head xs + y) :: a
2610 The pattern type signatures on the left hand side of
2611 <literal>f</literal> express the fact that <literal>xs</literal>
2612 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2613 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2614 specifies that this expression must have the same type <literal>a</literal>.
2615 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2616 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2617 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2618 rules, which specified that a pattern-bound type variable should be universally quantified.)
2619 For example, all of these are legal:</para>
2622 t (x::a) (y::a) = x+y*2
2624 f (x::a) (y::b) = [x,y] -- a unifies with b
2626 g (x::a) = x + 1::Int -- a unifies with Int
2628 h x = let k (y::a) = [x,y] -- a is free in the
2629 in k x -- environment
2631 k (x::a) True = ... -- a unifies with Int
2632 k (x::Int) False = ...
2635 w (x::a) = x -- a unifies with [b]
2641 <title>Scope and implicit quantification</title>
2649 All the type variables mentioned in a pattern,
2650 that are not already in scope,
2651 are brought into scope by the pattern. We describe this set as
2652 the <emphasis>type variables bound by the pattern</emphasis>.
2655 f (x::a) = let g (y::(a,b)) = fst y
2659 The pattern <literal>(x::a)</literal> brings the type variable
2660 <literal>a</literal> into scope, as well as the term
2661 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2662 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2663 and brings into scope the type variable <literal>b</literal>.
2669 The type variable(s) bound by the pattern have the same scope
2670 as the term variable(s) bound by the pattern. For example:
2673 f (x::a) = <...rhs of f...>
2674 (p::b, q::b) = (1,2)
2675 in <...body of let...>
2677 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2678 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2679 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2680 just like <literal>p</literal> and <literal>q</literal> do.
2681 Indeed, the newly bound type variables also scope over any ordinary, separate
2682 type signatures in the <literal>let</literal> group.
2689 The type variables bound by the pattern may be
2690 mentioned in ordinary type signatures or pattern
2691 type signatures anywhere within their scope.
2698 In ordinary type signatures, any type variable mentioned in the
2699 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2707 Ordinary type signatures do not bring any new type variables
2708 into scope (except in the type signature itself!). So this is illegal:
2715 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2716 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2717 and that is an incorrect typing.
2724 The pattern type signature is a monotype:
2729 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2733 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2734 not to type schemes.
2738 There is no implicit universal quantification on pattern type signatures (in contrast to
2739 ordinary type signatures).
2749 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2750 scope over the methods defined in the <literal>where</literal> part. For example:
2764 (Not implemented in Hugs yet, Dec 98).
2775 <title>Where a pattern type signature can occur</title>
2778 A pattern type signature can occur in any pattern. For example:
2783 A pattern type signature can be on an arbitrary sub-pattern, not
2788 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2797 Pattern type signatures, including the result part, can be used
2798 in lambda abstractions:
2801 (\ (x::a, y) :: a -> x)
2808 Pattern type signatures, including the result part, can be used
2809 in <literal>case</literal> expressions:
2813 case e of { (x::a, y) :: a -> x }
2821 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2822 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2823 token or a parenthesised type of some sort). To see why,
2824 consider how one would parse this:
2838 Pattern type signatures can bind existential type variables.
2843 data T = forall a. MkT [a]
2846 f (MkT [t::a]) = MkT t3
2859 Pattern type signatures
2860 can be used in pattern bindings:
2863 f x = let (y, z::a) = x in ...
2864 f1 x = let (y, z::Int) = x in ...
2865 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2866 f3 :: (b->b) = \x -> x
2869 In all such cases, the binding is not generalised over the pattern-bound
2870 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2871 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2872 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2873 In contrast, the binding
2878 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2879 in <literal>f4</literal>'s scope.
2889 <title>Result type signatures</title>
2892 The result type of a function can be given a signature, thus:
2896 f (x::a) :: [a] = [x,x,x]
2900 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2901 result type. Sometimes this is the only way of naming the type variable
2906 f :: Int -> [a] -> [a]
2907 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2908 in \xs -> map g (reverse xs `zip` xs)
2913 The type variables bound in a result type signature scope over the right hand side
2914 of the definition. However, consider this corner-case:
2916 rev1 :: [a] -> [a] = \xs -> reverse xs
2918 foo ys = rev (ys::[a])
2920 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2921 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2922 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2923 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
2924 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
2927 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
2928 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
2932 rev1 :: [a] -> [a] = \xs -> reverse xs
2937 Result type signatures are not yet implemented in Hugs.
2944 <sect2 id="deriving-typeable">
2945 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2948 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2949 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2950 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2951 classes <literal>Eq</literal>, <literal>Ord</literal>,
2952 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2955 GHC extends this list with two more classes that may be automatically derived
2956 (provided the <option>-fglasgow-exts</option> flag is specified):
2957 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2958 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
2959 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2963 <sect2 id="newtype-deriving">
2964 <title>Generalised derived instances for newtypes</title>
2967 When you define an abstract type using <literal>newtype</literal>, you may want
2968 the new type to inherit some instances from its representation. In
2969 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2970 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2971 other classes you have to write an explicit instance declaration. For
2972 example, if you define
2975 newtype Dollars = Dollars Int
2978 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2979 explicitly define an instance of <literal>Num</literal>:
2982 instance Num Dollars where
2983 Dollars a + Dollars b = Dollars (a+b)
2986 All the instance does is apply and remove the <literal>newtype</literal>
2987 constructor. It is particularly galling that, since the constructor
2988 doesn't appear at run-time, this instance declaration defines a
2989 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2990 dictionary, only slower!
2994 <sect3> <title> Generalising the deriving clause </title>
2996 GHC now permits such instances to be derived instead, so one can write
2998 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3001 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3002 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3003 derives an instance declaration of the form
3006 instance Num Int => Num Dollars
3009 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3013 We can also derive instances of constructor classes in a similar
3014 way. For example, suppose we have implemented state and failure monad
3015 transformers, such that
3018 instance Monad m => Monad (State s m)
3019 instance Monad m => Monad (Failure m)
3021 In Haskell 98, we can define a parsing monad by
3023 type Parser tok m a = State [tok] (Failure m) a
3026 which is automatically a monad thanks to the instance declarations
3027 above. With the extension, we can make the parser type abstract,
3028 without needing to write an instance of class <literal>Monad</literal>, via
3031 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3034 In this case the derived instance declaration is of the form
3036 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3039 Notice that, since <literal>Monad</literal> is a constructor class, the
3040 instance is a <emphasis>partial application</emphasis> of the new type, not the
3041 entire left hand side. We can imagine that the type declaration is
3042 ``eta-converted'' to generate the context of the instance
3047 We can even derive instances of multi-parameter classes, provided the
3048 newtype is the last class parameter. In this case, a ``partial
3049 application'' of the class appears in the <literal>deriving</literal>
3050 clause. For example, given the class
3053 class StateMonad s m | m -> s where ...
3054 instance Monad m => StateMonad s (State s m) where ...
3056 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3058 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3059 deriving (Monad, StateMonad [tok])
3062 The derived instance is obtained by completing the application of the
3063 class to the new type:
3066 instance StateMonad [tok] (State [tok] (Failure m)) =>
3067 StateMonad [tok] (Parser tok m)
3072 As a result of this extension, all derived instances in newtype
3073 declarations are treated uniformly (and implemented just by reusing
3074 the dictionary for the representation type), <emphasis>except</emphasis>
3075 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3076 the newtype and its representation.
3080 <sect3> <title> A more precise specification </title>
3082 Derived instance declarations are constructed as follows. Consider the
3083 declaration (after expansion of any type synonyms)
3086 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3092 <literal>S</literal> is a type constructor,
3095 <literal>t1...tk</literal> are types,
3098 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3099 the <literal>ti</literal>, and
3102 the <literal>ci</literal> are partial applications of
3103 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3104 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3107 Then, for each <literal>ci</literal>, the derived instance
3110 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3112 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3113 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3117 As an example which does <emphasis>not</emphasis> work, consider
3119 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3121 Here we cannot derive the instance
3123 instance Monad (State s m) => Monad (NonMonad m)
3126 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3127 and so cannot be "eta-converted" away. It is a good thing that this
3128 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3129 not, in fact, a monad --- for the same reason. Try defining
3130 <literal>>>=</literal> with the correct type: you won't be able to.
3134 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3135 important, since we can only derive instances for the last one. If the
3136 <literal>StateMonad</literal> class above were instead defined as
3139 class StateMonad m s | m -> s where ...
3142 then we would not have been able to derive an instance for the
3143 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3144 classes usually have one "main" parameter for which deriving new
3145 instances is most interesting.
3153 <!-- ==================== End of type system extensions ================= -->
3155 <!-- ====================== TEMPLATE HASKELL ======================= -->
3157 <sect1 id="template-haskell">
3158 <title>Template Haskell</title>
3160 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3161 Template Haskell at <ulink url="http://www.haskell.org/th/">
3162 http://www.haskell.org/th/</ulink>, while
3164 the main technical innovations is discussed in "<ulink
3165 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3166 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3169 <para> The first example from that paper is set out below as a worked example to help get you started.
3173 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3174 Tim Sheard is going to expand it.)
3177 <sect2> <title> Syntax </title>
3179 Template Haskell has the following new syntactic constructions. You need to use the flag
3180 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
3184 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3185 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3186 There must be no space between the "$" and the identifier or parenthesis. This use
3187 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3188 of "." as an infix operator. If you want the infix operator, put spaces around it.
3190 <para> A splice can occur in place of
3192 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3193 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3194 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3196 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3197 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3203 A expression quotation is written in Oxford brackets, thus:
3205 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3206 the quotation has type <literal>Expr</literal>.</para></listitem>
3207 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3208 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3209 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3210 the quotation has type <literal>Type</literal>.</para></listitem>
3211 </itemizedlist></para></listitem>
3214 Reification is written thus:
3216 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3217 has type <literal>Dec</literal>. </para></listitem>
3218 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3219 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3220 <listitem><para> Still to come: fixities </para></listitem>
3222 </itemizedlist></para>
3230 <sect2> <title> Using Template Haskell </title>
3234 The data types and monadic constructor functions for Template Haskell are in the library
3235 <literal>Language.Haskell.THSyntax</literal>.
3239 You can only run a function at compile time if it is imported from another module. That is,
3240 you can't define a function in a module, and call it from within a splice in the same module.
3241 (It would make sense to do so, but it's hard to implement.)
3245 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3248 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3249 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3250 compiles and runs a program, and then looks at the result. So it's important that
3251 the program it compiles produces results whose representations are identical to
3252 those of the compiler itself.
3256 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3257 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3262 <sect2> <title> A Template Haskell Worked Example </title>
3263 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3264 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3270 -- Import our template "pr"
3271 import Printf ( pr )
3273 -- The splice operator $ takes the Haskell source code
3274 -- generated at compile time by "pr" and splices it into
3275 -- the argument of "putStrLn".
3276 main = putStrLn ( $(pr "Hello") )
3283 -- Skeletal printf from the paper.
3284 -- It needs to be in a separate module to the one where
3285 -- you intend to use it.
3287 -- Import some Template Haskell syntax
3288 import Language.Haskell.THSyntax
3290 -- Describe a format string
3291 data Format = D | S | L String
3293 -- Parse a format string. This is left largely to you
3294 -- as we are here interested in building our first ever
3295 -- Template Haskell program and not in building printf.
3296 parse :: String -> [Format]
3299 -- Generate Haskell source code from a parsed representation
3300 -- of the format string. This code will be spliced into
3301 -- the module which calls "pr", at compile time.
3302 gen :: [Format] -> Expr
3303 gen [D] = [| \n -> show n |]
3304 gen [S] = [| \s -> s |]
3305 gen [L s] = string s
3307 -- Here we generate the Haskell code for the splice
3308 -- from an input format string.
3309 pr :: String -> Expr
3310 pr s = gen (parse s)
3313 <para>Now run the compiler (here we are using a "stage three" build of GHC, at a Cygwin prompt on Windows):
3316 ghc/compiler/stage3/ghc-inplace --make -fglasgow-exts -package haskell-src main.hs -o main.exe
3319 <para>Run "main.exe" and here is your output:
3331 <!-- ===================== Arrow notation =================== -->
3333 <sect1 id="arrow-notation">
3334 <title>Arrow notation
3337 <para>Arrows are a generalization of monads introduced by John Hughes.
3338 For more details, see
3343 “Generalising Monads to Arrows”,
3344 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3345 pp67–111, May 2000.
3351 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3352 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3358 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3359 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3365 and the arrows web page at
3366 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3367 With the <option>-farrows</option> flag, GHC supports the arrow
3368 notation described in the second of these papers.
3369 What follows is a brief introduction to the notation;
3370 it won't make much sense unless you've read Hughes's paper.
3371 This notation is translated to ordinary Haskell,
3372 using combinators from the
3373 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3377 <para>The extension adds a new kind of expression for defining arrows,
3378 of the form <literal>proc pat -> cmd</literal>,
3379 where <literal>proc</literal> is a new keyword.
3380 The variables of the pattern are bound in the body of the
3381 <literal>proc</literal>-expression,
3382 which is a new sort of thing called a <firstterm>command</firstterm>.
3383 The syntax of commands is as follows:
3385 cmd ::= exp1 -< exp2
3386 | exp1 -<< exp2
3387 | do { cstmt1 .. cstmtn ; cmd }
3389 | if exp then cmd1 else cmd2
3390 | case exp of { calts }
3392 | (| aexp cmd1 .. cmdn |)
3393 | \ pat1 .. patn -> cmd
3399 | rec { cstmt1 .. cstmtn }
3402 Commands produce values, but (like monadic computations)
3403 may yield more than one value,
3404 or none, and may do other things as well.
3405 For the most part, familiarity with monadic notation is a good guide to
3407 However the values of expressions, even monadic ones,
3408 are determined by the values of the variables they contain;
3409 this is not necessarily the case for commands.
3413 A simple example of the new notation is the expression
3415 proc x -> f -< x+1
3417 We call this a <firstterm>procedure</firstterm> or
3418 <firstterm>arrow abstraction</firstterm>.
3419 As with a lambda expression, the variable <literal>x</literal>
3420 is a new variable bound within the <literal>proc</literal>-expression.
3421 It refers to the input to the arrow.
3422 In the above example, <literal>-<</literal> is not an identifier but an
3423 new reserved symbol used for building commands from an expression of arrow
3424 type and an expression to be fed as input to that arrow.
3425 (The weird look will make more sense later.)
3426 It may be read as analogue of application for arrows.
3427 The above example is equivalent to the Haskell expression
3429 arr (\ x -> x+1) >>> f
3431 That would make no sense if the expression to the left of
3432 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3433 More generally, the expression to the left of <literal>-<</literal>
3434 may not involve any <firstterm>local variable</firstterm>,
3435 i.e. a variable bound in the current arrow abstraction.
3436 For such a situation there is a variant <literal>-<<</literal>, as in
3438 proc x -> f x -<< x+1
3440 which is equivalent to
3442 arr (\ x -> (f, x+1)) >>> app
3444 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3446 Such an arrow is equivalent to a monad, so if you're using this form
3447 you may find a monadic formulation more convenient.
3451 <title>do-notation for commands</title>
3454 Another form of command is a form of <literal>do</literal>-notation.
3455 For example, you can write
3464 You can read this much like ordinary <literal>do</literal>-notation,
3465 but with commands in place of monadic expressions.
3466 The first line sends the value of <literal>x+1</literal> as an input to
3467 the arrow <literal>f</literal>, and matches its output against
3468 <literal>y</literal>.
3469 In the next line, the output is discarded.
3470 The arrow <literal>returnA</literal> is defined in the
3471 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3472 module as <literal>arr id</literal>.
3473 The above example is treated as an abbreviation for
3475 arr (\ x -> (x, x)) >>>
3476 first (arr (\ x -> x+1) >>> f) >>>
3477 arr (\ (y, x) -> (y, (x, y))) >>>
3478 first (arr (\ y -> 2*y) >>> g) >>>
3480 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3481 first (arr (\ (x, z) -> x*z) >>> h) >>>
3482 arr (\ (t, z) -> t+z) >>>
3485 Note that variables not used later in the composition are projected out.
3486 After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
3488 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3489 module, this reduces to
3491 arr (\ x -> (x+1, x)) >>>
3493 arr (\ (y, x) -> (2*y, (x, y))) >>>
3495 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3497 arr (\ (t, z) -> t+z)
3499 which is what you might have written by hand.
3500 With arrow notation, GHC keeps track of all those tuples of variables for you.
3504 Note that although the above translation suggests that
3505 <literal>let</literal>-bound variables like <literal>z</literal> must be
3506 monomorphic, the actual translation produces Core,
3507 so polymorphic variables are allowed.
3511 It's also possible to have mutually recursive bindings,
3512 using the new <literal>rec</literal> keyword, as in the following example:
3514 counter :: ArrowCircuit a => a Bool Int
3515 counter = proc reset -> do
3516 rec output <- returnA -< if reset then 0 else next
3517 next <- delay 0 -< output+1
3518 returnA -< output
3520 The translation of such forms uses the <literal>loop</literal> combinator,
3521 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3527 <title>Conditional commands</title>
3530 In the previous example, we used a conditional expression to construct the
3532 Sometimes we want to conditionally execute different commands, as in
3539 which is translated to
3541 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3542 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3544 Since the translation uses <literal>|||</literal>,
3545 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3549 There are also <literal>case</literal> commands, like
3555 y <- h -< (x1, x2)
3559 The syntax is the same as for <literal>case</literal> expressions,
3560 except that the bodies of the alternatives are commands rather than expressions.
3561 The translation is similar to that of <literal>if</literal> commands.
3567 <title>Defining your own control structures</title>
3570 As we're seen, arrow notation provides constructs,
3571 modelled on those for expressions,
3572 for sequencing, value recursion and conditionals.
3573 But suitable combinators,
3574 which you can define in ordinary Haskell,
3575 may also be used to build new commands out of existing ones.
3576 The basic idea is that a command defines an arrow from environments to values.
3577 These environments assign values to the free local variables of the command.
3578 Thus combinators that produce arrows from arrows
3579 may also be used to build commands from commands.
3580 For example, the <literal>ArrowChoice</literal> class includes a combinator
3582 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3584 so we can use it to build commands:
3589 symbol Plus -< ()
3590 y <- term -< ()
3593 symbol Minus -< ()
3594 y <- term -< ()
3597 This is equivalent to
3599 expr' = (proc x -> returnA -< x)
3600 <+> (proc x -> do
3601 symbol Plus -< ()
3602 y <- term -< ()
3604 <+> (proc x -> do
3605 symbol Minus -< ()
3606 y <- term -< ()
3609 It is essential that this operator be polymorphic in <literal>e</literal>
3610 (representing the environment input to the command
3611 and thence to its subcommands)
3612 and satisfy the corresponding naturality property
3614 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3616 at least for strict <literal>k</literal>.
3617 (This should be automatic if you're not using <literal>seq</literal>.)
3618 This ensures that environments seen by the subcommands are environments
3619 of the whole command,
3620 and also allows the translation to safely trim these environments.
3621 The operator must also not use any variable defined within the current
3626 We could define our own operator
3628 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3629 untilA body cond = proc x ->
3630 if cond x then returnA -< ()
3633 untilA body cond -< x
3635 and use it in the same way.
3636 Of course this infix syntax only makes sense for binary operators;
3637 there is also a more general syntax involving special brackets:
3641 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3648 <title>Primitive constructs</title>
3651 Some operators will need to pass additional inputs to their subcommands.
3652 For example, in an arrow type supporting exceptions,
3653 the operator that attaches an exception handler will wish to pass the
3654 exception that occurred to the handler.
3655 Such an operator might have a type
3657 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3659 where <literal>Ex</literal> is the type of exceptions handled.
3660 You could then use this with arrow notation by writing a command
3662 body `handleA` \ ex -> handler
3664 so that if an exception is raised in the command <literal>body</literal>,
3665 the variable <literal>ex</literal> is bound to the value of the exception
3666 and the command <literal>handler</literal>,
3667 which typically refers to <literal>ex</literal>, is entered.
3668 Though the syntax here looks like a functional lambda,
3669 we are talking about commands, and something different is going on.
3670 The input to the arrow represented by a command consists of values for
3671 the free local variables in the command, plus a stack of anonymous values.
3672 In all the prior examples, this stack was empty.
3673 In the second argument to <literal>handleA</literal>,
3674 this stack consists of one value, the value of the exception.
3675 The command form of lambda merely gives this value a name.
3680 the values on the stack are paired to the right of the environment.
3681 So when designing operators like <literal>handleA</literal> that pass
3682 extra inputs to their subcommands,
3683 More precisely, the type of each argument of the operator (and its result)
3684 should have the form
3686 a (...(e,t1), ... tn) t
3688 where <replaceable>e</replaceable> is a polymorphic variable
3689 (representing the environment)
3690 and <replaceable>ti</replaceable> are the types of the values on the stack,
3691 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3692 The polymorphic variable <replaceable>e</replaceable> must not occur in
3693 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3694 <replaceable>t</replaceable>.
3695 However the arrows involved need not be the same.
3696 Here are some more examples of suitable operators:
3698 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3699 runReader :: ... => a e c -> a' (e,State) c
3700 runState :: ... => a e c -> a' (e,State) (c,State)
3702 We can supply the extra input required by commands built with the last two
3703 by applying them to ordinary expressions, as in
3707 (|runReader (do { ... })|) s
3709 which adds <literal>s</literal> to the stack of inputs to the command
3710 built using <literal>runReader</literal>.
3714 The command versions of lambda abstraction and application are analogous to
3715 the expression versions.
3716 In particular, the beta and eta rules describe equivalences of commands.
3717 These three features (operators, lambda abstraction and application)
3718 are the core of the notation; everything else can be built using them,
3719 though the results would be somewhat clumsy.
3720 For example, we could simulate <literal>do</literal>-notation by defining
3722 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3723 u `bind` f = returnA &&& u >>> f
3725 bind_ :: Arrow a => a e b -> a e c -> a e c
3726 u `bind_` f = u `bind` (arr fst >>> f)
3728 We could simulate <literal>do</literal> by defining
3730 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3731 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3738 <title>Differences with the paper</title>
3743 <para>Instead of a single form of arrow application (arrow tail) with two
3744 translations, the implementation provides two forms
3745 <quote><literal>-<</literal></quote> (first-order)
3746 and <quote><literal>-<<</literal></quote> (higher-order).
3751 <para>User-defined operators are flagged with banana brackets instead of
3752 a new <literal>form</literal> keyword.
3761 <title>Portability</title>
3764 Although only GHC implements arrow notation directly,
3765 there is also a preprocessor
3767 <ulink url="http://www.haskell.org/arrows/">arrows web page></ulink>)
3768 that translates arrow notation into Haskell 98
3769 for use with other Haskell systems.
3770 You would still want to check arrow programs with GHC;
3771 tracing type errors in the preprocessor output is not easy.
3772 Modules intended for both GHC and the preprocessor must observe some
3773 additional restrictions:
3778 The module must import
3779 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3785 The preprocessor cannot cope with other Haskell extensions.
3786 These would have to go in separate modules.
3792 Because the preprocessor targets Haskell (rather than Core),
3793 <literal>let</literal>-bound variables are monomorphic.
3804 <!-- ==================== ASSERTIONS ================= -->
3806 <sect1 id="sec-assertions">
3808 <indexterm><primary>Assertions</primary></indexterm>
3812 If you want to make use of assertions in your standard Haskell code, you
3813 could define a function like the following:
3819 assert :: Bool -> a -> a
3820 assert False x = error "assertion failed!"
3827 which works, but gives you back a less than useful error message --
3828 an assertion failed, but which and where?
3832 One way out is to define an extended <function>assert</function> function which also
3833 takes a descriptive string to include in the error message and
3834 perhaps combine this with the use of a pre-processor which inserts
3835 the source location where <function>assert</function> was used.
3839 Ghc offers a helping hand here, doing all of this for you. For every
3840 use of <function>assert</function> in the user's source:
3846 kelvinToC :: Double -> Double
3847 kelvinToC k = assert (k >= 0.0) (k+273.15)
3853 Ghc will rewrite this to also include the source location where the
3860 assert pred val ==> assertError "Main.hs|15" pred val
3866 The rewrite is only performed by the compiler when it spots
3867 applications of <function>Control.Exception.assert</function>, so you
3868 can still define and use your own versions of
3869 <function>assert</function>, should you so wish. If not, import
3870 <literal>Control.Exception</literal> to make use
3871 <function>assert</function> in your code.
3875 To have the compiler ignore uses of assert, use the compiler option
3876 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3877 option</primary></indexterm> That is, expressions of the form
3878 <literal>assert pred e</literal> will be rewritten to
3879 <literal>e</literal>.
3883 Assertion failures can be caught, see the documentation for the
3884 <literal>Control.Exception</literal> library for the details.
3890 <!-- =============================== PRAGMAS =========================== -->
3892 <sect1 id="pragmas">
3893 <title>Pragmas</title>
3895 <indexterm><primary>pragma</primary></indexterm>
3897 <para>GHC supports several pragmas, or instructions to the
3898 compiler placed in the source code. Pragmas don't normally affect
3899 the meaning of the program, but they might affect the efficiency
3900 of the generated code.</para>
3902 <para>Pragmas all take the form
3904 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3906 where <replaceable>word</replaceable> indicates the type of
3907 pragma, and is followed optionally by information specific to that
3908 type of pragma. Case is ignored in
3909 <replaceable>word</replaceable>. The various values for
3910 <replaceable>word</replaceable> that GHC understands are described
3911 in the following sections; any pragma encountered with an
3912 unrecognised <replaceable>word</replaceable> is (silently)
3915 <sect2 id="deprecated-pragma">
3916 <title>DEPRECATED pragma</title>
3917 <indexterm><primary>DEPRECATED</primary>
3920 <para>The DEPRECATED pragma lets you specify that a particular
3921 function, class, or type, is deprecated. There are two
3926 <para>You can deprecate an entire module thus:</para>
3928 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3931 <para>When you compile any module that import
3932 <literal>Wibble</literal>, GHC will print the specified
3937 <para>You can deprecate a function, class, or type, with the
3938 following top-level declaration:</para>
3940 {-# DEPRECATED f, C, T "Don't use these" #-}
3942 <para>When you compile any module that imports and uses any
3943 of the specifed entities, GHC will print the specified
3948 <para>You can suppress the warnings with the flag
3949 <option>-fno-warn-deprecations</option>.</para>
3952 <sect2 id="inline-noinline-pragma">
3953 <title>INLINE and NOINLINE pragmas</title>
3955 <para>These pragmas control the inlining of function
3958 <sect3 id="inline-pragma">
3959 <title>INLINE pragma</title>
3960 <indexterm><primary>INLINE</primary></indexterm>
3962 <para>GHC (with <option>-O</option>, as always) tries to
3963 inline (or “unfold”) functions/values that are
3964 “small enough,” thus avoiding the call overhead
3965 and possibly exposing other more-wonderful optimisations.
3966 Normally, if GHC decides a function is “too
3967 expensive” to inline, it will not do so, nor will it
3968 export that unfolding for other modules to use.</para>
3970 <para>The sledgehammer you can bring to bear is the
3971 <literal>INLINE</literal><indexterm><primary>INLINE
3972 pragma</primary></indexterm> pragma, used thusly:</para>
3975 key_function :: Int -> String -> (Bool, Double)
3977 #ifdef __GLASGOW_HASKELL__
3978 {-# INLINE key_function #-}
3982 <para>(You don't need to do the C pre-processor carry-on
3983 unless you're going to stick the code through HBC—it
3984 doesn't like <literal>INLINE</literal> pragmas.)</para>
3986 <para>The major effect of an <literal>INLINE</literal> pragma
3987 is to declare a function's “cost” to be very low.
3988 The normal unfolding machinery will then be very keen to
3991 <para>Syntactially, an <literal>INLINE</literal> pragma for a
3992 function can be put anywhere its type signature could be
3995 <para><literal>INLINE</literal> pragmas are a particularly
3997 <literal>then</literal>/<literal>return</literal> (or
3998 <literal>bind</literal>/<literal>unit</literal>) functions in
3999 a monad. For example, in GHC's own
4000 <literal>UniqueSupply</literal> monad code, we have:</para>
4003 #ifdef __GLASGOW_HASKELL__
4004 {-# INLINE thenUs #-}
4005 {-# INLINE returnUs #-}
4009 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4010 linkend="noinline-pragma">).</para>
4013 <sect3 id="noinline-pragma">
4014 <title>NOINLINE pragma</title>
4016 <indexterm><primary>NOINLINE</primary></indexterm>
4017 <indexterm><primary>NOTINLINE</primary></indexterm>
4019 <para>The <literal>NOINLINE</literal> pragma does exactly what
4020 you'd expect: it stops the named function from being inlined
4021 by the compiler. You shouldn't ever need to do this, unless
4022 you're very cautious about code size.</para>
4024 <para><literal>NOTINLINE</literal> is a synonym for
4025 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4026 specified by Haskell 98 as the standard way to disable
4027 inlining, so it should be used if you want your code to be
4031 <sect3 id="phase-control">
4032 <title>Phase control</title>
4034 <para> Sometimes you want to control exactly when in GHC's
4035 pipeline the INLINE pragma is switched on. Inlining happens
4036 only during runs of the <emphasis>simplifier</emphasis>. Each
4037 run of the simplifier has a different <emphasis>phase
4038 number</emphasis>; the phase number decreases towards zero.
4039 If you use <option>-dverbose-core2core</option> you'll see the
4040 sequence of phase numbers for successive runs of the
4041 simpifier. In an INLINE pragma you can optionally specify a
4042 phase number, thus:</para>
4046 <para>You can say "inline <literal>f</literal> in Phase 2
4047 and all subsequent phases":
4049 {-# INLINE [2] f #-}
4055 <para>You can say "inline <literal>g</literal> in all
4056 phases up to, but not including, Phase 3":
4058 {-# INLINE [~3] g #-}
4064 <para>If you omit the phase indicator, you mean "inline in
4069 <para>You can use a phase number on a NOINLINE pragma too:</para>
4073 <para>You can say "do not inline <literal>f</literal>
4074 until Phase 2; in Phase 2 and subsequently behave as if
4075 there was no pragma at all":
4077 {-# NOINLINE [2] f #-}
4083 <para>You can say "do not inline <literal>g</literal> in
4084 Phase 3 or any subsequent phase; before that, behave as if
4085 there was no pragma":
4087 {-# NOINLINE [~3] g #-}
4093 <para>If you omit the phase indicator, you mean "never
4094 inline this function".</para>
4098 <para>The same phase-numbering control is available for RULES
4099 (<xref LinkEnd="rewrite-rules">).</para>
4103 <sect2 id="line-pragma">
4104 <title>LINE pragma</title>
4106 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4107 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4108 <para>This pragma is similar to C's <literal>#line</literal>
4109 pragma, and is mainly for use in automatically generated Haskell
4110 code. It lets you specify the line number and filename of the
4111 original code; for example</para>
4114 {-# LINE 42 "Foo.vhs" #-}
4117 <para>if you'd generated the current file from something called
4118 <filename>Foo.vhs</filename> and this line corresponds to line
4119 42 in the original. GHC will adjust its error messages to refer
4120 to the line/file named in the <literal>LINE</literal>
4124 <sect2 id="options-pragma">
4125 <title>OPTIONS pragma</title>
4126 <indexterm><primary>OPTIONS</primary>
4128 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4131 <para>The <literal>OPTIONS</literal> pragma is used to specify
4132 additional options that are given to the compiler when compiling
4133 this source file. See <xref linkend="source-file-options"> for
4138 <title>RULES pragma</title>
4140 <para>The RULES pragma lets you specify rewrite rules. It is
4141 described in <xref LinkEnd="rewrite-rules">.</para>
4144 <sect2 id="specialize-pragma">
4145 <title>SPECIALIZE pragma</title>
4147 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4148 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4149 <indexterm><primary>overloading, death to</primary></indexterm>
4151 <para>(UK spelling also accepted.) For key overloaded
4152 functions, you can create extra versions (NB: more code space)
4153 specialised to particular types. Thus, if you have an
4154 overloaded function:</para>
4157 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4160 <para>If it is heavily used on lists with
4161 <literal>Widget</literal> keys, you could specialise it as
4165 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4168 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4169 be put anywhere its type signature could be put.</para>
4171 <para>A <literal>SPECIALIZE</literal> has the effect of generating (a) a specialised
4172 version of the function and (b) a rewrite rule (see <xref linkend="rules">) that
4173 rewrites a call to the un-specialised function into a call to the specialised
4174 one. You can, instead, provide your own specialised function and your own rewrite rule.
4175 For example, suppose that:
4177 genericLookup :: Ord a => Table a b -> a -> b
4178 intLookup :: Table Int b -> Int -> b
4180 where <literal>intLookup</literal> is an implementation of <literal>genericLookup</literal>
4181 that works very fast for keys of type <literal>Int</literal>. Then you can write the rule
4183 {-# RULES "intLookup" genericLookup = intLookup #-}
4185 (see <xref linkend="rule-spec">). It is <emphasis>Your
4186 Responsibility</emphasis> to make sure that
4187 <function>intLookup</function> really behaves as a specialised
4188 version of <function>genericLookup</function>!!!</para>
4190 <para>An example in which using <literal>RULES</literal> for
4191 specialisation will Win Big:
4194 toDouble :: Real a => a -> Double
4195 toDouble = fromRational . toRational
4197 {-# RULES "toDouble/Int" toDouble = i2d #-}
4198 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4201 The <function>i2d</function> function is virtually one machine
4202 instruction; the default conversion—via an intermediate
4203 <literal>Rational</literal>—is obscenely expensive by
4208 <sect2 id="specialize-instance-pragma">
4209 <title>SPECIALIZE instance pragma
4213 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4214 <indexterm><primary>overloading, death to</primary></indexterm>
4215 Same idea, except for instance declarations. For example:
4218 instance (Eq a) => Eq (Foo a) where {
4219 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4223 The pragma must occur inside the <literal>where</literal> part
4224 of the instance declaration.
4227 Compatible with HBC, by the way, except perhaps in the placement
4237 <!-- ======================= REWRITE RULES ======================== -->
4239 <sect1 id="rewrite-rules">
4240 <title>Rewrite rules
4242 <indexterm><primary>RULES pagma</primary></indexterm>
4243 <indexterm><primary>pragma, RULES</primary></indexterm>
4244 <indexterm><primary>rewrite rules</primary></indexterm></title>
4247 The programmer can specify rewrite rules as part of the source program
4248 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4249 the <option>-O</option> flag (<xref LinkEnd="options-optimise">) is on,
4250 and (b) the <option>-frules-off</option> flag
4251 (<xref LinkEnd="options-f">) is not specified.
4259 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4266 <title>Syntax</title>
4269 From a syntactic point of view:
4275 There may be zero or more rules in a <literal>RULES</literal> pragma.
4282 Each rule has a name, enclosed in double quotes. The name itself has
4283 no significance at all. It is only used when reporting how many times the rule fired.
4289 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
4290 immediately after the name of the rule. Thus:
4293 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4296 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4297 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4306 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4307 is set, so you must lay out your rules starting in the same column as the
4308 enclosing definitions.
4315 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4316 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4317 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4318 by spaces, just like in a type <literal>forall</literal>.
4324 A pattern variable may optionally have a type signature.
4325 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4326 For example, here is the <literal>foldr/build</literal> rule:
4329 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4330 foldr k z (build g) = g k z
4333 Since <function>g</function> has a polymorphic type, it must have a type signature.
4340 The left hand side of a rule must consist of a top-level variable applied
4341 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4344 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4345 "wrong2" forall f. f True = True
4348 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4355 A rule does not need to be in the same module as (any of) the
4356 variables it mentions, though of course they need to be in scope.
4362 Rules are automatically exported from a module, just as instance declarations are.
4373 <title>Semantics</title>
4376 From a semantic point of view:
4382 Rules are only applied if you use the <option>-O</option> flag.
4388 Rules are regarded as left-to-right rewrite rules.
4389 When GHC finds an expression that is a substitution instance of the LHS
4390 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4391 By "a substitution instance" we mean that the LHS can be made equal to the
4392 expression by substituting for the pattern variables.
4399 The LHS and RHS of a rule are typechecked, and must have the
4407 GHC makes absolutely no attempt to verify that the LHS and RHS
4408 of a rule have the same meaning. That is undecideable in general, and
4409 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4416 GHC makes no attempt to make sure that the rules are confluent or
4417 terminating. For example:
4420 "loop" forall x,y. f x y = f y x
4423 This rule will cause the compiler to go into an infinite loop.
4430 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4436 GHC currently uses a very simple, syntactic, matching algorithm
4437 for matching a rule LHS with an expression. It seeks a substitution
4438 which makes the LHS and expression syntactically equal modulo alpha
4439 conversion. The pattern (rule), but not the expression, is eta-expanded if
4440 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4441 But not beta conversion (that's called higher-order matching).
4445 Matching is carried out on GHC's intermediate language, which includes
4446 type abstractions and applications. So a rule only matches if the
4447 types match too. See <xref LinkEnd="rule-spec"> below.
4453 GHC keeps trying to apply the rules as it optimises the program.
4454 For example, consider:
4463 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4464 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
4465 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4466 not be substituted, and the rule would not fire.
4473 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4474 that appears on the LHS of a rule</emphasis>, because once you have substituted
4475 for something you can't match against it (given the simple minded
4476 matching). So if you write the rule
4479 "map/map" forall f,g. map f . map g = map (f.g)
4482 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4483 It will only match something written with explicit use of ".".
4484 Well, not quite. It <emphasis>will</emphasis> match the expression
4490 where <function>wibble</function> is defined:
4493 wibble f g = map f . map g
4496 because <function>wibble</function> will be inlined (it's small).
4498 Later on in compilation, GHC starts inlining even things on the
4499 LHS of rules, but still leaves the rules enabled. This inlining
4500 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4507 All rules are implicitly exported from the module, and are therefore
4508 in force in any module that imports the module that defined the rule, directly
4509 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4510 in force when compiling A.) The situation is very similar to that for instance
4522 <title>List fusion</title>
4525 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4526 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4527 intermediate list should be eliminated entirely.
4531 The following are good producers:
4543 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4549 Explicit lists (e.g. <literal>[True, False]</literal>)
4555 The cons constructor (e.g <literal>3:4:[]</literal>)
4561 <function>++</function>
4567 <function>map</function>
4573 <function>filter</function>
4579 <function>iterate</function>, <function>repeat</function>
4585 <function>zip</function>, <function>zipWith</function>
4594 The following are good consumers:
4606 <function>array</function> (on its second argument)
4612 <function>length</function>
4618 <function>++</function> (on its first argument)
4624 <function>foldr</function>
4630 <function>map</function>
4636 <function>filter</function>
4642 <function>concat</function>
4648 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4654 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4655 will fuse with one but not the other)
4661 <function>partition</function>
4667 <function>head</function>
4673 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4679 <function>sequence_</function>
4685 <function>msum</function>
4691 <function>sortBy</function>
4700 So, for example, the following should generate no intermediate lists:
4703 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4709 This list could readily be extended; if there are Prelude functions that you use
4710 a lot which are not included, please tell us.
4714 If you want to write your own good consumers or producers, look at the
4715 Prelude definitions of the above functions to see how to do so.
4720 <sect2 id="rule-spec">
4721 <title>Specialisation
4725 Rewrite rules can be used to get the same effect as a feature
4726 present in earlier version of GHC:
4729 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4732 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4733 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4734 specialising the original definition of <function>fromIntegral</function> the programmer is
4735 promising that it is safe to use <function>int8ToInt16</function> instead.
4739 This feature is no longer in GHC. But rewrite rules let you do the
4744 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4748 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4749 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4750 GHC adds the type and dictionary applications to get the typed rule
4753 forall (d1::Integral Int8) (d2::Num Int16) .
4754 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4758 this rule does not need to be in the same file as fromIntegral,
4759 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4760 have an original definition available to specialise).
4766 <title>Controlling what's going on</title>
4774 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4780 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4781 If you add <option>-dppr-debug</option> you get a more detailed listing.
4787 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4790 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4791 {-# INLINE build #-}
4795 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4796 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4797 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4798 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4805 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4806 see how to write rules that will do fusion and yet give an efficient
4807 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4817 <sect2 id="core-pragma">
4818 <title>CORE pragma</title>
4820 <indexterm><primary>CORE pragma</primary></indexterm>
4821 <indexterm><primary>pragma, CORE</primary></indexterm>
4822 <indexterm><primary>core, annotation</primary></indexterm>
4825 The external core format supports <quote>Note</quote> annotations;
4826 the <literal>CORE</literal> pragma gives a way to specify what these
4827 should be in your Haskell source code. Syntactically, core
4828 annotations are attached to expressions and take a Haskell string
4829 literal as an argument. The following function definition shows an
4833 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
4836 Sematically, this is equivalent to:
4844 However, when external for is generated (via
4845 <option>-fext-core</option>), there will be Notes attached to the
4846 expressions <function>show</function> and <VarName>x</VarName>.
4847 The core function declaration for <function>f</function> is:
4851 f :: %forall a . GHCziShow.ZCTShow a ->
4852 a -> GHCziBase.ZMZN GHCziBase.Char =
4853 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
4855 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
4857 (tpl1::GHCziBase.Int ->
4859 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4861 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
4862 (tpl3::GHCziBase.ZMZN a ->
4863 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4871 Here, we can see that the function <function>show</function> (which
4872 has been expanded out to a case expression over the Show dictionary)
4873 has a <literal>%note</literal> attached to it, as does the
4874 expression <VarName>eta</VarName> (which used to be called
4875 <VarName>x</VarName>).
4882 <sect1 id="generic-classes">
4883 <title>Generic classes</title>
4885 <para>(Note: support for generic classes is currently broken in
4889 The ideas behind this extension are described in detail in "Derivable type classes",
4890 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4891 An example will give the idea:
4899 fromBin :: [Int] -> (a, [Int])
4901 toBin {| Unit |} Unit = []
4902 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4903 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4904 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4906 fromBin {| Unit |} bs = (Unit, bs)
4907 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4908 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4909 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4910 (y,bs'') = fromBin bs'
4913 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4914 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4915 which are defined thus in the library module <literal>Generics</literal>:
4919 data a :+: b = Inl a | Inr b
4920 data a :*: b = a :*: b
4923 Now you can make a data type into an instance of Bin like this:
4925 instance (Bin a, Bin b) => Bin (a,b)
4926 instance Bin a => Bin [a]
4928 That is, just leave off the "where" clause. Of course, you can put in the
4929 where clause and over-ride whichever methods you please.
4933 <title> Using generics </title>
4934 <para>To use generics you need to</para>
4937 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4938 <option>-fgenerics</option> (to generate extra per-data-type code),
4939 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4943 <para>Import the module <literal>Generics</literal> from the
4944 <literal>lang</literal> package. This import brings into
4945 scope the data types <literal>Unit</literal>,
4946 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4947 don't need this import if you don't mention these types
4948 explicitly; for example, if you are simply giving instance
4949 declarations.)</para>
4954 <sect2> <title> Changes wrt the paper </title>
4956 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4957 can be written infix (indeed, you can now use
4958 any operator starting in a colon as an infix type constructor). Also note that
4959 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4960 Finally, note that the syntax of the type patterns in the class declaration
4961 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4962 alone would ambiguous when they appear on right hand sides (an extension we
4963 anticipate wanting).
4967 <sect2> <title>Terminology and restrictions</title>
4969 Terminology. A "generic default method" in a class declaration
4970 is one that is defined using type patterns as above.
4971 A "polymorphic default method" is a default method defined as in Haskell 98.
4972 A "generic class declaration" is a class declaration with at least one
4973 generic default method.
4981 Alas, we do not yet implement the stuff about constructor names and
4988 A generic class can have only one parameter; you can't have a generic
4989 multi-parameter class.
4995 A default method must be defined entirely using type patterns, or entirely
4996 without. So this is illegal:
4999 op :: a -> (a, Bool)
5000 op {| Unit |} Unit = (Unit, True)
5003 However it is perfectly OK for some methods of a generic class to have
5004 generic default methods and others to have polymorphic default methods.
5010 The type variable(s) in the type pattern for a generic method declaration
5011 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:
5015 op {| p :*: q |} (x :*: y) = op (x :: p)
5023 The type patterns in a generic default method must take one of the forms:
5029 where "a" and "b" are type variables. Furthermore, all the type patterns for
5030 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5031 must use the same type variables. So this is illegal:
5035 op {| a :+: b |} (Inl x) = True
5036 op {| p :+: q |} (Inr y) = False
5038 The type patterns must be identical, even in equations for different methods of the class.
5039 So this too is illegal:
5043 op1 {| a :*: b |} (x :*: y) = True
5046 op2 {| p :*: q |} (x :*: y) = False
5048 (The reason for this restriction is that we gather all the equations for a particular type consructor
5049 into a single generic instance declaration.)
5055 A generic method declaration must give a case for each of the three type constructors.
5061 The type for a generic method can be built only from:
5063 <listitem> <para> Function arrows </para> </listitem>
5064 <listitem> <para> Type variables </para> </listitem>
5065 <listitem> <para> Tuples </para> </listitem>
5066 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5068 Here are some example type signatures for generic methods:
5071 op2 :: Bool -> (a,Bool)
5072 op3 :: [Int] -> a -> a
5075 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5079 This restriction is an implementation restriction: we just havn't got around to
5080 implementing the necessary bidirectional maps over arbitrary type constructors.
5081 It would be relatively easy to add specific type constructors, such as Maybe and list,
5082 to the ones that are allowed.</para>
5087 In an instance declaration for a generic class, the idea is that the compiler
5088 will fill in the methods for you, based on the generic templates. However it can only
5093 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5098 No constructor of the instance type has unboxed fields.
5102 (Of course, these things can only arise if you are already using GHC extensions.)
5103 However, you can still give an instance declarations for types which break these rules,
5104 provided you give explicit code to override any generic default methods.
5112 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5113 what the compiler does with generic declarations.
5118 <sect2> <title> Another example </title>
5120 Just to finish with, here's another example I rather like:
5124 nCons {| Unit |} _ = 1
5125 nCons {| a :*: b |} _ = 1
5126 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5129 tag {| Unit |} _ = 1
5130 tag {| a :*: b |} _ = 1
5131 tag {| a :+: b |} (Inl x) = tag x
5132 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5141 ;;; Local Variables: ***
5143 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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