1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individaully.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
137 <para> These two flags control how generalisation is done.
138 See <xref linkend="monomorphism"/>.
145 <option>-XExtendedDefaultRules</option>:
146 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
149 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
150 Independent of the <option>-fglasgow-exts</option>
157 <option>-XOverlappingInstances</option>
158 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
161 <option>-XUndecidableInstances</option>
162 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
165 <option>-XIncoherentInstances</option>
166 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
169 <option>-fcontext-stack=N</option>
170 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
173 <para> See <xref linkend="instance-decls"/>. Only relevant
174 if you also use <option>-fglasgow-exts</option>.</para>
180 <option>-finline-phase</option>
181 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
184 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
185 you also use <option>-fglasgow-exts</option>.</para>
191 <option>-XArrows</option>
192 <indexterm><primary><option>-XArrows</option></primary></indexterm>
195 <para>See <xref linkend="arrow-notation"/>. Independent of
196 <option>-fglasgow-exts</option>.</para>
198 <para>New reserved words/symbols: <literal>rec</literal>,
199 <literal>proc</literal>, <literal>-<</literal>,
200 <literal>>-</literal>, <literal>-<<</literal>,
201 <literal>>>-</literal>.</para>
203 <para>Other syntax stolen: <literal>(|</literal>,
204 <literal>|)</literal>.</para>
210 <option>-XGenerics</option>
211 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
214 <para>See <xref linkend="generic-classes"/>. Independent of
215 <option>-fglasgow-exts</option>.</para>
220 <term><option>-XNoImplicitPrelude</option></term>
222 <para><indexterm><primary>-XNoImplicitPrelude
223 option</primary></indexterm> GHC normally imports
224 <filename>Prelude.hi</filename> files for you. If you'd
225 rather it didn't, then give it a
226 <option>-XNoImplicitPrelude</option> option. The idea is
227 that you can then import a Prelude of your own. (But don't
228 call it <literal>Prelude</literal>; the Haskell module
229 namespace is flat, and you must not conflict with any
230 Prelude module.)</para>
232 <para>Even though you have not imported the Prelude, most of
233 the built-in syntax still refers to the built-in Haskell
234 Prelude types and values, as specified by the Haskell
235 Report. For example, the type <literal>[Int]</literal>
236 still means <literal>Prelude.[] Int</literal>; tuples
237 continue to refer to the standard Prelude tuples; the
238 translation for list comprehensions continues to use
239 <literal>Prelude.map</literal> etc.</para>
241 <para>However, <option>-XNoImplicitPrelude</option> does
242 change the handling of certain built-in syntax: see <xref
243 linkend="rebindable-syntax"/>.</para>
248 <term><option>-XImplicitParams</option></term>
250 <para>Enables implicit parameters (see <xref
251 linkend="implicit-parameters"/>). Currently also implied by
252 <option>-fglasgow-exts</option>.</para>
255 <literal>?<replaceable>varid</replaceable></literal>,
256 <literal>%<replaceable>varid</replaceable></literal>.</para>
261 <term><option>-XOverloadedStrings</option></term>
263 <para>Enables overloaded string literals (see <xref
264 linkend="overloaded-strings"/>).</para>
269 <term><option>-XScopedTypeVariables</option></term>
271 <para>Enables lexically-scoped type variables (see <xref
272 linkend="scoped-type-variables"/>). Implied by
273 <option>-fglasgow-exts</option>.</para>
278 <term><option>-XTemplateHaskell</option></term>
280 <para>Enables Template Haskell (see <xref
281 linkend="template-haskell"/>). This flag must
282 be given explicitly; it is no longer implied by
283 <option>-fglasgow-exts</option>.</para>
285 <para>Syntax stolen: <literal>[|</literal>,
286 <literal>[e|</literal>, <literal>[p|</literal>,
287 <literal>[d|</literal>, <literal>[t|</literal>,
288 <literal>$(</literal>,
289 <literal>$<replaceable>varid</replaceable></literal>.</para>
296 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
297 <sect1 id="primitives">
298 <title>Unboxed types and primitive operations</title>
300 <para>GHC is built on a raft of primitive data types and operations.
301 While you really can use this stuff to write fast code,
302 we generally find it a lot less painful, and more satisfying in the
303 long run, to use higher-level language features and libraries. With
304 any luck, the code you write will be optimised to the efficient
305 unboxed version in any case. And if it isn't, we'd like to know
308 <para>We do not currently have good, up-to-date documentation about the
309 primitives, perhaps because they are mainly intended for internal use.
310 There used to be a long section about them here in the User Guide, but it
311 became out of date, and wrong information is worse than none.</para>
313 <para>The Real Truth about what primitive types there are, and what operations
314 work over those types, is held in the file
315 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
316 This file is used directly to generate GHC's primitive-operation definitions, so
317 it is always correct! It is also intended for processing into text.</para>
320 the result of such processing is part of the description of the
322 url="http://www.haskell.org/ghc/docs/papers/core.ps.gz">External
323 Core language</ulink>.
324 So that document is a good place to look for a type-set version.
325 We would be very happy if someone wanted to volunteer to produce an SGML
326 back end to the program that processes <filename>primops.txt</filename> so that
327 we could include the results here in the User Guide.</para>
329 <para>What follows here is a brief summary of some main points.</para>
331 <sect2 id="glasgow-unboxed">
336 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
339 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
340 that values of that type are represented by a pointer to a heap
341 object. The representation of a Haskell <literal>Int</literal>, for
342 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
343 type, however, is represented by the value itself, no pointers or heap
344 allocation are involved.
348 Unboxed types correspond to the “raw machine” types you
349 would use in C: <literal>Int#</literal> (long int),
350 <literal>Double#</literal> (double), <literal>Addr#</literal>
351 (void *), etc. The <emphasis>primitive operations</emphasis>
352 (PrimOps) on these types are what you might expect; e.g.,
353 <literal>(+#)</literal> is addition on
354 <literal>Int#</literal>s, and is the machine-addition that we all
355 know and love—usually one instruction.
359 Primitive (unboxed) types cannot be defined in Haskell, and are
360 therefore built into the language and compiler. Primitive types are
361 always unlifted; that is, a value of a primitive type cannot be
362 bottom. We use the convention that primitive types, values, and
363 operations have a <literal>#</literal> suffix.
367 Primitive values are often represented by a simple bit-pattern, such
368 as <literal>Int#</literal>, <literal>Float#</literal>,
369 <literal>Double#</literal>. But this is not necessarily the case:
370 a primitive value might be represented by a pointer to a
371 heap-allocated object. Examples include
372 <literal>Array#</literal>, the type of primitive arrays. A
373 primitive array is heap-allocated because it is too big a value to fit
374 in a register, and would be too expensive to copy around; in a sense,
375 it is accidental that it is represented by a pointer. If a pointer
376 represents a primitive value, then it really does point to that value:
377 no unevaluated thunks, no indirections…nothing can be at the
378 other end of the pointer than the primitive value.
379 A numerically-intensive program using unboxed types can
380 go a <emphasis>lot</emphasis> faster than its “standard”
381 counterpart—we saw a threefold speedup on one example.
385 There are some restrictions on the use of primitive types:
387 <listitem><para>The main restriction
388 is that you can't pass a primitive value to a polymorphic
389 function or store one in a polymorphic data type. This rules out
390 things like <literal>[Int#]</literal> (i.e. lists of primitive
391 integers). The reason for this restriction is that polymorphic
392 arguments and constructor fields are assumed to be pointers: if an
393 unboxed integer is stored in one of these, the garbage collector would
394 attempt to follow it, leading to unpredictable space leaks. Or a
395 <function>seq</function> operation on the polymorphic component may
396 attempt to dereference the pointer, with disastrous results. Even
397 worse, the unboxed value might be larger than a pointer
398 (<literal>Double#</literal> for instance).
401 <listitem><para> You cannot define a newtype whose representation type
402 (the argument type of the data constructor) is an unboxed type. Thus,
408 <listitem><para> You cannot bind a variable with an unboxed type
409 in a <emphasis>top-level</emphasis> binding.
411 <listitem><para> You cannot bind a variable with an unboxed type
412 in a <emphasis>recursive</emphasis> binding.
414 <listitem><para> You may bind unboxed variables in a (non-recursive,
415 non-top-level) pattern binding, but any such variable causes the entire
417 to become strict. For example:
419 data Foo = Foo Int Int#
421 f x = let (Foo a b, w) = ..rhs.. in ..body..
423 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
425 is strict, and the program behaves as if you had written
427 data Foo = Foo Int Int#
429 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
438 <sect2 id="unboxed-tuples">
439 <title>Unboxed Tuples
443 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
444 they're available by default with <option>-fglasgow-exts</option>. An
445 unboxed tuple looks like this:
457 where <literal>e_1..e_n</literal> are expressions of any
458 type (primitive or non-primitive). The type of an unboxed tuple looks
463 Unboxed tuples are used for functions that need to return multiple
464 values, but they avoid the heap allocation normally associated with
465 using fully-fledged tuples. When an unboxed tuple is returned, the
466 components are put directly into registers or on the stack; the
467 unboxed tuple itself does not have a composite representation. Many
468 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
470 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
471 tuples to avoid unnecessary allocation during sequences of operations.
475 There are some pretty stringent restrictions on the use of unboxed tuples:
480 Values of unboxed tuple types are subject to the same restrictions as
481 other unboxed types; i.e. they may not be stored in polymorphic data
482 structures or passed to polymorphic functions.
489 No variable can have an unboxed tuple type, nor may a constructor or function
490 argument have an unboxed tuple type. The following are all illegal:
494 data Foo = Foo (# Int, Int #)
496 f :: (# Int, Int #) -> (# Int, Int #)
499 g :: (# Int, Int #) -> Int
502 h x = let y = (# x,x #) in ...
509 The typical use of unboxed tuples is simply to return multiple values,
510 binding those multiple results with a <literal>case</literal> expression, thus:
512 f x y = (# x+1, y-1 #)
513 g x = case f x x of { (# a, b #) -> a + b }
515 You can have an unboxed tuple in a pattern binding, thus
517 f x = let (# p,q #) = h x in ..body..
519 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
520 the resulting binding is lazy like any other Haskell pattern binding. The
521 above example desugars like this:
523 f x = let t = case h x o f{ (# p,q #) -> (p,q)
528 Indeed, the bindings can even be recursive.
535 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
537 <sect1 id="syntax-extns">
538 <title>Syntactic extensions</title>
540 <!-- ====================== HIERARCHICAL MODULES ======================= -->
542 <sect2 id="hierarchical-modules">
543 <title>Hierarchical Modules</title>
545 <para>GHC supports a small extension to the syntax of module
546 names: a module name is allowed to contain a dot
547 <literal>‘.’</literal>. This is also known as the
548 “hierarchical module namespace” extension, because
549 it extends the normally flat Haskell module namespace into a
550 more flexible hierarchy of modules.</para>
552 <para>This extension has very little impact on the language
553 itself; modules names are <emphasis>always</emphasis> fully
554 qualified, so you can just think of the fully qualified module
555 name as <quote>the module name</quote>. In particular, this
556 means that the full module name must be given after the
557 <literal>module</literal> keyword at the beginning of the
558 module; for example, the module <literal>A.B.C</literal> must
561 <programlisting>module A.B.C</programlisting>
564 <para>It is a common strategy to use the <literal>as</literal>
565 keyword to save some typing when using qualified names with
566 hierarchical modules. For example:</para>
569 import qualified Control.Monad.ST.Strict as ST
572 <para>For details on how GHC searches for source and interface
573 files in the presence of hierarchical modules, see <xref
574 linkend="search-path"/>.</para>
576 <para>GHC comes with a large collection of libraries arranged
577 hierarchically; see the accompanying <ulink
578 url="../libraries/index.html">library
579 documentation</ulink>. More libraries to install are available
581 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
584 <!-- ====================== PATTERN GUARDS ======================= -->
586 <sect2 id="pattern-guards">
587 <title>Pattern guards</title>
590 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
591 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.)
595 Suppose we have an abstract data type of finite maps, with a
599 lookup :: FiniteMap -> Int -> Maybe Int
602 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
603 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
607 clunky env var1 var2 | ok1 && ok2 = val1 + val2
608 | otherwise = var1 + var2
619 The auxiliary functions are
623 maybeToBool :: Maybe a -> Bool
624 maybeToBool (Just x) = True
625 maybeToBool Nothing = False
627 expectJust :: Maybe a -> a
628 expectJust (Just x) = x
629 expectJust Nothing = error "Unexpected Nothing"
633 What is <function>clunky</function> doing? The guard <literal>ok1 &&
634 ok2</literal> checks that both lookups succeed, using
635 <function>maybeToBool</function> to convert the <function>Maybe</function>
636 types to booleans. The (lazily evaluated) <function>expectJust</function>
637 calls extract the values from the results of the lookups, and binds the
638 returned values to <varname>val1</varname> and <varname>val2</varname>
639 respectively. If either lookup fails, then clunky takes the
640 <literal>otherwise</literal> case and returns the sum of its arguments.
644 This is certainly legal Haskell, but it is a tremendously verbose and
645 un-obvious way to achieve the desired effect. Arguably, a more direct way
646 to write clunky would be to use case expressions:
650 clunky env var1 var2 = case lookup env var1 of
652 Just val1 -> case lookup env var2 of
654 Just val2 -> val1 + val2
660 This is a bit shorter, but hardly better. Of course, we can rewrite any set
661 of pattern-matching, guarded equations as case expressions; that is
662 precisely what the compiler does when compiling equations! The reason that
663 Haskell provides guarded equations is because they allow us to write down
664 the cases we want to consider, one at a time, independently of each other.
665 This structure is hidden in the case version. Two of the right-hand sides
666 are really the same (<function>fail</function>), and the whole expression
667 tends to become more and more indented.
671 Here is how I would write clunky:
676 | Just val1 <- lookup env var1
677 , Just val2 <- lookup env var2
679 ...other equations for clunky...
683 The semantics should be clear enough. The qualifiers are matched in order.
684 For a <literal><-</literal> qualifier, which I call a pattern guard, the
685 right hand side is evaluated and matched against the pattern on the left.
686 If the match fails then the whole guard fails and the next equation is
687 tried. If it succeeds, then the appropriate binding takes place, and the
688 next qualifier is matched, in the augmented environment. Unlike list
689 comprehensions, however, the type of the expression to the right of the
690 <literal><-</literal> is the same as the type of the pattern to its
691 left. The bindings introduced by pattern guards scope over all the
692 remaining guard qualifiers, and over the right hand side of the equation.
696 Just as with list comprehensions, boolean expressions can be freely mixed
697 with among the pattern guards. For example:
708 Haskell's current guards therefore emerge as a special case, in which the
709 qualifier list has just one element, a boolean expression.
713 <!-- ===================== View patterns =================== -->
715 <sect2 id="view-patterns">
720 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
721 More information and examples of view patterns can be found on the
722 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
727 View patterns are somewhat like pattern guards that can be nested inside
728 of other patterns. They are a convenient way of pattern-matching
729 against values of abstract types. For example, in a programming language
730 implementation, we might represent the syntax of the types of the
739 view :: Type -> TypeView
741 -- additional operations for constructing Typ's ...
744 The representation of Typ is held abstract, permitting implementations
745 to use a fancy representation (e.g., hash-consing to managage sharing).
747 Without view patterns, using this signature a little inconvenient:
749 size :: Typ -> Integer
750 size t = case view t of
752 Arrow t1 t2 -> size t1 + size t2
755 It is necessary to iterate the case, rather than using an equational
756 function definition. And the situation is even worse when the matching
757 against <literal>t</literal> is buried deep inside another pattern.
761 View patterns permit calling the view function inside the pattern and
762 matching against the result:
764 size (view -> Unit) = 1
765 size (view -> Arrow t1 t2) = size t1 + size t2
768 That is, we add a new form of pattern, written
769 <replaceable>expression</replaceable> <literal>-></literal>
770 <replaceable>pattern</replaceable> that means "apply the expression to
771 whatever we're trying to match against, and then match the result of
772 that application against the pattern". The expression can be any Haskell
773 expression of function type, and view patterns can be used wherever
778 The semantics of a pattern <literal>(</literal>
779 <replaceable>exp</replaceable> <literal>-></literal>
780 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
786 <para>The variables bound by the view pattern are the variables bound by
787 <replaceable>pat</replaceable>.
791 Any variables in <replaceable>exp</replaceable> are bound occurrences,
792 but variables bound "to the left" in a pattern are in scope. This
793 feature permits, for example, one argument to a function to be used in
794 the view of another argument. For example, the function
795 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
796 written using view patterns as follows:
799 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
800 ...other equations for clunky...
805 More precisely, the scoping rules are:
809 In a single pattern, variables bound by patterns to the left of a view
810 pattern expression are in scope. For example:
812 example :: Maybe ((String -> Integer,Integer), String) -> Bool
813 example Just ((f,_), f -> 4) = True
816 Additionally, in function definitions, variables bound by matching earlier curried
817 arguments may be used in view pattern expressions in later arguments:
819 example :: (String -> Integer) -> String -> Bool
820 example f (f -> 4) = True
822 That is, the scoping is the same as it would be if the curried arguments
823 were collected into a tuple.
829 In mutually recursive bindings, such as <literal>let</literal>,
830 <literal>where</literal>, or the top level, view patterns in one
831 declaration may not mention variables bound by other declarations. That
832 is, each declaration must be self-contained. For example, the following
833 program is not allowed:
840 restriction in the future; the only cost is that type checking patterns
841 would get a little more complicated.)
851 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
852 <replaceable>T1</replaceable> <literal>-></literal>
853 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
854 a <replaceable>T2</replaceable>, then the whole view pattern matches a
855 <replaceable>T1</replaceable>.
858 <listitem><para> Matching: To the equations in Section 3.17.3 of the
859 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
860 Report</ulink>, add the following:
862 case v of { (e -> p) -> e1 ; _ -> e2 }
864 case (e v) of { p -> e1 ; _ -> e2 }
866 That is, to match a variable <replaceable>v</replaceable> against a pattern
867 <literal>(</literal> <replaceable>exp</replaceable>
868 <literal>-></literal> <replaceable>pat</replaceable>
869 <literal>)</literal>, evaluate <literal>(</literal>
870 <replaceable>exp</replaceable> <replaceable> v</replaceable>
871 <literal>)</literal> and match the result against
872 <replaceable>pat</replaceable>.
875 <listitem><para> Efficiency: When the same view function is applied in
876 multiple branches of a function definition or a case expression (e.g.,
877 in <literal>size</literal> above), GHC makes an attempt to collect these
878 applications into a single nested case expression, so that the view
879 function is only applied once. Pattern compilation in GHC follows the
880 matrix algorithm described in Chapter 4 of <ulink
881 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
882 Implementation of Functional Programming Languages</ulink>. When the
883 top rows of the first column of a matrix are all view patterns with the
884 "same" expression, these patterns are transformed into a single nested
885 case. This includes, for example, adjacent view patterns that line up
888 f ((view -> A, p1), p2) = e1
889 f ((view -> B, p3), p4) = e2
893 <para> The current notion of when two view pattern expressions are "the
894 same" is very restricted: it is not even full syntactic equality.
895 However, it does include variables, literals, applications, and tuples;
896 e.g., two instances of <literal>view ("hi", "there")</literal> will be
897 collected. However, the current implementation does not compare up to
898 alpha-equivalence, so two instances of <literal>(x, view x ->
899 y)</literal> will not be coalesced.
909 <!-- ===================== Recursive do-notation =================== -->
911 <sect2 id="mdo-notation">
912 <title>The recursive do-notation
915 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
916 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
917 by Levent Erkok, John Launchbury,
918 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
919 This paper is essential reading for anyone making non-trivial use of mdo-notation,
920 and we do not repeat it here.
923 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
924 that is, the variables bound in a do-expression are visible only in the textually following
925 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
926 group. It turns out that several applications can benefit from recursive bindings in
927 the do-notation, and this extension provides the necessary syntactic support.
930 Here is a simple (yet contrived) example:
933 import Control.Monad.Fix
935 justOnes = mdo xs <- Just (1:xs)
939 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
943 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
946 class Monad m => MonadFix m where
947 mfix :: (a -> m a) -> m a
950 The function <literal>mfix</literal>
951 dictates how the required recursion operation should be performed. For example,
952 <literal>justOnes</literal> desugars as follows:
954 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
956 For full details of the way in which mdo is typechecked and desugared, see
957 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
958 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
961 If recursive bindings are required for a monad,
962 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
963 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
964 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
965 for Haskell's internal state monad (strict and lazy, respectively).
968 Here are some important points in using the recursive-do notation:
971 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
972 than <literal>do</literal>).
976 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
977 <literal>-fglasgow-exts</literal>.
981 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
982 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
983 be distinct (Section 3.3 of the paper).
987 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
988 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
989 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
990 and improve termination (Section 3.2 of the paper).
996 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb/">http://www.cse.ogi.edu/PacSoft/projects/rmb/</ulink>
997 contains up to date information on recursive monadic bindings.
1001 Historical note: The old implementation of the mdo-notation (and most
1002 of the existing documents) used the name
1003 <literal>MonadRec</literal> for the class and the corresponding library.
1004 This name is not supported by GHC.
1010 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1012 <sect2 id="parallel-list-comprehensions">
1013 <title>Parallel List Comprehensions</title>
1014 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1016 <indexterm><primary>parallel list comprehensions</primary>
1019 <para>Parallel list comprehensions are a natural extension to list
1020 comprehensions. List comprehensions can be thought of as a nice
1021 syntax for writing maps and filters. Parallel comprehensions
1022 extend this to include the zipWith family.</para>
1024 <para>A parallel list comprehension has multiple independent
1025 branches of qualifier lists, each separated by a `|' symbol. For
1026 example, the following zips together two lists:</para>
1029 [ (x, y) | x <- xs | y <- ys ]
1032 <para>The behavior of parallel list comprehensions follows that of
1033 zip, in that the resulting list will have the same length as the
1034 shortest branch.</para>
1036 <para>We can define parallel list comprehensions by translation to
1037 regular comprehensions. Here's the basic idea:</para>
1039 <para>Given a parallel comprehension of the form: </para>
1042 [ e | p1 <- e11, p2 <- e12, ...
1043 | q1 <- e21, q2 <- e22, ...
1048 <para>This will be translated to: </para>
1051 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1052 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1057 <para>where `zipN' is the appropriate zip for the given number of
1062 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1064 <sect2 id="generalised-list-comprehensions">
1065 <title>Generalised (SQL-Like) List Comprehensions</title>
1066 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1068 <indexterm><primary>extended list comprehensions</primary>
1070 <indexterm><primary>group</primary></indexterm>
1071 <indexterm><primary>sql</primary></indexterm>
1074 <para>Generalised list comprehensions are a further enhancement to the
1075 list comprehension syntatic sugar to allow operations such as sorting
1076 and grouping which are familiar from SQL. They are fully described in the
1077 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1078 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1079 except that the syntax we use differs slightly from the paper.</para>
1080 <para>Here is an example:
1082 employees = [ ("Simon", "MS", 80)
1083 , ("Erik", "MS", 100)
1084 , ("Phil", "Ed", 40)
1085 , ("Gordon", "Ed", 45)
1086 , ("Paul", "Yale", 60)]
1088 output = [ (the dept, sum salary)
1089 | (name, dept, salary) <- employees
1090 , then group by dept
1091 , then sortWith by (sum salary)
1094 In this example, the list <literal>output</literal> would take on
1098 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1101 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1102 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1103 function that is exported by <literal>GHC.Exts</literal>.)</para>
1105 <para>There are five new forms of compehension qualifier,
1106 all introduced by the (existing) keyword <literal>then</literal>:
1114 This statement requires that <literal>f</literal> have the type <literal>
1115 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1116 motivating example, as this form is used to apply <literal>take 5</literal>.
1127 This form is similar to the previous one, but allows you to create a function
1128 which will be passed as the first argument to f. As a consequence f must have
1129 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1130 from the type, this function lets f "project out" some information
1131 from the elements of the list it is transforming.</para>
1133 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1134 is supplied with a function that lets it find out the <literal>sum salary</literal>
1135 for any item in the list comprehension it transforms.</para>
1143 then group by e using f
1146 <para>This is the most general of the grouping-type statements. In this form,
1147 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1148 As with the <literal>then f by e</literal> case above, the first argument
1149 is a function supplied to f by the compiler which lets it compute e on every
1150 element of the list being transformed. However, unlike the non-grouping case,
1151 f additionally partitions the list into a number of sublists: this means that
1152 at every point after this statement, binders occuring before it in the comprehension
1153 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1154 this, let's look at an example:</para>
1157 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1158 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1159 groupRuns f = groupBy (\x y -> f x == f y)
1161 output = [ (the x, y)
1162 | x <- ([1..3] ++ [1..2])
1164 , then group by x using groupRuns ]
1167 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1170 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1173 <para>Note that we have used the <literal>the</literal> function to change the type
1174 of x from a list to its original numeric type. The variable y, in contrast, is left
1175 unchanged from the list form introduced by the grouping.</para>
1185 <para>This form of grouping is essentially the same as the one described above. However,
1186 since no function to use for the grouping has been supplied it will fall back on the
1187 <literal>groupWith</literal> function defined in
1188 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1189 is the form of the group statement that we made use of in the opening example.</para>
1200 <para>With this form of the group statement, f is required to simply have the type
1201 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1202 comprehension so far directly. An example of this form is as follows:</para>
1208 , then group using inits]
1211 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1214 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1222 <!-- ===================== REBINDABLE SYNTAX =================== -->
1224 <sect2 id="rebindable-syntax">
1225 <title>Rebindable syntax</title>
1227 <para>GHC allows most kinds of built-in syntax to be rebound by
1228 the user, to facilitate replacing the <literal>Prelude</literal>
1229 with a home-grown version, for example.</para>
1231 <para>You may want to define your own numeric class
1232 hierarchy. It completely defeats that purpose if the
1233 literal "1" means "<literal>Prelude.fromInteger
1234 1</literal>", which is what the Haskell Report specifies.
1235 So the <option>-XNoImplicitPrelude</option> flag causes
1236 the following pieces of built-in syntax to refer to
1237 <emphasis>whatever is in scope</emphasis>, not the Prelude
1242 <para>An integer literal <literal>368</literal> means
1243 "<literal>fromInteger (368::Integer)</literal>", rather than
1244 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1247 <listitem><para>Fractional literals are handed in just the same way,
1248 except that the translation is
1249 <literal>fromRational (3.68::Rational)</literal>.
1252 <listitem><para>The equality test in an overloaded numeric pattern
1253 uses whatever <literal>(==)</literal> is in scope.
1256 <listitem><para>The subtraction operation, and the
1257 greater-than-or-equal test, in <literal>n+k</literal> patterns
1258 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1262 <para>Negation (e.g. "<literal>- (f x)</literal>")
1263 means "<literal>negate (f x)</literal>", both in numeric
1264 patterns, and expressions.
1268 <para>"Do" notation is translated using whatever
1269 functions <literal>(>>=)</literal>,
1270 <literal>(>>)</literal>, and <literal>fail</literal>,
1271 are in scope (not the Prelude
1272 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1273 comprehensions, are unaffected. </para></listitem>
1277 notation (see <xref linkend="arrow-notation"/>)
1278 uses whatever <literal>arr</literal>,
1279 <literal>(>>>)</literal>, <literal>first</literal>,
1280 <literal>app</literal>, <literal>(|||)</literal> and
1281 <literal>loop</literal> functions are in scope. But unlike the
1282 other constructs, the types of these functions must match the
1283 Prelude types very closely. Details are in flux; if you want
1287 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1288 even if that is a little unexpected. For emample, the
1289 static semantics of the literal <literal>368</literal>
1290 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1291 <literal>fromInteger</literal> to have any of the types:
1293 fromInteger :: Integer -> Integer
1294 fromInteger :: forall a. Foo a => Integer -> a
1295 fromInteger :: Num a => a -> Integer
1296 fromInteger :: Integer -> Bool -> Bool
1300 <para>Be warned: this is an experimental facility, with
1301 fewer checks than usual. Use <literal>-dcore-lint</literal>
1302 to typecheck the desugared program. If Core Lint is happy
1303 you should be all right.</para>
1307 <sect2 id="postfix-operators">
1308 <title>Postfix operators</title>
1311 GHC allows a small extension to the syntax of left operator sections, which
1312 allows you to define postfix operators. The extension is this: the left section
1316 is equivalent (from the point of view of both type checking and execution) to the expression
1320 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1321 The strict Haskell 98 interpretation is that the section is equivalent to
1325 That is, the operator must be a function of two arguments. GHC allows it to
1326 take only one argument, and that in turn allows you to write the function
1329 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1330 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1331 change their behaviour, of course.)
1333 <para>The extension does not extend to the left-hand side of function
1334 definitions; you must define such a function in prefix form.</para>
1338 <sect2 id="disambiguate-fields">
1339 <title>Record field disambiguation</title>
1341 In record construction and record pattern matching
1342 it is entirely unambiguous which field is referred to, even if there are two different
1343 data types in scope with a common field name. For example:
1346 data S = MkS { x :: Int, y :: Bool }
1351 data T = MkT { x :: Int }
1353 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1355 ok2 n = MkT { x = n+1 } -- Unambiguous
1357 bad1 k = k { x = 3 } -- Ambiguous
1358 bad2 k = x k -- Ambiguous
1360 Even though there are two <literal>x</literal>'s in scope,
1361 it is clear that the <literal>x</literal> in the pattern in the
1362 definition of <literal>ok1</literal> can only mean the field
1363 <literal>x</literal> from type <literal>S</literal>. Similarly for
1364 the function <literal>ok2</literal>. However, in the record update
1365 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1366 it is not clear which of the two types is intended.
1369 Haskell 98 regards all four as ambiguous, but with the
1370 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1371 the former two. The rules are precisely the same as those for instance
1372 declarations in Haskell 98, where the method names on the left-hand side
1373 of the method bindings in an instance declaration refer unambiguously
1374 to the method of that class (provided they are in scope at all), even
1375 if there are other variables in scope with the same name.
1376 This reduces the clutter of qualified names when you import two
1377 records from different modules that use the same field name.
1381 <!-- ===================== Record puns =================== -->
1383 <sect2 id="record-puns">
1388 Record puns are enabled by the flag <literal>-XRecordPuns</literal>.
1392 When using records, it is common to write a pattern that binds a
1393 variable with the same name as a record field, such as:
1396 data C = C {a :: Int}
1402 Record punning permits the variable name to be elided, so one can simply
1409 to mean the same pattern as above. That is, in a record pattern, the
1410 pattern <literal>a</literal> expands into the pattern <literal>a =
1411 a</literal> for the same name <literal>a</literal>.
1415 Note that puns and other patterns can be mixed in the same record:
1417 data C = C {a :: Int, b :: Int}
1418 f (C {a, b = 4}) = a
1420 and that puns can be used wherever record patterns occur (e.g. in
1421 <literal>let</literal> bindings or at the top-level).
1425 Record punning can also be used in an expression, writing, for example,
1431 let a = 1 in C {a = a}
1434 Note that this expansion is purely syntactic, so the record pun
1435 expression refers to the nearest enclosing variable that is spelled the
1436 same as the field name.
1441 <!-- ===================== Record wildcards =================== -->
1443 <sect2 id="record-wildcards">
1444 <title>Record wildcards
1448 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1452 For records with many fields, it can be tiresome to write out each field
1453 individually in a record pattern, as in
1455 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1456 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1461 Record wildcard syntax permits a (<literal>..</literal>) in a record
1462 pattern, where each elided field <literal>f</literal> is replaced by the
1463 pattern <literal>f = f</literal>. For example, the above pattern can be
1466 f (C {a = 1, ..}) = b + c + d
1471 Note that wildcards can be mixed with other patterns, including puns
1472 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1473 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1474 wherever record patterns occur, including in <literal>let</literal>
1475 bindings and at the top-level. For example, the top-level binding
1479 defines <literal>b</literal>, <literal>c</literal>, and
1480 <literal>d</literal>.
1484 Record wildcards can also be used in expressions, writing, for example,
1487 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1493 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1496 Note that this expansion is purely syntactic, so the record wildcard
1497 expression refers to the nearest enclosing variables that are spelled
1498 the same as the omitted field names.
1503 <!-- ===================== Local fixity declarations =================== -->
1505 <sect2 id="local-fixity-declarations">
1506 <title>Local Fixity Declarations
1509 <para>A careful reading of the Haskell 98 Report reveals that fixity
1510 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1511 <literal>infixr</literal>) are permitted to appear inside local bindings
1512 such those introduced by <literal>let</literal> and
1513 <literal>where</literal>. However, the Haskell Report does not specify
1514 the semantics of such bindings very precisely.
1517 <para>In GHC, a fixity declaration may accompany a local binding:
1524 and the fixity declaration applies wherever the binding is in scope.
1525 For example, in a <literal>let</literal>, it applies in the right-hand
1526 sides of other <literal>let</literal>-bindings and the body of the
1527 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1528 expressions (<xref linkend="mdo-notation"/>), the local fixity
1529 declarations of aA <literal>let</literal> statement scope over other
1530 statements in the group, just as the bound name does.
1533 Moreover, a local fixity declatation *must* accompany a local binding of
1534 that name: it is not possible to revise the fixity of name bound
1537 let infixr 9 $ in ...
1540 Because local fixity declarations are technically Haskell 98, no flag is
1541 necessary to enable them.
1547 <!-- TYPE SYSTEM EXTENSIONS -->
1548 <sect1 id="data-type-extensions">
1549 <title>Extensions to data types and type synonyms</title>
1551 <sect2 id="nullary-types">
1552 <title>Data types with no constructors</title>
1554 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1555 a data type with no constructors. For example:</para>
1559 data T a -- T :: * -> *
1562 <para>Syntactically, the declaration lacks the "= constrs" part. The
1563 type can be parameterised over types of any kind, but if the kind is
1564 not <literal>*</literal> then an explicit kind annotation must be used
1565 (see <xref linkend="kinding"/>).</para>
1567 <para>Such data types have only one value, namely bottom.
1568 Nevertheless, they can be useful when defining "phantom types".</para>
1571 <sect2 id="infix-tycons">
1572 <title>Infix type constructors, classes, and type variables</title>
1575 GHC allows type constructors, classes, and type variables to be operators, and
1576 to be written infix, very much like expressions. More specifically:
1579 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1580 The lexical syntax is the same as that for data constructors.
1583 Data type and type-synonym declarations can be written infix, parenthesised
1584 if you want further arguments. E.g.
1586 data a :*: b = Foo a b
1587 type a :+: b = Either a b
1588 class a :=: b where ...
1590 data (a :**: b) x = Baz a b x
1591 type (a :++: b) y = Either (a,b) y
1595 Types, and class constraints, can be written infix. For example
1598 f :: (a :=: b) => a -> b
1602 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1603 The lexical syntax is the same as that for variable operators, excluding "(.)",
1604 "(!)", and "(*)". In a binding position, the operator must be
1605 parenthesised. For example:
1607 type T (+) = Int + Int
1611 liftA2 :: Arrow (~>)
1612 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1618 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1619 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1622 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1623 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1624 sets the fixity for a data constructor and the corresponding type constructor. For example:
1628 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1629 and similarly for <literal>:*:</literal>.
1630 <literal>Int `a` Bool</literal>.
1633 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1640 <sect2 id="type-synonyms">
1641 <title>Liberalised type synonyms</title>
1644 Type synonyms are like macros at the type level, and
1645 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1646 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1648 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1649 in a type synonym, thus:
1651 type Discard a = forall b. Show b => a -> b -> (a, String)
1656 g :: Discard Int -> (Int,String) -- A rank-2 type
1663 You can write an unboxed tuple in a type synonym:
1665 type Pr = (# Int, Int #)
1673 You can apply a type synonym to a forall type:
1675 type Foo a = a -> a -> Bool
1677 f :: Foo (forall b. b->b)
1679 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1681 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1686 You can apply a type synonym to a partially applied type synonym:
1688 type Generic i o = forall x. i x -> o x
1691 foo :: Generic Id []
1693 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1695 foo :: forall x. x -> [x]
1703 GHC currently does kind checking before expanding synonyms (though even that
1707 After expanding type synonyms, GHC does validity checking on types, looking for
1708 the following mal-formedness which isn't detected simply by kind checking:
1711 Type constructor applied to a type involving for-alls.
1714 Unboxed tuple on left of an arrow.
1717 Partially-applied type synonym.
1721 this will be rejected:
1723 type Pr = (# Int, Int #)
1728 because GHC does not allow unboxed tuples on the left of a function arrow.
1733 <sect2 id="existential-quantification">
1734 <title>Existentially quantified data constructors
1738 The idea of using existential quantification in data type declarations
1739 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1740 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1741 London, 1991). It was later formalised by Laufer and Odersky
1742 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1743 TOPLAS, 16(5), pp1411-1430, 1994).
1744 It's been in Lennart
1745 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1746 proved very useful. Here's the idea. Consider the declaration:
1752 data Foo = forall a. MkFoo a (a -> Bool)
1759 The data type <literal>Foo</literal> has two constructors with types:
1765 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1772 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1773 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1774 For example, the following expression is fine:
1780 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1786 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1787 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1788 isUpper</function> packages a character with a compatible function. These
1789 two things are each of type <literal>Foo</literal> and can be put in a list.
1793 What can we do with a value of type <literal>Foo</literal>?. In particular,
1794 what happens when we pattern-match on <function>MkFoo</function>?
1800 f (MkFoo val fn) = ???
1806 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1807 are compatible, the only (useful) thing we can do with them is to
1808 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1815 f (MkFoo val fn) = fn val
1821 What this allows us to do is to package heterogenous values
1822 together with a bunch of functions that manipulate them, and then treat
1823 that collection of packages in a uniform manner. You can express
1824 quite a bit of object-oriented-like programming this way.
1827 <sect3 id="existential">
1828 <title>Why existential?
1832 What has this to do with <emphasis>existential</emphasis> quantification?
1833 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1839 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1845 But Haskell programmers can safely think of the ordinary
1846 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1847 adding a new existential quantification construct.
1852 <sect3 id="existential-with-context">
1853 <title>Existentials and type classes</title>
1856 An easy extension is to allow
1857 arbitrary contexts before the constructor. For example:
1863 data Baz = forall a. Eq a => Baz1 a a
1864 | forall b. Show b => Baz2 b (b -> b)
1870 The two constructors have the types you'd expect:
1876 Baz1 :: forall a. Eq a => a -> a -> Baz
1877 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1883 But when pattern matching on <function>Baz1</function> the matched values can be compared
1884 for equality, and when pattern matching on <function>Baz2</function> the first matched
1885 value can be converted to a string (as well as applying the function to it).
1886 So this program is legal:
1893 f (Baz1 p q) | p == q = "Yes"
1895 f (Baz2 v fn) = show (fn v)
1901 Operationally, in a dictionary-passing implementation, the
1902 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1903 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1904 extract it on pattern matching.
1909 <sect3 id="existential-records">
1910 <title>Record Constructors</title>
1913 GHC allows existentials to be used with records syntax as well. For example:
1916 data Counter a = forall self. NewCounter
1918 , _inc :: self -> self
1919 , _display :: self -> IO ()
1923 Here <literal>tag</literal> is a public field, with a well-typed selector
1924 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1925 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1926 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1927 compile-time error. In other words, <emphasis>GHC defines a record selector function
1928 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1929 (This example used an underscore in the fields for which record selectors
1930 will not be defined, but that is only programming style; GHC ignores them.)
1934 To make use of these hidden fields, we need to create some helper functions:
1937 inc :: Counter a -> Counter a
1938 inc (NewCounter x i d t) = NewCounter
1939 { _this = i x, _inc = i, _display = d, tag = t }
1941 display :: Counter a -> IO ()
1942 display NewCounter{ _this = x, _display = d } = d x
1945 Now we can define counters with different underlying implementations:
1948 counterA :: Counter String
1949 counterA = NewCounter
1950 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1952 counterB :: Counter String
1953 counterB = NewCounter
1954 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1957 display (inc counterA) -- prints "1"
1958 display (inc (inc counterB)) -- prints "##"
1961 At the moment, record update syntax is only supported for Haskell 98 data types,
1962 so the following function does <emphasis>not</emphasis> work:
1965 -- This is invalid; use explicit NewCounter instead for now
1966 setTag :: Counter a -> a -> Counter a
1967 setTag obj t = obj{ tag = t }
1976 <title>Restrictions</title>
1979 There are several restrictions on the ways in which existentially-quantified
1980 constructors can be use.
1989 When pattern matching, each pattern match introduces a new,
1990 distinct, type for each existential type variable. These types cannot
1991 be unified with any other type, nor can they escape from the scope of
1992 the pattern match. For example, these fragments are incorrect:
2000 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2001 is the result of <function>f1</function>. One way to see why this is wrong is to
2002 ask what type <function>f1</function> has:
2006 f1 :: Foo -> a -- Weird!
2010 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2015 f1 :: forall a. Foo -> a -- Wrong!
2019 The original program is just plain wrong. Here's another sort of error
2023 f2 (Baz1 a b) (Baz1 p q) = a==q
2027 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2028 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2029 from the two <function>Baz1</function> constructors.
2037 You can't pattern-match on an existentially quantified
2038 constructor in a <literal>let</literal> or <literal>where</literal> group of
2039 bindings. So this is illegal:
2043 f3 x = a==b where { Baz1 a b = x }
2046 Instead, use a <literal>case</literal> expression:
2049 f3 x = case x of Baz1 a b -> a==b
2052 In general, you can only pattern-match
2053 on an existentially-quantified constructor in a <literal>case</literal> expression or
2054 in the patterns of a function definition.
2056 The reason for this restriction is really an implementation one.
2057 Type-checking binding groups is already a nightmare without
2058 existentials complicating the picture. Also an existential pattern
2059 binding at the top level of a module doesn't make sense, because it's
2060 not clear how to prevent the existentially-quantified type "escaping".
2061 So for now, there's a simple-to-state restriction. We'll see how
2069 You can't use existential quantification for <literal>newtype</literal>
2070 declarations. So this is illegal:
2074 newtype T = forall a. Ord a => MkT a
2078 Reason: a value of type <literal>T</literal> must be represented as a
2079 pair of a dictionary for <literal>Ord t</literal> and a value of type
2080 <literal>t</literal>. That contradicts the idea that
2081 <literal>newtype</literal> should have no concrete representation.
2082 You can get just the same efficiency and effect by using
2083 <literal>data</literal> instead of <literal>newtype</literal>. If
2084 there is no overloading involved, then there is more of a case for
2085 allowing an existentially-quantified <literal>newtype</literal>,
2086 because the <literal>data</literal> version does carry an
2087 implementation cost, but single-field existentially quantified
2088 constructors aren't much use. So the simple restriction (no
2089 existential stuff on <literal>newtype</literal>) stands, unless there
2090 are convincing reasons to change it.
2098 You can't use <literal>deriving</literal> to define instances of a
2099 data type with existentially quantified data constructors.
2101 Reason: in most cases it would not make sense. For example:;
2104 data T = forall a. MkT [a] deriving( Eq )
2107 To derive <literal>Eq</literal> in the standard way we would need to have equality
2108 between the single component of two <function>MkT</function> constructors:
2112 (MkT a) == (MkT b) = ???
2115 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2116 It's just about possible to imagine examples in which the derived instance
2117 would make sense, but it seems altogether simpler simply to prohibit such
2118 declarations. Define your own instances!
2129 <!-- ====================== Generalised algebraic data types ======================= -->
2131 <sect2 id="gadt-style">
2132 <title>Declaring data types with explicit constructor signatures</title>
2134 <para>GHC allows you to declare an algebraic data type by
2135 giving the type signatures of constructors explicitly. For example:
2139 Just :: a -> Maybe a
2141 The form is called a "GADT-style declaration"
2142 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2143 can only be declared using this form.</para>
2144 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2145 For example, these two declarations are equivalent:
2147 data Foo = forall a. MkFoo a (a -> Bool)
2148 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2151 <para>Any data type that can be declared in standard Haskell-98 syntax
2152 can also be declared using GADT-style syntax.
2153 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2154 they treat class constraints on the data constructors differently.
2155 Specifically, if the constructor is given a type-class context, that
2156 context is made available by pattern matching. For example:
2159 MkSet :: Eq a => [a] -> Set a
2161 makeSet :: Eq a => [a] -> Set a
2162 makeSet xs = MkSet (nub xs)
2164 insert :: a -> Set a -> Set a
2165 insert a (MkSet as) | a `elem` as = MkSet as
2166 | otherwise = MkSet (a:as)
2168 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2169 gives rise to a <literal>(Eq a)</literal>
2170 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2171 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2172 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2173 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2174 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2175 In the example, the equality dictionary is used to satisfy the equality constraint
2176 generated by the call to <literal>elem</literal>, so that the type of
2177 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2180 For example, one possible application is to reify dictionaries:
2182 data NumInst a where
2183 MkNumInst :: Num a => NumInst a
2185 intInst :: NumInst Int
2188 plus :: NumInst a -> a -> a -> a
2189 plus MkNumInst p q = p + q
2191 Here, a value of type <literal>NumInst a</literal> is equivalent
2192 to an explicit <literal>(Num a)</literal> dictionary.
2195 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2196 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2200 = Num a => MkNumInst (NumInst a)
2202 Notice that, unlike the situation when declaring an existental, there is
2203 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2204 data type's univerally quantified type variable <literal>a</literal>.
2205 A constructor may have both universal and existential type variables: for example,
2206 the following two declarations are equivalent:
2209 = forall b. (Num a, Eq b) => MkT1 a b
2211 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2214 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2215 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2216 In Haskell 98 the definition
2218 data Eq a => Set' a = MkSet' [a]
2220 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2221 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2222 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2223 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2224 GHC's behaviour is much more useful, as well as much more intuitive.
2228 The rest of this section gives further details about GADT-style data
2233 The result type of each data constructor must begin with the type constructor being defined.
2234 If the result type of all constructors
2235 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2236 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2237 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2241 The type signature of
2242 each constructor is independent, and is implicitly universally quantified as usual.
2243 Different constructors may have different universally-quantified type variables
2244 and different type-class constraints.
2245 For example, this is fine:
2248 T1 :: Eq b => b -> T b
2249 T2 :: (Show c, Ix c) => c -> [c] -> T c
2254 Unlike a Haskell-98-style
2255 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2256 have no scope. Indeed, one can write a kind signature instead:
2258 data Set :: * -> * where ...
2260 or even a mixture of the two:
2262 data Foo a :: (* -> *) -> * where ...
2264 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2267 data Foo a (b :: * -> *) where ...
2273 You can use strictness annotations, in the obvious places
2274 in the constructor type:
2277 Lit :: !Int -> Term Int
2278 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2279 Pair :: Term a -> Term b -> Term (a,b)
2284 You can use a <literal>deriving</literal> clause on a GADT-style data type
2285 declaration. For example, these two declarations are equivalent
2287 data Maybe1 a where {
2288 Nothing1 :: Maybe1 a ;
2289 Just1 :: a -> Maybe1 a
2290 } deriving( Eq, Ord )
2292 data Maybe2 a = Nothing2 | Just2 a
2298 You can use record syntax on a GADT-style data type declaration:
2302 Adult { name :: String, children :: [Person] } :: Person
2303 Child { name :: String } :: Person
2305 As usual, for every constructor that has a field <literal>f</literal>, the type of
2306 field <literal>f</literal> must be the same (modulo alpha conversion).
2309 At the moment, record updates are not yet possible with GADT-style declarations,
2310 so support is limited to record construction, selection and pattern matching.
2313 aPerson = Adult { name = "Fred", children = [] }
2315 shortName :: Person -> Bool
2316 hasChildren (Adult { children = kids }) = not (null kids)
2317 hasChildren (Child {}) = False
2322 As in the case of existentials declared using the Haskell-98-like record syntax
2323 (<xref linkend="existential-records"/>),
2324 record-selector functions are generated only for those fields that have well-typed
2326 Here is the example of that section, in GADT-style syntax:
2328 data Counter a where
2329 NewCounter { _this :: self
2330 , _inc :: self -> self
2331 , _display :: self -> IO ()
2336 As before, only one selector function is generated here, that for <literal>tag</literal>.
2337 Nevertheless, you can still use all the field names in pattern matching and record construction.
2339 </itemizedlist></para>
2343 <title>Generalised Algebraic Data Types (GADTs)</title>
2345 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2346 by allowing constructors to have richer return types. Here is an example:
2349 Lit :: Int -> Term Int
2350 Succ :: Term Int -> Term Int
2351 IsZero :: Term Int -> Term Bool
2352 If :: Term Bool -> Term a -> Term a -> Term a
2353 Pair :: Term a -> Term b -> Term (a,b)
2355 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2356 case with ordinary data types. This generality allows us to
2357 write a well-typed <literal>eval</literal> function
2358 for these <literal>Terms</literal>:
2362 eval (Succ t) = 1 + eval t
2363 eval (IsZero t) = eval t == 0
2364 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2365 eval (Pair e1 e2) = (eval e1, eval e2)
2367 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2368 For example, in the right hand side of the equation
2373 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2374 A precise specification of the type rules is beyond what this user manual aspires to,
2375 but the design closely follows that described in
2377 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2378 unification-based type inference for GADTs</ulink>,
2380 The general principle is this: <emphasis>type refinement is only carried out
2381 based on user-supplied type annotations</emphasis>.
2382 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2383 and lots of obscure error messages will
2384 occur. However, the refinement is quite general. For example, if we had:
2386 eval :: Term a -> a -> a
2387 eval (Lit i) j = i+j
2389 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2390 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2391 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2394 These and many other examples are given in papers by Hongwei Xi, and
2395 Tim Sheard. There is a longer introduction
2396 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2398 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
2399 may use different notation to that implemented in GHC.
2402 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2403 <option>-XGADTs</option>.
2406 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2407 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2408 The result type of each constructor must begin with the type constructor being defined,
2409 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2410 For example, in the <literal>Term</literal> data
2411 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2412 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
2417 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2418 an ordinary data type.
2422 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2426 Lit { val :: Int } :: Term Int
2427 Succ { num :: Term Int } :: Term Int
2428 Pred { num :: Term Int } :: Term Int
2429 IsZero { arg :: Term Int } :: Term Bool
2430 Pair { arg1 :: Term a
2433 If { cnd :: Term Bool
2438 However, for GADTs there is the following additional constraint:
2439 every constructor that has a field <literal>f</literal> must have
2440 the same result type (modulo alpha conversion)
2441 Hence, in the above example, we cannot merge the <literal>num</literal>
2442 and <literal>arg</literal> fields above into a
2443 single name. Although their field types are both <literal>Term Int</literal>,
2444 their selector functions actually have different types:
2447 num :: Term Int -> Term Int
2448 arg :: Term Bool -> Term Int
2458 <!-- ====================== End of Generalised algebraic data types ======================= -->
2460 <sect1 id="deriving">
2461 <title>Extensions to the "deriving" mechanism</title>
2463 <sect2 id="deriving-inferred">
2464 <title>Inferred context for deriving clauses</title>
2467 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2470 data T0 f a = MkT0 a deriving( Eq )
2471 data T1 f a = MkT1 (f a) deriving( Eq )
2472 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2474 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2476 instance Eq a => Eq (T0 f a) where ...
2477 instance Eq (f a) => Eq (T1 f a) where ...
2478 instance Eq (f (f a)) => Eq (T2 f a) where ...
2480 The first of these is obviously fine. The second is still fine, although less obviously.
2481 The third is not Haskell 98, and risks losing termination of instances.
2484 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2485 each constraint in the inferred instance context must consist only of type variables,
2486 with no repetitions.
2489 This rule is applied regardless of flags. If you want a more exotic context, you can write
2490 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2494 <sect2 id="stand-alone-deriving">
2495 <title>Stand-alone deriving declarations</title>
2498 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2500 data Foo a = Bar a | Baz String
2502 deriving instance Eq a => Eq (Foo a)
2504 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2505 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2506 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2507 exactly as you would in an ordinary instance declaration.
2508 (In contrast the context is inferred in a <literal>deriving</literal> clause
2509 attached to a data type declaration.) These <literal>deriving instance</literal>
2510 rules obey the same rules concerning form and termination as ordinary instance declarations,
2511 controlled by the same flags; see <xref linkend="instance-decls"/>. </para>
2513 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2514 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2517 newtype Foo a = MkFoo (State Int a)
2519 deriving instance MonadState Int Foo
2521 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2522 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2528 <sect2 id="deriving-typeable">
2529 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2532 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2533 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2534 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2535 classes <literal>Eq</literal>, <literal>Ord</literal>,
2536 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2539 GHC extends this list with two more classes that may be automatically derived
2540 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2541 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2542 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2543 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2545 <para>An instance of <literal>Typeable</literal> can only be derived if the
2546 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2547 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2549 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2550 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2552 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2553 are used, and only <literal>Typeable1</literal> up to
2554 <literal>Typeable7</literal> are provided in the library.)
2555 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2556 class, whose kind suits that of the data type constructor, and
2557 then writing the data type instance by hand.
2561 <sect2 id="newtype-deriving">
2562 <title>Generalised derived instances for newtypes</title>
2565 When you define an abstract type using <literal>newtype</literal>, you may want
2566 the new type to inherit some instances from its representation. In
2567 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2568 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2569 other classes you have to write an explicit instance declaration. For
2570 example, if you define
2573 newtype Dollars = Dollars Int
2576 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2577 explicitly define an instance of <literal>Num</literal>:
2580 instance Num Dollars where
2581 Dollars a + Dollars b = Dollars (a+b)
2584 All the instance does is apply and remove the <literal>newtype</literal>
2585 constructor. It is particularly galling that, since the constructor
2586 doesn't appear at run-time, this instance declaration defines a
2587 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2588 dictionary, only slower!
2592 <sect3> <title> Generalising the deriving clause </title>
2594 GHC now permits such instances to be derived instead,
2595 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2598 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2601 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2602 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2603 derives an instance declaration of the form
2606 instance Num Int => Num Dollars
2609 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2613 We can also derive instances of constructor classes in a similar
2614 way. For example, suppose we have implemented state and failure monad
2615 transformers, such that
2618 instance Monad m => Monad (State s m)
2619 instance Monad m => Monad (Failure m)
2621 In Haskell 98, we can define a parsing monad by
2623 type Parser tok m a = State [tok] (Failure m) a
2626 which is automatically a monad thanks to the instance declarations
2627 above. With the extension, we can make the parser type abstract,
2628 without needing to write an instance of class <literal>Monad</literal>, via
2631 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2634 In this case the derived instance declaration is of the form
2636 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2639 Notice that, since <literal>Monad</literal> is a constructor class, the
2640 instance is a <emphasis>partial application</emphasis> of the new type, not the
2641 entire left hand side. We can imagine that the type declaration is
2642 "eta-converted" to generate the context of the instance
2647 We can even derive instances of multi-parameter classes, provided the
2648 newtype is the last class parameter. In this case, a ``partial
2649 application'' of the class appears in the <literal>deriving</literal>
2650 clause. For example, given the class
2653 class StateMonad s m | m -> s where ...
2654 instance Monad m => StateMonad s (State s m) where ...
2656 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2658 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2659 deriving (Monad, StateMonad [tok])
2662 The derived instance is obtained by completing the application of the
2663 class to the new type:
2666 instance StateMonad [tok] (State [tok] (Failure m)) =>
2667 StateMonad [tok] (Parser tok m)
2672 As a result of this extension, all derived instances in newtype
2673 declarations are treated uniformly (and implemented just by reusing
2674 the dictionary for the representation type), <emphasis>except</emphasis>
2675 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2676 the newtype and its representation.
2680 <sect3> <title> A more precise specification </title>
2682 Derived instance declarations are constructed as follows. Consider the
2683 declaration (after expansion of any type synonyms)
2686 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2692 The <literal>ci</literal> are partial applications of
2693 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2694 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2697 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2700 The type <literal>t</literal> is an arbitrary type.
2703 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2704 nor in the <literal>ci</literal>, and
2707 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2708 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2709 should not "look through" the type or its constructor. You can still
2710 derive these classes for a newtype, but it happens in the usual way, not
2711 via this new mechanism.
2714 Then, for each <literal>ci</literal>, the derived instance
2717 instance ci t => ci (T v1...vk)
2719 As an example which does <emphasis>not</emphasis> work, consider
2721 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2723 Here we cannot derive the instance
2725 instance Monad (State s m) => Monad (NonMonad m)
2728 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2729 and so cannot be "eta-converted" away. It is a good thing that this
2730 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2731 not, in fact, a monad --- for the same reason. Try defining
2732 <literal>>>=</literal> with the correct type: you won't be able to.
2736 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2737 important, since we can only derive instances for the last one. If the
2738 <literal>StateMonad</literal> class above were instead defined as
2741 class StateMonad m s | m -> s where ...
2744 then we would not have been able to derive an instance for the
2745 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2746 classes usually have one "main" parameter for which deriving new
2747 instances is most interesting.
2749 <para>Lastly, all of this applies only for classes other than
2750 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2751 and <literal>Data</literal>, for which the built-in derivation applies (section
2752 4.3.3. of the Haskell Report).
2753 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2754 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2755 the standard method is used or the one described here.)
2762 <!-- TYPE SYSTEM EXTENSIONS -->
2763 <sect1 id="type-class-extensions">
2764 <title>Class and instances declarations</title>
2766 <sect2 id="multi-param-type-classes">
2767 <title>Class declarations</title>
2770 This section, and the next one, documents GHC's type-class extensions.
2771 There's lots of background in the paper <ulink
2772 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2773 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2774 Jones, Erik Meijer).
2777 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2781 <title>Multi-parameter type classes</title>
2783 Multi-parameter type classes are permitted. For example:
2787 class Collection c a where
2788 union :: c a -> c a -> c a
2796 <title>The superclasses of a class declaration</title>
2799 There are no restrictions on the context in a class declaration
2800 (which introduces superclasses), except that the class hierarchy must
2801 be acyclic. So these class declarations are OK:
2805 class Functor (m k) => FiniteMap m k where
2808 class (Monad m, Monad (t m)) => Transform t m where
2809 lift :: m a -> (t m) a
2815 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2816 of "acyclic" involves only the superclass relationships. For example,
2822 op :: D b => a -> b -> b
2825 class C a => D a where { ... }
2829 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2830 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2831 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2838 <sect3 id="class-method-types">
2839 <title>Class method types</title>
2842 Haskell 98 prohibits class method types to mention constraints on the
2843 class type variable, thus:
2846 fromList :: [a] -> s a
2847 elem :: Eq a => a -> s a -> Bool
2849 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2850 contains the constraint <literal>Eq a</literal>, constrains only the
2851 class type variable (in this case <literal>a</literal>).
2852 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2859 <sect2 id="functional-dependencies">
2860 <title>Functional dependencies
2863 <para> Functional dependencies are implemented as described by Mark Jones
2864 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2865 In Proceedings of the 9th European Symposium on Programming,
2866 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2870 Functional dependencies are introduced by a vertical bar in the syntax of a
2871 class declaration; e.g.
2873 class (Monad m) => MonadState s m | m -> s where ...
2875 class Foo a b c | a b -> c where ...
2877 There should be more documentation, but there isn't (yet). Yell if you need it.
2880 <sect3><title>Rules for functional dependencies </title>
2882 In a class declaration, all of the class type variables must be reachable (in the sense
2883 mentioned in <xref linkend="type-restrictions"/>)
2884 from the free variables of each method type.
2888 class Coll s a where
2890 insert :: s -> a -> s
2893 is not OK, because the type of <literal>empty</literal> doesn't mention
2894 <literal>a</literal>. Functional dependencies can make the type variable
2897 class Coll s a | s -> a where
2899 insert :: s -> a -> s
2902 Alternatively <literal>Coll</literal> might be rewritten
2905 class Coll s a where
2907 insert :: s a -> a -> s a
2911 which makes the connection between the type of a collection of
2912 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2913 Occasionally this really doesn't work, in which case you can split the
2921 class CollE s => Coll s a where
2922 insert :: s -> a -> s
2929 <title>Background on functional dependencies</title>
2931 <para>The following description of the motivation and use of functional dependencies is taken
2932 from the Hugs user manual, reproduced here (with minor changes) by kind
2933 permission of Mark Jones.
2936 Consider the following class, intended as part of a
2937 library for collection types:
2939 class Collects e ce where
2941 insert :: e -> ce -> ce
2942 member :: e -> ce -> Bool
2944 The type variable e used here represents the element type, while ce is the type
2945 of the container itself. Within this framework, we might want to define
2946 instances of this class for lists or characteristic functions (both of which
2947 can be used to represent collections of any equality type), bit sets (which can
2948 be used to represent collections of characters), or hash tables (which can be
2949 used to represent any collection whose elements have a hash function). Omitting
2950 standard implementation details, this would lead to the following declarations:
2952 instance Eq e => Collects e [e] where ...
2953 instance Eq e => Collects e (e -> Bool) where ...
2954 instance Collects Char BitSet where ...
2955 instance (Hashable e, Collects a ce)
2956 => Collects e (Array Int ce) where ...
2958 All this looks quite promising; we have a class and a range of interesting
2959 implementations. Unfortunately, there are some serious problems with the class
2960 declaration. First, the empty function has an ambiguous type:
2962 empty :: Collects e ce => ce
2964 By "ambiguous" we mean that there is a type variable e that appears on the left
2965 of the <literal>=></literal> symbol, but not on the right. The problem with
2966 this is that, according to the theoretical foundations of Haskell overloading,
2967 we cannot guarantee a well-defined semantics for any term with an ambiguous
2971 We can sidestep this specific problem by removing the empty member from the
2972 class declaration. However, although the remaining members, insert and member,
2973 do not have ambiguous types, we still run into problems when we try to use
2974 them. For example, consider the following two functions:
2976 f x y = insert x . insert y
2979 for which GHC infers the following types:
2981 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2982 g :: (Collects Bool c, Collects Char c) => c -> c
2984 Notice that the type for f allows the two parameters x and y to be assigned
2985 different types, even though it attempts to insert each of the two values, one
2986 after the other, into the same collection. If we're trying to model collections
2987 that contain only one type of value, then this is clearly an inaccurate
2988 type. Worse still, the definition for g is accepted, without causing a type
2989 error. As a result, the error in this code will not be flagged at the point
2990 where it appears. Instead, it will show up only when we try to use g, which
2991 might even be in a different module.
2994 <sect4><title>An attempt to use constructor classes</title>
2997 Faced with the problems described above, some Haskell programmers might be
2998 tempted to use something like the following version of the class declaration:
3000 class Collects e c where
3002 insert :: e -> c e -> c e
3003 member :: e -> c e -> Bool
3005 The key difference here is that we abstract over the type constructor c that is
3006 used to form the collection type c e, and not over that collection type itself,
3007 represented by ce in the original class declaration. This avoids the immediate
3008 problems that we mentioned above: empty has type <literal>Collects e c => c
3009 e</literal>, which is not ambiguous.
3012 The function f from the previous section has a more accurate type:
3014 f :: (Collects e c) => e -> e -> c e -> c e
3016 The function g from the previous section is now rejected with a type error as
3017 we would hope because the type of f does not allow the two arguments to have
3019 This, then, is an example of a multiple parameter class that does actually work
3020 quite well in practice, without ambiguity problems.
3021 There is, however, a catch. This version of the Collects class is nowhere near
3022 as general as the original class seemed to be: only one of the four instances
3023 for <literal>Collects</literal>
3024 given above can be used with this version of Collects because only one of
3025 them---the instance for lists---has a collection type that can be written in
3026 the form c e, for some type constructor c, and element type e.
3030 <sect4><title>Adding functional dependencies</title>
3033 To get a more useful version of the Collects class, Hugs provides a mechanism
3034 that allows programmers to specify dependencies between the parameters of a
3035 multiple parameter class (For readers with an interest in theoretical
3036 foundations and previous work: The use of dependency information can be seen
3037 both as a generalization of the proposal for `parametric type classes' that was
3038 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3039 later framework for "improvement" of qualified types. The
3040 underlying ideas are also discussed in a more theoretical and abstract setting
3041 in a manuscript [implparam], where they are identified as one point in a
3042 general design space for systems of implicit parameterization.).
3044 To start with an abstract example, consider a declaration such as:
3046 class C a b where ...
3048 which tells us simply that C can be thought of as a binary relation on types
3049 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3050 included in the definition of classes to add information about dependencies
3051 between parameters, as in the following examples:
3053 class D a b | a -> b where ...
3054 class E a b | a -> b, b -> a where ...
3056 The notation <literal>a -> b</literal> used here between the | and where
3057 symbols --- not to be
3058 confused with a function type --- indicates that the a parameter uniquely
3059 determines the b parameter, and might be read as "a determines b." Thus D is
3060 not just a relation, but actually a (partial) function. Similarly, from the two
3061 dependencies that are included in the definition of E, we can see that E
3062 represents a (partial) one-one mapping between types.
3065 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3066 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3067 m>=0, meaning that the y parameters are uniquely determined by the x
3068 parameters. Spaces can be used as separators if more than one variable appears
3069 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3070 annotated with multiple dependencies using commas as separators, as in the
3071 definition of E above. Some dependencies that we can write in this notation are
3072 redundant, and will be rejected because they don't serve any useful
3073 purpose, and may instead indicate an error in the program. Examples of
3074 dependencies like this include <literal>a -> a </literal>,
3075 <literal>a -> a a </literal>,
3076 <literal>a -> </literal>, etc. There can also be
3077 some redundancy if multiple dependencies are given, as in
3078 <literal>a->b</literal>,
3079 <literal>b->c </literal>, <literal>a->c </literal>, and
3080 in which some subset implies the remaining dependencies. Examples like this are
3081 not treated as errors. Note that dependencies appear only in class
3082 declarations, and not in any other part of the language. In particular, the
3083 syntax for instance declarations, class constraints, and types is completely
3087 By including dependencies in a class declaration, we provide a mechanism for
3088 the programmer to specify each multiple parameter class more precisely. The
3089 compiler, on the other hand, is responsible for ensuring that the set of
3090 instances that are in scope at any given point in the program is consistent
3091 with any declared dependencies. For example, the following pair of instance
3092 declarations cannot appear together in the same scope because they violate the
3093 dependency for D, even though either one on its own would be acceptable:
3095 instance D Bool Int where ...
3096 instance D Bool Char where ...
3098 Note also that the following declaration is not allowed, even by itself:
3100 instance D [a] b where ...
3102 The problem here is that this instance would allow one particular choice of [a]
3103 to be associated with more than one choice for b, which contradicts the
3104 dependency specified in the definition of D. More generally, this means that,
3105 in any instance of the form:
3107 instance D t s where ...
3109 for some particular types t and s, the only variables that can appear in s are
3110 the ones that appear in t, and hence, if the type t is known, then s will be
3111 uniquely determined.
3114 The benefit of including dependency information is that it allows us to define
3115 more general multiple parameter classes, without ambiguity problems, and with
3116 the benefit of more accurate types. To illustrate this, we return to the
3117 collection class example, and annotate the original definition of <literal>Collects</literal>
3118 with a simple dependency:
3120 class Collects e ce | ce -> e where
3122 insert :: e -> ce -> ce
3123 member :: e -> ce -> Bool
3125 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3126 determined by the type of the collection ce. Note that both parameters of
3127 Collects are of kind *; there are no constructor classes here. Note too that
3128 all of the instances of Collects that we gave earlier can be used
3129 together with this new definition.
3132 What about the ambiguity problems that we encountered with the original
3133 definition? The empty function still has type Collects e ce => ce, but it is no
3134 longer necessary to regard that as an ambiguous type: Although the variable e
3135 does not appear on the right of the => symbol, the dependency for class
3136 Collects tells us that it is uniquely determined by ce, which does appear on
3137 the right of the => symbol. Hence the context in which empty is used can still
3138 give enough information to determine types for both ce and e, without
3139 ambiguity. More generally, we need only regard a type as ambiguous if it
3140 contains a variable on the left of the => that is not uniquely determined
3141 (either directly or indirectly) by the variables on the right.
3144 Dependencies also help to produce more accurate types for user defined
3145 functions, and hence to provide earlier detection of errors, and less cluttered
3146 types for programmers to work with. Recall the previous definition for a
3149 f x y = insert x y = insert x . insert y
3151 for which we originally obtained a type:
3153 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3155 Given the dependency information that we have for Collects, however, we can
3156 deduce that a and b must be equal because they both appear as the second
3157 parameter in a Collects constraint with the same first parameter c. Hence we
3158 can infer a shorter and more accurate type for f:
3160 f :: (Collects a c) => a -> a -> c -> c
3162 In a similar way, the earlier definition of g will now be flagged as a type error.
3165 Although we have given only a few examples here, it should be clear that the
3166 addition of dependency information can help to make multiple parameter classes
3167 more useful in practice, avoiding ambiguity problems, and allowing more general
3168 sets of instance declarations.
3174 <sect2 id="instance-decls">
3175 <title>Instance declarations</title>
3177 <sect3 id="instance-rules">
3178 <title>Relaxed rules for instance declarations</title>
3180 <para>An instance declaration has the form
3182 instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) => <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
3184 The part before the "<literal>=></literal>" is the
3185 <emphasis>context</emphasis>, while the part after the
3186 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3190 In Haskell 98 the head of an instance declaration
3191 must be of the form <literal>C (T a1 ... an)</literal>, where
3192 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3193 and the <literal>a1 ... an</literal> are distinct type variables.
3194 Furthermore, the assertions in the context of the instance declaration
3195 must be of the form <literal>C a</literal> where <literal>a</literal>
3196 is a type variable that occurs in the head.
3199 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3200 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3201 the context and head of the instance declaration can each consist of arbitrary
3202 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3206 The Paterson Conditions: for each assertion in the context
3208 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3209 <listitem><para>The assertion has fewer constructors and variables (taken together
3210 and counting repetitions) than the head</para></listitem>
3214 <listitem><para>The Coverage Condition. For each functional dependency,
3215 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3216 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3217 every type variable in
3218 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3219 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3220 substitution mapping each type variable in the class declaration to the
3221 corresponding type in the instance declaration.
3224 These restrictions ensure that context reduction terminates: each reduction
3225 step makes the problem smaller by at least one
3226 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3227 if you give the <option>-fallow-undecidable-instances</option>
3228 flag (<xref linkend="undecidable-instances"/>).
3229 You can find lots of background material about the reason for these
3230 restrictions in the paper <ulink
3231 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3232 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3235 For example, these are OK:
3237 instance C Int [a] -- Multiple parameters
3238 instance Eq (S [a]) -- Structured type in head
3240 -- Repeated type variable in head
3241 instance C4 a a => C4 [a] [a]
3242 instance Stateful (ST s) (MutVar s)
3244 -- Head can consist of type variables only
3246 instance (Eq a, Show b) => C2 a b
3248 -- Non-type variables in context
3249 instance Show (s a) => Show (Sized s a)
3250 instance C2 Int a => C3 Bool [a]
3251 instance C2 Int a => C3 [a] b
3255 -- Context assertion no smaller than head
3256 instance C a => C a where ...
3257 -- (C b b) has more more occurrences of b than the head
3258 instance C b b => Foo [b] where ...
3263 The same restrictions apply to instances generated by
3264 <literal>deriving</literal> clauses. Thus the following is accepted:
3266 data MinHeap h a = H a (h a)
3269 because the derived instance
3271 instance (Show a, Show (h a)) => Show (MinHeap h a)
3273 conforms to the above rules.
3277 A useful idiom permitted by the above rules is as follows.
3278 If one allows overlapping instance declarations then it's quite
3279 convenient to have a "default instance" declaration that applies if
3280 something more specific does not:
3288 <sect3 id="undecidable-instances">
3289 <title>Undecidable instances</title>
3292 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3293 For example, sometimes you might want to use the following to get the
3294 effect of a "class synonym":
3296 class (C1 a, C2 a, C3 a) => C a where { }
3298 instance (C1 a, C2 a, C3 a) => C a where { }
3300 This allows you to write shorter signatures:
3306 f :: (C1 a, C2 a, C3 a) => ...
3308 The restrictions on functional dependencies (<xref
3309 linkend="functional-dependencies"/>) are particularly troublesome.
3310 It is tempting to introduce type variables in the context that do not appear in
3311 the head, something that is excluded by the normal rules. For example:
3313 class HasConverter a b | a -> b where
3316 data Foo a = MkFoo a
3318 instance (HasConverter a b,Show b) => Show (Foo a) where
3319 show (MkFoo value) = show (convert value)
3321 This is dangerous territory, however. Here, for example, is a program that would make the
3326 instance F [a] [[a]]
3327 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3329 Similarly, it can be tempting to lift the coverage condition:
3331 class Mul a b c | a b -> c where
3332 (.*.) :: a -> b -> c
3334 instance Mul Int Int Int where (.*.) = (*)
3335 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3336 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3338 The third instance declaration does not obey the coverage condition;
3339 and indeed the (somewhat strange) definition:
3341 f = \ b x y -> if b then x .*. [y] else y
3343 makes instance inference go into a loop, because it requires the constraint
3344 <literal>(Mul a [b] b)</literal>.
3347 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3348 the experimental flag <option>-XUndecidableInstances</option>
3349 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3350 both the Paterson Conditions and the Coverage Condition
3351 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3352 fixed-depth recursion stack. If you exceed the stack depth you get a
3353 sort of backtrace, and the opportunity to increase the stack depth
3354 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3360 <sect3 id="instance-overlap">
3361 <title>Overlapping instances</title>
3363 In general, <emphasis>GHC requires that that it be unambiguous which instance
3365 should be used to resolve a type-class constraint</emphasis>. This behaviour
3366 can be modified by two flags: <option>-XOverlappingInstances</option>
3367 <indexterm><primary>-XOverlappingInstances
3368 </primary></indexterm>
3369 and <option>-XIncoherentInstances</option>
3370 <indexterm><primary>-XIncoherentInstances
3371 </primary></indexterm>, as this section discusses. Both these
3372 flags are dynamic flags, and can be set on a per-module basis, using
3373 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3375 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3376 it tries to match every instance declaration against the
3378 by instantiating the head of the instance declaration. For example, consider
3381 instance context1 => C Int a where ... -- (A)
3382 instance context2 => C a Bool where ... -- (B)
3383 instance context3 => C Int [a] where ... -- (C)
3384 instance context4 => C Int [Int] where ... -- (D)
3386 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3387 but (C) and (D) do not. When matching, GHC takes
3388 no account of the context of the instance declaration
3389 (<literal>context1</literal> etc).
3390 GHC's default behaviour is that <emphasis>exactly one instance must match the
3391 constraint it is trying to resolve</emphasis>.
3392 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3393 including both declarations (A) and (B), say); an error is only reported if a
3394 particular constraint matches more than one.
3398 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3399 more than one instance to match, provided there is a most specific one. For
3400 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3401 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3402 most-specific match, the program is rejected.
3405 However, GHC is conservative about committing to an overlapping instance. For example:
3410 Suppose that from the RHS of <literal>f</literal> we get the constraint
3411 <literal>C Int [b]</literal>. But
3412 GHC does not commit to instance (C), because in a particular
3413 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3414 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3415 So GHC rejects the program.
3416 (If you add the flag <option>-XIncoherentInstances</option>,
3417 GHC will instead pick (C), without complaining about
3418 the problem of subsequent instantiations.)
3421 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3422 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3423 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3424 it instead. In this case, GHC will refrain from
3425 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3426 as before) but, rather than rejecting the program, it will infer the type
3428 f :: C Int b => [b] -> [b]
3430 That postpones the question of which instance to pick to the
3431 call site for <literal>f</literal>
3432 by which time more is known about the type <literal>b</literal>.
3435 The willingness to be overlapped or incoherent is a property of
3436 the <emphasis>instance declaration</emphasis> itself, controlled by the
3437 presence or otherwise of the <option>-XOverlappingInstances</option>
3438 and <option>-XIncoherentInstances</option> flags when that module is
3439 being defined. Neither flag is required in a module that imports and uses the
3440 instance declaration. Specifically, during the lookup process:
3443 An instance declaration is ignored during the lookup process if (a) a more specific
3444 match is found, and (b) the instance declaration was compiled with
3445 <option>-XOverlappingInstances</option>. The flag setting for the
3446 more-specific instance does not matter.
3449 Suppose an instance declaration does not match the constraint being looked up, but
3450 does unify with it, so that it might match when the constraint is further
3451 instantiated. Usually GHC will regard this as a reason for not committing to
3452 some other constraint. But if the instance declaration was compiled with
3453 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3454 check for that declaration.
3457 These rules make it possible for a library author to design a library that relies on
3458 overlapping instances without the library client having to know.
3461 If an instance declaration is compiled without
3462 <option>-XOverlappingInstances</option>,
3463 then that instance can never be overlapped. This could perhaps be
3464 inconvenient. Perhaps the rule should instead say that the
3465 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3466 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3467 at a usage site should be permitted regardless of how the instance declarations
3468 are compiled, if the <option>-XOverlappingInstances</option> flag is
3469 used at the usage site. (Mind you, the exact usage site can occasionally be
3470 hard to pin down.) We are interested to receive feedback on these points.
3472 <para>The <option>-XIncoherentInstances</option> flag implies the
3473 <option>-XOverlappingInstances</option> flag, but not vice versa.
3478 <title>Type synonyms in the instance head</title>
3481 <emphasis>Unlike Haskell 98, instance heads may use type
3482 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3483 As always, using a type synonym is just shorthand for
3484 writing the RHS of the type synonym definition. For example:
3488 type Point = (Int,Int)
3489 instance C Point where ...
3490 instance C [Point] where ...
3494 is legal. However, if you added
3498 instance C (Int,Int) where ...
3502 as well, then the compiler will complain about the overlapping
3503 (actually, identical) instance declarations. As always, type synonyms
3504 must be fully applied. You cannot, for example, write:
3509 instance Monad P where ...
3513 This design decision is independent of all the others, and easily
3514 reversed, but it makes sense to me.
3522 <sect2 id="overloaded-strings">
3523 <title>Overloaded string literals
3527 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3528 string literal has type <literal>String</literal>, but with overloaded string
3529 literals enabled (with <literal>-XOverloadedStrings</literal>)
3530 a string literal has type <literal>(IsString a) => a</literal>.
3533 This means that the usual string syntax can be used, e.g., for packed strings
3534 and other variations of string like types. String literals behave very much
3535 like integer literals, i.e., they can be used in both expressions and patterns.
3536 If used in a pattern the literal with be replaced by an equality test, in the same
3537 way as an integer literal is.
3540 The class <literal>IsString</literal> is defined as:
3542 class IsString a where
3543 fromString :: String -> a
3545 The only predefined instance is the obvious one to make strings work as usual:
3547 instance IsString [Char] where
3550 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3551 it explicitly (for example, to give an instance declaration for it), you can import it
3552 from module <literal>GHC.Exts</literal>.
3555 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3559 Each type in a default declaration must be an
3560 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3564 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3565 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3566 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3567 <emphasis>or</emphasis> <literal>IsString</literal>.
3576 import GHC.Exts( IsString(..) )
3578 newtype MyString = MyString String deriving (Eq, Show)
3579 instance IsString MyString where
3580 fromString = MyString
3582 greet :: MyString -> MyString
3583 greet "hello" = "world"
3587 print $ greet "hello"
3588 print $ greet "fool"
3592 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3593 to work since it gets translated into an equality comparison.
3599 <sect1 id="other-type-extensions">
3600 <title>Other type system extensions</title>
3602 <sect2 id="type-restrictions">
3603 <title>Type signatures</title>
3605 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3607 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3608 the form <emphasis>(class type-variable)</emphasis> or
3609 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3610 these type signatures are perfectly OK
3613 g :: Ord (T a ()) => ...
3617 GHC imposes the following restrictions on the constraints in a type signature.
3621 forall tv1..tvn (c1, ...,cn) => type
3624 (Here, we write the "foralls" explicitly, although the Haskell source
3625 language omits them; in Haskell 98, all the free type variables of an
3626 explicit source-language type signature are universally quantified,
3627 except for the class type variables in a class declaration. However,
3628 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3637 <emphasis>Each universally quantified type variable
3638 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3640 A type variable <literal>a</literal> is "reachable" if it it appears
3641 in the same constraint as either a type variable free in in
3642 <literal>type</literal>, or another reachable type variable.
3643 A value with a type that does not obey
3644 this reachability restriction cannot be used without introducing
3645 ambiguity; that is why the type is rejected.
3646 Here, for example, is an illegal type:
3650 forall a. Eq a => Int
3654 When a value with this type was used, the constraint <literal>Eq tv</literal>
3655 would be introduced where <literal>tv</literal> is a fresh type variable, and
3656 (in the dictionary-translation implementation) the value would be
3657 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3658 can never know which instance of <literal>Eq</literal> to use because we never
3659 get any more information about <literal>tv</literal>.
3663 that the reachability condition is weaker than saying that <literal>a</literal> is
3664 functionally dependent on a type variable free in
3665 <literal>type</literal> (see <xref
3666 linkend="functional-dependencies"/>). The reason for this is there
3667 might be a "hidden" dependency, in a superclass perhaps. So
3668 "reachable" is a conservative approximation to "functionally dependent".
3669 For example, consider:
3671 class C a b | a -> b where ...
3672 class C a b => D a b where ...
3673 f :: forall a b. D a b => a -> a
3675 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3676 but that is not immediately apparent from <literal>f</literal>'s type.
3682 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3683 universally quantified type variables <literal>tvi</literal></emphasis>.
3685 For example, this type is OK because <literal>C a b</literal> mentions the
3686 universally quantified type variable <literal>b</literal>:
3690 forall a. C a b => burble
3694 The next type is illegal because the constraint <literal>Eq b</literal> does not
3695 mention <literal>a</literal>:
3699 forall a. Eq b => burble
3703 The reason for this restriction is milder than the other one. The
3704 excluded types are never useful or necessary (because the offending
3705 context doesn't need to be witnessed at this point; it can be floated
3706 out). Furthermore, floating them out increases sharing. Lastly,
3707 excluding them is a conservative choice; it leaves a patch of
3708 territory free in case we need it later.
3722 <sect2 id="implicit-parameters">
3723 <title>Implicit parameters</title>
3725 <para> Implicit parameters are implemented as described in
3726 "Implicit parameters: dynamic scoping with static types",
3727 J Lewis, MB Shields, E Meijer, J Launchbury,
3728 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3732 <para>(Most of the following, still rather incomplete, documentation is
3733 due to Jeff Lewis.)</para>
3735 <para>Implicit parameter support is enabled with the option
3736 <option>-XImplicitParams</option>.</para>
3739 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3740 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3741 context. In Haskell, all variables are statically bound. Dynamic
3742 binding of variables is a notion that goes back to Lisp, but was later
3743 discarded in more modern incarnations, such as Scheme. Dynamic binding
3744 can be very confusing in an untyped language, and unfortunately, typed
3745 languages, in particular Hindley-Milner typed languages like Haskell,
3746 only support static scoping of variables.
3749 However, by a simple extension to the type class system of Haskell, we
3750 can support dynamic binding. Basically, we express the use of a
3751 dynamically bound variable as a constraint on the type. These
3752 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3753 function uses a dynamically-bound variable <literal>?x</literal>
3754 of type <literal>t'</literal>". For
3755 example, the following expresses the type of a sort function,
3756 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3758 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3760 The dynamic binding constraints are just a new form of predicate in the type class system.
3763 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3764 where <literal>x</literal> is
3765 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3766 Use of this construct also introduces a new
3767 dynamic-binding constraint in the type of the expression.
3768 For example, the following definition
3769 shows how we can define an implicitly parameterized sort function in
3770 terms of an explicitly parameterized <literal>sortBy</literal> function:
3772 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3774 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3780 <title>Implicit-parameter type constraints</title>
3782 Dynamic binding constraints behave just like other type class
3783 constraints in that they are automatically propagated. Thus, when a
3784 function is used, its implicit parameters are inherited by the
3785 function that called it. For example, our <literal>sort</literal> function might be used
3786 to pick out the least value in a list:
3788 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3789 least xs = head (sort xs)
3791 Without lifting a finger, the <literal>?cmp</literal> parameter is
3792 propagated to become a parameter of <literal>least</literal> as well. With explicit
3793 parameters, the default is that parameters must always be explicit
3794 propagated. With implicit parameters, the default is to always
3798 An implicit-parameter type constraint differs from other type class constraints in the
3799 following way: All uses of a particular implicit parameter must have
3800 the same type. This means that the type of <literal>(?x, ?x)</literal>
3801 is <literal>(?x::a) => (a,a)</literal>, and not
3802 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3806 <para> You can't have an implicit parameter in the context of a class or instance
3807 declaration. For example, both these declarations are illegal:
3809 class (?x::Int) => C a where ...
3810 instance (?x::a) => Foo [a] where ...
3812 Reason: exactly which implicit parameter you pick up depends on exactly where
3813 you invoke a function. But the ``invocation'' of instance declarations is done
3814 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3815 Easiest thing is to outlaw the offending types.</para>
3817 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3819 f :: (?x :: [a]) => Int -> Int
3822 g :: (Read a, Show a) => String -> String
3825 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3826 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3827 quite unambiguous, and fixes the type <literal>a</literal>.
3832 <title>Implicit-parameter bindings</title>
3835 An implicit parameter is <emphasis>bound</emphasis> using the standard
3836 <literal>let</literal> or <literal>where</literal> binding forms.
3837 For example, we define the <literal>min</literal> function by binding
3838 <literal>cmp</literal>.
3841 min = let ?cmp = (<=) in least
3845 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3846 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3847 (including in a list comprehension, or do-notation, or pattern guards),
3848 or a <literal>where</literal> clause.
3849 Note the following points:
3852 An implicit-parameter binding group must be a
3853 collection of simple bindings to implicit-style variables (no
3854 function-style bindings, and no type signatures); these bindings are
3855 neither polymorphic or recursive.
3858 You may not mix implicit-parameter bindings with ordinary bindings in a
3859 single <literal>let</literal>
3860 expression; use two nested <literal>let</literal>s instead.
3861 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3865 You may put multiple implicit-parameter bindings in a
3866 single binding group; but they are <emphasis>not</emphasis> treated
3867 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3868 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3869 parameter. The bindings are not nested, and may be re-ordered without changing
3870 the meaning of the program.
3871 For example, consider:
3873 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3875 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3876 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3878 f :: (?x::Int) => Int -> Int
3886 <sect3><title>Implicit parameters and polymorphic recursion</title>
3889 Consider these two definitions:
3892 len1 xs = let ?acc = 0 in len_acc1 xs
3895 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3900 len2 xs = let ?acc = 0 in len_acc2 xs
3902 len_acc2 :: (?acc :: Int) => [a] -> Int
3904 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3906 The only difference between the two groups is that in the second group
3907 <literal>len_acc</literal> is given a type signature.
3908 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3909 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3910 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3911 has a type signature, the recursive call is made to the
3912 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3913 as an implicit parameter. So we get the following results in GHCi:
3920 Adding a type signature dramatically changes the result! This is a rather
3921 counter-intuitive phenomenon, worth watching out for.
3925 <sect3><title>Implicit parameters and monomorphism</title>
3927 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3928 Haskell Report) to implicit parameters. For example, consider:
3936 Since the binding for <literal>y</literal> falls under the Monomorphism
3937 Restriction it is not generalised, so the type of <literal>y</literal> is
3938 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3939 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3940 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3941 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3942 <literal>y</literal> in the body of the <literal>let</literal> will see the
3943 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3944 <literal>14</literal>.
3949 <!-- ======================= COMMENTED OUT ========================
3951 We intend to remove linear implicit parameters, so I'm at least removing
3952 them from the 6.6 user manual
3954 <sect2 id="linear-implicit-parameters">
3955 <title>Linear implicit parameters</title>
3957 Linear implicit parameters are an idea developed by Koen Claessen,
3958 Mark Shields, and Simon PJ. They address the long-standing
3959 problem that monads seem over-kill for certain sorts of problem, notably:
3962 <listitem> <para> distributing a supply of unique names </para> </listitem>
3963 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3964 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3968 Linear implicit parameters are just like ordinary implicit parameters,
3969 except that they are "linear"; that is, they cannot be copied, and
3970 must be explicitly "split" instead. Linear implicit parameters are
3971 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3972 (The '/' in the '%' suggests the split!)
3977 import GHC.Exts( Splittable )
3979 data NameSupply = ...
3981 splitNS :: NameSupply -> (NameSupply, NameSupply)
3982 newName :: NameSupply -> Name
3984 instance Splittable NameSupply where
3988 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3989 f env (Lam x e) = Lam x' (f env e)
3992 env' = extend env x x'
3993 ...more equations for f...
3995 Notice that the implicit parameter %ns is consumed
3997 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3998 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4002 So the translation done by the type checker makes
4003 the parameter explicit:
4005 f :: NameSupply -> Env -> Expr -> Expr
4006 f ns env (Lam x e) = Lam x' (f ns1 env e)
4008 (ns1,ns2) = splitNS ns
4010 env = extend env x x'
4012 Notice the call to 'split' introduced by the type checker.
4013 How did it know to use 'splitNS'? Because what it really did
4014 was to introduce a call to the overloaded function 'split',
4015 defined by the class <literal>Splittable</literal>:
4017 class Splittable a where
4020 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4021 split for name supplies. But we can simply write
4027 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4029 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4030 <literal>GHC.Exts</literal>.
4035 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4036 are entirely distinct implicit parameters: you
4037 can use them together and they won't interfere with each other. </para>
4040 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4042 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4043 in the context of a class or instance declaration. </para></listitem>
4047 <sect3><title>Warnings</title>
4050 The monomorphism restriction is even more important than usual.
4051 Consider the example above:
4053 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4054 f env (Lam x e) = Lam x' (f env e)
4057 env' = extend env x x'
4059 If we replaced the two occurrences of x' by (newName %ns), which is
4060 usually a harmless thing to do, we get:
4062 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4063 f env (Lam x e) = Lam (newName %ns) (f env e)
4065 env' = extend env x (newName %ns)
4067 But now the name supply is consumed in <emphasis>three</emphasis> places
4068 (the two calls to newName,and the recursive call to f), so
4069 the result is utterly different. Urk! We don't even have
4073 Well, this is an experimental change. With implicit
4074 parameters we have already lost beta reduction anyway, and
4075 (as John Launchbury puts it) we can't sensibly reason about
4076 Haskell programs without knowing their typing.
4081 <sect3><title>Recursive functions</title>
4082 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4085 foo :: %x::T => Int -> [Int]
4087 foo n = %x : foo (n-1)
4089 where T is some type in class Splittable.</para>
4091 Do you get a list of all the same T's or all different T's
4092 (assuming that split gives two distinct T's back)?
4094 If you supply the type signature, taking advantage of polymorphic
4095 recursion, you get what you'd probably expect. Here's the
4096 translated term, where the implicit param is made explicit:
4099 foo x n = let (x1,x2) = split x
4100 in x1 : foo x2 (n-1)
4102 But if you don't supply a type signature, GHC uses the Hindley
4103 Milner trick of using a single monomorphic instance of the function
4104 for the recursive calls. That is what makes Hindley Milner type inference
4105 work. So the translation becomes
4109 foom n = x : foom (n-1)
4113 Result: 'x' is not split, and you get a list of identical T's. So the
4114 semantics of the program depends on whether or not foo has a type signature.
4117 You may say that this is a good reason to dislike linear implicit parameters
4118 and you'd be right. That is why they are an experimental feature.
4124 ================ END OF Linear Implicit Parameters commented out -->
4126 <sect2 id="kinding">
4127 <title>Explicitly-kinded quantification</title>
4130 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4131 to give the kind explicitly as (machine-checked) documentation,
4132 just as it is nice to give a type signature for a function. On some occasions,
4133 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4134 John Hughes had to define the data type:
4136 data Set cxt a = Set [a]
4137 | Unused (cxt a -> ())
4139 The only use for the <literal>Unused</literal> constructor was to force the correct
4140 kind for the type variable <literal>cxt</literal>.
4143 GHC now instead allows you to specify the kind of a type variable directly, wherever
4144 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4147 This flag enables kind signatures in the following places:
4149 <listitem><para><literal>data</literal> declarations:
4151 data Set (cxt :: * -> *) a = Set [a]
4152 </screen></para></listitem>
4153 <listitem><para><literal>type</literal> declarations:
4155 type T (f :: * -> *) = f Int
4156 </screen></para></listitem>
4157 <listitem><para><literal>class</literal> declarations:
4159 class (Eq a) => C (f :: * -> *) a where ...
4160 </screen></para></listitem>
4161 <listitem><para><literal>forall</literal>'s in type signatures:
4163 f :: forall (cxt :: * -> *). Set cxt Int
4164 </screen></para></listitem>
4169 The parentheses are required. Some of the spaces are required too, to
4170 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4171 will get a parse error, because "<literal>::*->*</literal>" is a
4172 single lexeme in Haskell.
4176 As part of the same extension, you can put kind annotations in types
4179 f :: (Int :: *) -> Int
4180 g :: forall a. a -> (a :: *)
4184 atype ::= '(' ctype '::' kind ')
4186 The parentheses are required.
4191 <sect2 id="universal-quantification">
4192 <title>Arbitrary-rank polymorphism
4196 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4197 allows us to say exactly what this means. For example:
4205 g :: forall b. (b -> b)
4207 The two are treated identically.
4211 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4212 explicit universal quantification in
4214 For example, all the following types are legal:
4216 f1 :: forall a b. a -> b -> a
4217 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4219 f2 :: (forall a. a->a) -> Int -> Int
4220 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4222 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4224 f4 :: Int -> (forall a. a -> a)
4226 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4227 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4228 The <literal>forall</literal> makes explicit the universal quantification that
4229 is implicitly added by Haskell.
4232 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4233 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4234 shows, the polymorphic type on the left of the function arrow can be overloaded.
4237 The function <literal>f3</literal> has a rank-3 type;
4238 it has rank-2 types on the left of a function arrow.
4241 GHC has three flags to control higher-rank types:
4244 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argment types.
4247 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4250 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4251 That is, you can nest <literal>forall</literal>s
4252 arbitrarily deep in function arrows.
4253 In particular, a forall-type (also called a "type scheme"),
4254 including an operational type class context, is legal:
4256 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4257 of a function arrow </para> </listitem>
4258 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4259 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4260 field type signatures.</para> </listitem>
4261 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4262 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4266 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4267 a type variable any more!
4276 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4277 the types of the constructor arguments. Here are several examples:
4283 data T a = T1 (forall b. b -> b -> b) a
4285 data MonadT m = MkMonad { return :: forall a. a -> m a,
4286 bind :: forall a b. m a -> (a -> m b) -> m b
4289 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4295 The constructors have rank-2 types:
4301 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4302 MkMonad :: forall m. (forall a. a -> m a)
4303 -> (forall a b. m a -> (a -> m b) -> m b)
4305 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4311 Notice that you don't need to use a <literal>forall</literal> if there's an
4312 explicit context. For example in the first argument of the
4313 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4314 prefixed to the argument type. The implicit <literal>forall</literal>
4315 quantifies all type variables that are not already in scope, and are
4316 mentioned in the type quantified over.
4320 As for type signatures, implicit quantification happens for non-overloaded
4321 types too. So if you write this:
4324 data T a = MkT (Either a b) (b -> b)
4327 it's just as if you had written this:
4330 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4333 That is, since the type variable <literal>b</literal> isn't in scope, it's
4334 implicitly universally quantified. (Arguably, it would be better
4335 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4336 where that is what is wanted. Feedback welcomed.)
4340 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4341 the constructor to suitable values, just as usual. For example,
4352 a3 = MkSwizzle reverse
4355 a4 = let r x = Just x
4362 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4363 mkTs f x y = [T1 f x, T1 f y]
4369 The type of the argument can, as usual, be more general than the type
4370 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4371 does not need the <literal>Ord</literal> constraint.)
4375 When you use pattern matching, the bound variables may now have
4376 polymorphic types. For example:
4382 f :: T a -> a -> (a, Char)
4383 f (T1 w k) x = (w k x, w 'c' 'd')
4385 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4386 g (MkSwizzle s) xs f = s (map f (s xs))
4388 h :: MonadT m -> [m a] -> m [a]
4389 h m [] = return m []
4390 h m (x:xs) = bind m x $ \y ->
4391 bind m (h m xs) $ \ys ->
4398 In the function <function>h</function> we use the record selectors <literal>return</literal>
4399 and <literal>bind</literal> to extract the polymorphic bind and return functions
4400 from the <literal>MonadT</literal> data structure, rather than using pattern
4406 <title>Type inference</title>
4409 In general, type inference for arbitrary-rank types is undecidable.
4410 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4411 to get a decidable algorithm by requiring some help from the programmer.
4412 We do not yet have a formal specification of "some help" but the rule is this:
4415 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4416 provides an explicit polymorphic type for x, or GHC's type inference will assume
4417 that x's type has no foralls in it</emphasis>.
4420 What does it mean to "provide" an explicit type for x? You can do that by
4421 giving a type signature for x directly, using a pattern type signature
4422 (<xref linkend="scoped-type-variables"/>), thus:
4424 \ f :: (forall a. a->a) -> (f True, f 'c')
4426 Alternatively, you can give a type signature to the enclosing
4427 context, which GHC can "push down" to find the type for the variable:
4429 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4431 Here the type signature on the expression can be pushed inwards
4432 to give a type signature for f. Similarly, and more commonly,
4433 one can give a type signature for the function itself:
4435 h :: (forall a. a->a) -> (Bool,Char)
4436 h f = (f True, f 'c')
4438 You don't need to give a type signature if the lambda bound variable
4439 is a constructor argument. Here is an example we saw earlier:
4441 f :: T a -> a -> (a, Char)
4442 f (T1 w k) x = (w k x, w 'c' 'd')
4444 Here we do not need to give a type signature to <literal>w</literal>, because
4445 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4452 <sect3 id="implicit-quant">
4453 <title>Implicit quantification</title>
4456 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4457 user-written types, if and only if there is no explicit <literal>forall</literal>,
4458 GHC finds all the type variables mentioned in the type that are not already
4459 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4463 f :: forall a. a -> a
4470 h :: forall b. a -> b -> b
4476 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4479 f :: (a -> a) -> Int
4481 f :: forall a. (a -> a) -> Int
4483 f :: (forall a. a -> a) -> Int
4486 g :: (Ord a => a -> a) -> Int
4487 -- MEANS the illegal type
4488 g :: forall a. (Ord a => a -> a) -> Int
4490 g :: (forall a. Ord a => a -> a) -> Int
4492 The latter produces an illegal type, which you might think is silly,
4493 but at least the rule is simple. If you want the latter type, you
4494 can write your for-alls explicitly. Indeed, doing so is strongly advised
4501 <sect2 id="impredicative-polymorphism">
4502 <title>Impredicative polymorphism
4504 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4505 enabled with <option>-XImpredicativeTypes</option>.
4507 that you can call a polymorphic function at a polymorphic type, and
4508 parameterise data structures over polymorphic types. For example:
4510 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4511 f (Just g) = Just (g [3], g "hello")
4514 Notice here that the <literal>Maybe</literal> type is parameterised by the
4515 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4518 <para>The technical details of this extension are described in the paper
4519 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4520 type inference for higher-rank types and impredicativity</ulink>,
4521 which appeared at ICFP 2006.
4525 <sect2 id="scoped-type-variables">
4526 <title>Lexically scoped type variables
4530 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4531 which some type signatures are simply impossible to write. For example:
4533 f :: forall a. [a] -> [a]
4539 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4540 the entire definition of <literal>f</literal>.
4541 In particular, it is in scope at the type signature for <varname>ys</varname>.
4542 In Haskell 98 it is not possible to declare
4543 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4544 it becomes possible to do so.
4546 <para>Lexically-scoped type variables are enabled by
4547 <option>-fglasgow-exts</option>.
4549 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4550 variables work, compared to earlier releases. Read this section
4554 <title>Overview</title>
4556 <para>The design follows the following principles
4558 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4559 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4560 design.)</para></listitem>
4561 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4562 type variables. This means that every programmer-written type signature
4563 (including one that contains free scoped type variables) denotes a
4564 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4565 checker, and no inference is involved.</para></listitem>
4566 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4567 changing the program.</para></listitem>
4571 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4573 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4574 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4575 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4576 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4580 In Haskell, a programmer-written type signature is implicitly quantified over
4581 its free type variables (<ulink
4582 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4584 of the Haskel Report).
4585 Lexically scoped type variables affect this implicit quantification rules
4586 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4587 quantified. For example, if type variable <literal>a</literal> is in scope,
4590 (e :: a -> a) means (e :: a -> a)
4591 (e :: b -> b) means (e :: forall b. b->b)
4592 (e :: a -> b) means (e :: forall b. a->b)
4600 <sect3 id="decl-type-sigs">
4601 <title>Declaration type signatures</title>
4602 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4603 quantification (using <literal>forall</literal>) brings into scope the
4604 explicitly-quantified
4605 type variables, in the definition of the named function(s). For example:
4607 f :: forall a. [a] -> [a]
4608 f (x:xs) = xs ++ [ x :: a ]
4610 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4611 the definition of "<literal>f</literal>".
4613 <para>This only happens if the quantification in <literal>f</literal>'s type
4614 signature is explicit. For example:
4617 g (x:xs) = xs ++ [ x :: a ]
4619 This program will be rejected, because "<literal>a</literal>" does not scope
4620 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4621 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4622 quantification rules.
4626 <sect3 id="exp-type-sigs">
4627 <title>Expression type signatures</title>
4629 <para>An expression type signature that has <emphasis>explicit</emphasis>
4630 quantification (using <literal>forall</literal>) brings into scope the
4631 explicitly-quantified
4632 type variables, in the annotated expression. For example:
4634 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4636 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4637 type variable <literal>s</literal> into scope, in the annotated expression
4638 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4643 <sect3 id="pattern-type-sigs">
4644 <title>Pattern type signatures</title>
4646 A type signature may occur in any pattern; this is a <emphasis>pattern type
4647 signature</emphasis>.
4650 -- f and g assume that 'a' is already in scope
4651 f = \(x::Int, y::a) -> x
4653 h ((x,y) :: (Int,Bool)) = (y,x)
4655 In the case where all the type variables in the pattern type signature are
4656 already in scope (i.e. bound by the enclosing context), matters are simple: the
4657 signature simply constrains the type of the pattern in the obvious way.
4660 Unlike expression and declaration type signatures, pattern type signatures are not implictly generalised.
4661 The pattern in a <emphasis>patterm binding</emphasis> may only mention type variables
4662 that are already in scope. For example:
4664 f :: forall a. [a] -> (Int, [a])
4667 (ys::[a], n) = (reverse xs, length xs) -- OK
4668 zs::[a] = xs ++ ys -- OK
4670 Just (v::b) = ... -- Not OK; b is not in scope
4672 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4673 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4677 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4678 type signature may mention a type variable that is not in scope; in this case,
4679 <emphasis>the signature brings that type variable into scope</emphasis>.
4680 This is particularly important for existential data constructors. For example:
4682 data T = forall a. MkT [a]
4685 k (MkT [t::a]) = MkT t3
4689 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4690 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4691 because it is bound by the pattern match. GHC's rule is that in this situation
4692 (and only then), a pattern type signature can mention a type variable that is
4693 not already in scope; the effect is to bring it into scope, standing for the
4694 existentially-bound type variable.
4697 When a pattern type signature binds a type variable in this way, GHC insists that the
4698 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4699 This means that any user-written type signature always stands for a completely known type.
4702 If all this seems a little odd, we think so too. But we must have
4703 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4704 could not name existentially-bound type variables in subsequent type signatures.
4707 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4708 signature is allowed to mention a lexical variable that is not already in
4710 For example, both <literal>f</literal> and <literal>g</literal> would be
4711 illegal if <literal>a</literal> was not already in scope.
4717 <!-- ==================== Commented out part about result type signatures
4719 <sect3 id="result-type-sigs">
4720 <title>Result type signatures</title>
4723 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4726 {- f assumes that 'a' is already in scope -}
4727 f x y :: [a] = [x,y,x]
4729 g = \ x :: [Int] -> [3,4]
4731 h :: forall a. [a] -> a
4735 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4736 the result of the function. Similarly, the body of the lambda in the RHS of
4737 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4738 alternative in <literal>h</literal> is <literal>a</literal>.
4740 <para> A result type signature never brings new type variables into scope.</para>
4742 There are a couple of syntactic wrinkles. First, notice that all three
4743 examples would parse quite differently with parentheses:
4745 {- f assumes that 'a' is already in scope -}
4746 f x (y :: [a]) = [x,y,x]
4748 g = \ (x :: [Int]) -> [3,4]
4750 h :: forall a. [a] -> a
4754 Now the signature is on the <emphasis>pattern</emphasis>; and
4755 <literal>h</literal> would certainly be ill-typed (since the pattern
4756 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4758 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4759 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4760 token or a parenthesised type of some sort). To see why,
4761 consider how one would parse this:
4770 <sect3 id="cls-inst-scoped-tyvars">
4771 <title>Class and instance declarations</title>
4774 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4775 scope over the methods defined in the <literal>where</literal> part. For example:
4793 <sect2 id="typing-binds">
4794 <title>Generalised typing of mutually recursive bindings</title>
4797 The Haskell Report specifies that a group of bindings (at top level, or in a
4798 <literal>let</literal> or <literal>where</literal>) should be sorted into
4799 strongly-connected components, and then type-checked in dependency order
4800 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4801 Report, Section 4.5.1</ulink>).
4802 As each group is type-checked, any binders of the group that
4804 an explicit type signature are put in the type environment with the specified
4806 and all others are monomorphic until the group is generalised
4807 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4810 <para>Following a suggestion of Mark Jones, in his paper
4811 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4813 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4815 <emphasis>the dependency analysis ignores references to variables that have an explicit
4816 type signature</emphasis>.
4817 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4818 typecheck. For example, consider:
4820 f :: Eq a => a -> Bool
4821 f x = (x == x) || g True || g "Yes"
4823 g y = (y <= y) || f True
4825 This is rejected by Haskell 98, but under Jones's scheme the definition for
4826 <literal>g</literal> is typechecked first, separately from that for
4827 <literal>f</literal>,
4828 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4829 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4830 type is generalised, to get
4832 g :: Ord a => a -> Bool
4834 Now, the definition for <literal>f</literal> is typechecked, with this type for
4835 <literal>g</literal> in the type environment.
4839 The same refined dependency analysis also allows the type signatures of
4840 mutually-recursive functions to have different contexts, something that is illegal in
4841 Haskell 98 (Section 4.5.2, last sentence). With
4842 <option>-XRelaxedPolyRec</option>
4843 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4844 type signatures; in practice this means that only variables bound by the same
4845 pattern binding must have the same context. For example, this is fine:
4847 f :: Eq a => a -> Bool
4848 f x = (x == x) || g True
4850 g :: Ord a => a -> Bool
4851 g y = (y <= y) || f True
4856 <sect2 id="type-families">
4857 <title>Type families
4861 GHC supports the definition of type families indexed by types. They may be
4862 seen as an extension of Haskell 98's class-based overloading of values to
4863 types. When type families are declared in classes, they are also known as
4867 There are two forms of type families: data families and type synonym families.
4868 Currently, only the former are fully implemented, while we are still working
4869 on the latter. As a result, the specification of the language extension is
4870 also still to some degree in flux. Hence, a more detailed description of
4871 the language extension and its use is currently available
4872 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4873 wiki page on type families</ulink>. The material will be moved to this user's
4874 guide when it has stabilised.
4877 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4884 <!-- ==================== End of type system extensions ================= -->
4886 <!-- ====================== TEMPLATE HASKELL ======================= -->
4888 <sect1 id="template-haskell">
4889 <title>Template Haskell</title>
4891 <para>Template Haskell allows you to do compile-time meta-programming in
4894 the main technical innovations is discussed in "<ulink
4895 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
4896 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4899 There is a Wiki page about
4900 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
4901 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4905 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4906 Haskell library reference material</ulink>
4907 (look for module <literal>Language.Haskell.TH</literal>).
4908 Many changes to the original design are described in
4909 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4910 Notes on Template Haskell version 2</ulink>.
4911 Not all of these changes are in GHC, however.
4914 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4915 as a worked example to help get you started.
4919 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4920 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4925 <title>Syntax</title>
4927 <para> Template Haskell has the following new syntactic
4928 constructions. You need to use the flag
4929 <option>-XTemplateHaskell</option>
4930 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4931 </indexterm>to switch these syntactic extensions on
4932 (<option>-XTemplateHaskell</option> is no longer implied by
4933 <option>-fglasgow-exts</option>).</para>
4937 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4938 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4939 There must be no space between the "$" and the identifier or parenthesis. This use
4940 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4941 of "." as an infix operator. If you want the infix operator, put spaces around it.
4943 <para> A splice can occur in place of
4945 <listitem><para> an expression; the spliced expression must
4946 have type <literal>Q Exp</literal></para></listitem>
4947 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4950 Inside a splice you can can only call functions defined in imported modules,
4951 not functions defined elsewhere in the same module.</listitem>
4955 A expression quotation is written in Oxford brackets, thus:
4957 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4958 the quotation has type <literal>Q Exp</literal>.</para></listitem>
4959 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4960 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4961 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4962 the quotation has type <literal>Q Typ</literal>.</para></listitem>
4963 </itemizedlist></para></listitem>
4966 A name can be quoted with either one or two prefix single quotes:
4968 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
4969 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
4970 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
4972 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
4973 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
4976 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, delarations etc. They
4977 may also be given as an argument to the <literal>reify</literal> function.
4983 (Compared to the original paper, there are many differnces of detail.
4984 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
4985 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
4986 Type splices are not implemented, and neither are pattern splices or quotations.
4990 <sect2> <title> Using Template Haskell </title>
4994 The data types and monadic constructor functions for Template Haskell are in the library
4995 <literal>Language.Haskell.THSyntax</literal>.
4999 You can only run a function at compile time if it is imported from another module. That is,
5000 you can't define a function in a module, and call it from within a splice in the same module.
5001 (It would make sense to do so, but it's hard to implement.)
5005 You can only run a function at compile time if it is imported
5006 from another module <emphasis>that is not part of a mutually-recursive group of modules
5007 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5008 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5009 splice is to be run.</para>
5011 For example, when compiling module A,
5012 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5013 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5017 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5020 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5021 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5022 compiles and runs a program, and then looks at the result. So it's important that
5023 the program it compiles produces results whose representations are identical to
5024 those of the compiler itself.
5028 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5029 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5034 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5035 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5036 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5043 -- Import our template "pr"
5044 import Printf ( pr )
5046 -- The splice operator $ takes the Haskell source code
5047 -- generated at compile time by "pr" and splices it into
5048 -- the argument of "putStrLn".
5049 main = putStrLn ( $(pr "Hello") )
5055 -- Skeletal printf from the paper.
5056 -- It needs to be in a separate module to the one where
5057 -- you intend to use it.
5059 -- Import some Template Haskell syntax
5060 import Language.Haskell.TH
5062 -- Describe a format string
5063 data Format = D | S | L String
5065 -- Parse a format string. This is left largely to you
5066 -- as we are here interested in building our first ever
5067 -- Template Haskell program and not in building printf.
5068 parse :: String -> [Format]
5071 -- Generate Haskell source code from a parsed representation
5072 -- of the format string. This code will be spliced into
5073 -- the module which calls "pr", at compile time.
5074 gen :: [Format] -> Q Exp
5075 gen [D] = [| \n -> show n |]
5076 gen [S] = [| \s -> s |]
5077 gen [L s] = stringE s
5079 -- Here we generate the Haskell code for the splice
5080 -- from an input format string.
5081 pr :: String -> Q Exp
5082 pr s = gen (parse s)
5085 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5088 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5091 <para>Run "main.exe" and here is your output:</para>
5101 <title>Using Template Haskell with Profiling</title>
5102 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5104 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5105 interpreter to run the splice expressions. The bytecode interpreter
5106 runs the compiled expression on top of the same runtime on which GHC
5107 itself is running; this means that the compiled code referred to by
5108 the interpreted expression must be compatible with this runtime, and
5109 in particular this means that object code that is compiled for
5110 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5111 expression, because profiled object code is only compatible with the
5112 profiling version of the runtime.</para>
5114 <para>This causes difficulties if you have a multi-module program
5115 containing Template Haskell code and you need to compile it for
5116 profiling, because GHC cannot load the profiled object code and use it
5117 when executing the splices. Fortunately GHC provides a workaround.
5118 The basic idea is to compile the program twice:</para>
5122 <para>Compile the program or library first the normal way, without
5123 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5126 <para>Then compile it again with <option>-prof</option>, and
5127 additionally use <option>-osuf
5128 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5129 to name the object files differently (you can choose any suffix
5130 that isn't the normal object suffix here). GHC will automatically
5131 load the object files built in the first step when executing splice
5132 expressions. If you omit the <option>-osuf</option> flag when
5133 building with <option>-prof</option> and Template Haskell is used,
5134 GHC will emit an error message. </para>
5141 <!-- ===================== Arrow notation =================== -->
5143 <sect1 id="arrow-notation">
5144 <title>Arrow notation
5147 <para>Arrows are a generalization of monads introduced by John Hughes.
5148 For more details, see
5153 “Generalising Monads to Arrows”,
5154 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5155 pp67–111, May 2000.
5161 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5162 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5168 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5169 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5175 and the arrows web page at
5176 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5177 With the <option>-XArrows</option> flag, GHC supports the arrow
5178 notation described in the second of these papers.
5179 What follows is a brief introduction to the notation;
5180 it won't make much sense unless you've read Hughes's paper.
5181 This notation is translated to ordinary Haskell,
5182 using combinators from the
5183 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5187 <para>The extension adds a new kind of expression for defining arrows:
5189 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5190 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5192 where <literal>proc</literal> is a new keyword.
5193 The variables of the pattern are bound in the body of the
5194 <literal>proc</literal>-expression,
5195 which is a new sort of thing called a <firstterm>command</firstterm>.
5196 The syntax of commands is as follows:
5198 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5199 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5200 | <replaceable>cmd</replaceable><superscript>0</superscript>
5202 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5203 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5204 infix operators as for expressions, and
5206 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5207 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5208 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5209 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5210 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5211 | <replaceable>fcmd</replaceable>
5213 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5214 | ( <replaceable>cmd</replaceable> )
5215 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5217 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5218 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5219 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5220 | <replaceable>cmd</replaceable>
5222 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5223 except that the bodies are commands instead of expressions.
5227 Commands produce values, but (like monadic computations)
5228 may yield more than one value,
5229 or none, and may do other things as well.
5230 For the most part, familiarity with monadic notation is a good guide to
5232 However the values of expressions, even monadic ones,
5233 are determined by the values of the variables they contain;
5234 this is not necessarily the case for commands.
5238 A simple example of the new notation is the expression
5240 proc x -> f -< x+1
5242 We call this a <firstterm>procedure</firstterm> or
5243 <firstterm>arrow abstraction</firstterm>.
5244 As with a lambda expression, the variable <literal>x</literal>
5245 is a new variable bound within the <literal>proc</literal>-expression.
5246 It refers to the input to the arrow.
5247 In the above example, <literal>-<</literal> is not an identifier but an
5248 new reserved symbol used for building commands from an expression of arrow
5249 type and an expression to be fed as input to that arrow.
5250 (The weird look will make more sense later.)
5251 It may be read as analogue of application for arrows.
5252 The above example is equivalent to the Haskell expression
5254 arr (\ x -> x+1) >>> f
5256 That would make no sense if the expression to the left of
5257 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5258 More generally, the expression to the left of <literal>-<</literal>
5259 may not involve any <firstterm>local variable</firstterm>,
5260 i.e. a variable bound in the current arrow abstraction.
5261 For such a situation there is a variant <literal>-<<</literal>, as in
5263 proc x -> f x -<< x+1
5265 which is equivalent to
5267 arr (\ x -> (f x, x+1)) >>> app
5269 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5271 Such an arrow is equivalent to a monad, so if you're using this form
5272 you may find a monadic formulation more convenient.
5276 <title>do-notation for commands</title>
5279 Another form of command is a form of <literal>do</literal>-notation.
5280 For example, you can write
5289 You can read this much like ordinary <literal>do</literal>-notation,
5290 but with commands in place of monadic expressions.
5291 The first line sends the value of <literal>x+1</literal> as an input to
5292 the arrow <literal>f</literal>, and matches its output against
5293 <literal>y</literal>.
5294 In the next line, the output is discarded.
5295 The arrow <function>returnA</function> is defined in the
5296 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5297 module as <literal>arr id</literal>.
5298 The above example is treated as an abbreviation for
5300 arr (\ x -> (x, x)) >>>
5301 first (arr (\ x -> x+1) >>> f) >>>
5302 arr (\ (y, x) -> (y, (x, y))) >>>
5303 first (arr (\ y -> 2*y) >>> g) >>>
5305 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5306 first (arr (\ (x, z) -> x*z) >>> h) >>>
5307 arr (\ (t, z) -> t+z) >>>
5310 Note that variables not used later in the composition are projected out.
5311 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5313 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5314 module, this reduces to
5316 arr (\ x -> (x+1, x)) >>>
5318 arr (\ (y, x) -> (2*y, (x, y))) >>>
5320 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5322 arr (\ (t, z) -> t+z)
5324 which is what you might have written by hand.
5325 With arrow notation, GHC keeps track of all those tuples of variables for you.
5329 Note that although the above translation suggests that
5330 <literal>let</literal>-bound variables like <literal>z</literal> must be
5331 monomorphic, the actual translation produces Core,
5332 so polymorphic variables are allowed.
5336 It's also possible to have mutually recursive bindings,
5337 using the new <literal>rec</literal> keyword, as in the following example:
5339 counter :: ArrowCircuit a => a Bool Int
5340 counter = proc reset -> do
5341 rec output <- returnA -< if reset then 0 else next
5342 next <- delay 0 -< output+1
5343 returnA -< output
5345 The translation of such forms uses the <function>loop</function> combinator,
5346 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5352 <title>Conditional commands</title>
5355 In the previous example, we used a conditional expression to construct the
5357 Sometimes we want to conditionally execute different commands, as in
5364 which is translated to
5366 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5367 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5369 Since the translation uses <function>|||</function>,
5370 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5374 There are also <literal>case</literal> commands, like
5380 y <- h -< (x1, x2)
5384 The syntax is the same as for <literal>case</literal> expressions,
5385 except that the bodies of the alternatives are commands rather than expressions.
5386 The translation is similar to that of <literal>if</literal> commands.
5392 <title>Defining your own control structures</title>
5395 As we're seen, arrow notation provides constructs,
5396 modelled on those for expressions,
5397 for sequencing, value recursion and conditionals.
5398 But suitable combinators,
5399 which you can define in ordinary Haskell,
5400 may also be used to build new commands out of existing ones.
5401 The basic idea is that a command defines an arrow from environments to values.
5402 These environments assign values to the free local variables of the command.
5403 Thus combinators that produce arrows from arrows
5404 may also be used to build commands from commands.
5405 For example, the <literal>ArrowChoice</literal> class includes a combinator
5407 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5409 so we can use it to build commands:
5411 expr' = proc x -> do
5414 symbol Plus -< ()
5415 y <- term -< ()
5418 symbol Minus -< ()
5419 y <- term -< ()
5422 (The <literal>do</literal> on the first line is needed to prevent the first
5423 <literal><+> ...</literal> from being interpreted as part of the
5424 expression on the previous line.)
5425 This is equivalent to
5427 expr' = (proc x -> returnA -< x)
5428 <+> (proc x -> do
5429 symbol Plus -< ()
5430 y <- term -< ()
5432 <+> (proc x -> do
5433 symbol Minus -< ()
5434 y <- term -< ()
5437 It is essential that this operator be polymorphic in <literal>e</literal>
5438 (representing the environment input to the command
5439 and thence to its subcommands)
5440 and satisfy the corresponding naturality property
5442 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5444 at least for strict <literal>k</literal>.
5445 (This should be automatic if you're not using <function>seq</function>.)
5446 This ensures that environments seen by the subcommands are environments
5447 of the whole command,
5448 and also allows the translation to safely trim these environments.
5449 The operator must also not use any variable defined within the current
5454 We could define our own operator
5456 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5457 untilA body cond = proc x ->
5458 if cond x then returnA -< ()
5461 untilA body cond -< x
5463 and use it in the same way.
5464 Of course this infix syntax only makes sense for binary operators;
5465 there is also a more general syntax involving special brackets:
5469 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5476 <title>Primitive constructs</title>
5479 Some operators will need to pass additional inputs to their subcommands.
5480 For example, in an arrow type supporting exceptions,
5481 the operator that attaches an exception handler will wish to pass the
5482 exception that occurred to the handler.
5483 Such an operator might have a type
5485 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5487 where <literal>Ex</literal> is the type of exceptions handled.
5488 You could then use this with arrow notation by writing a command
5490 body `handleA` \ ex -> handler
5492 so that if an exception is raised in the command <literal>body</literal>,
5493 the variable <literal>ex</literal> is bound to the value of the exception
5494 and the command <literal>handler</literal>,
5495 which typically refers to <literal>ex</literal>, is entered.
5496 Though the syntax here looks like a functional lambda,
5497 we are talking about commands, and something different is going on.
5498 The input to the arrow represented by a command consists of values for
5499 the free local variables in the command, plus a stack of anonymous values.
5500 In all the prior examples, this stack was empty.
5501 In the second argument to <function>handleA</function>,
5502 this stack consists of one value, the value of the exception.
5503 The command form of lambda merely gives this value a name.
5508 the values on the stack are paired to the right of the environment.
5509 So operators like <function>handleA</function> that pass
5510 extra inputs to their subcommands can be designed for use with the notation
5511 by pairing the values with the environment in this way.
5512 More precisely, the type of each argument of the operator (and its result)
5513 should have the form
5515 a (...(e,t1), ... tn) t
5517 where <replaceable>e</replaceable> is a polymorphic variable
5518 (representing the environment)
5519 and <replaceable>ti</replaceable> are the types of the values on the stack,
5520 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5521 The polymorphic variable <replaceable>e</replaceable> must not occur in
5522 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5523 <replaceable>t</replaceable>.
5524 However the arrows involved need not be the same.
5525 Here are some more examples of suitable operators:
5527 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5528 runReader :: ... => a e c -> a' (e,State) c
5529 runState :: ... => a e c -> a' (e,State) (c,State)
5531 We can supply the extra input required by commands built with the last two
5532 by applying them to ordinary expressions, as in
5536 (|runReader (do { ... })|) s
5538 which adds <literal>s</literal> to the stack of inputs to the command
5539 built using <function>runReader</function>.
5543 The command versions of lambda abstraction and application are analogous to
5544 the expression versions.
5545 In particular, the beta and eta rules describe equivalences of commands.
5546 These three features (operators, lambda abstraction and application)
5547 are the core of the notation; everything else can be built using them,
5548 though the results would be somewhat clumsy.
5549 For example, we could simulate <literal>do</literal>-notation by defining
5551 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5552 u `bind` f = returnA &&& u >>> f
5554 bind_ :: Arrow a => a e b -> a e c -> a e c
5555 u `bind_` f = u `bind` (arr fst >>> f)
5557 We could simulate <literal>if</literal> by defining
5559 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5560 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5567 <title>Differences with the paper</title>
5572 <para>Instead of a single form of arrow application (arrow tail) with two
5573 translations, the implementation provides two forms
5574 <quote><literal>-<</literal></quote> (first-order)
5575 and <quote><literal>-<<</literal></quote> (higher-order).
5580 <para>User-defined operators are flagged with banana brackets instead of
5581 a new <literal>form</literal> keyword.
5590 <title>Portability</title>
5593 Although only GHC implements arrow notation directly,
5594 there is also a preprocessor
5596 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5597 that translates arrow notation into Haskell 98
5598 for use with other Haskell systems.
5599 You would still want to check arrow programs with GHC;
5600 tracing type errors in the preprocessor output is not easy.
5601 Modules intended for both GHC and the preprocessor must observe some
5602 additional restrictions:
5607 The module must import
5608 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5614 The preprocessor cannot cope with other Haskell extensions.
5615 These would have to go in separate modules.
5621 Because the preprocessor targets Haskell (rather than Core),
5622 <literal>let</literal>-bound variables are monomorphic.
5633 <!-- ==================== BANG PATTERNS ================= -->
5635 <sect1 id="bang-patterns">
5636 <title>Bang patterns
5637 <indexterm><primary>Bang patterns</primary></indexterm>
5639 <para>GHC supports an extension of pattern matching called <emphasis>bang
5640 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5642 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5643 prime feature description</ulink> contains more discussion and examples
5644 than the material below.
5647 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5650 <sect2 id="bang-patterns-informal">
5651 <title>Informal description of bang patterns
5654 The main idea is to add a single new production to the syntax of patterns:
5658 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5659 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5664 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5665 whereas without the bang it would be lazy.
5666 Bang patterns can be nested of course:
5670 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5671 <literal>y</literal>.
5672 A bang only really has an effect if it precedes a variable or wild-card pattern:
5677 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5678 forces evaluation anyway does nothing.
5680 Bang patterns work in <literal>case</literal> expressions too, of course:
5682 g5 x = let y = f x in body
5683 g6 x = case f x of { y -> body }
5684 g7 x = case f x of { !y -> body }
5686 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5687 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5688 result, and then evaluates <literal>body</literal>.
5690 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5691 definitions too. For example:
5695 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5696 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5697 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5698 in a function argument <literal>![x,y]</literal> means the
5699 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5700 is part of the syntax of <literal>let</literal> bindings.
5705 <sect2 id="bang-patterns-sem">
5706 <title>Syntax and semantics
5710 We add a single new production to the syntax of patterns:
5714 There is one problem with syntactic ambiguity. Consider:
5718 Is this a definition of the infix function "<literal>(!)</literal>",
5719 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5720 ambiguity in favour of the latter. If you want to define
5721 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5726 The semantics of Haskell pattern matching is described in <ulink
5727 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5728 Section 3.17.2</ulink> of the Haskell Report. To this description add
5729 one extra item 10, saying:
5730 <itemizedlist><listitem><para>Matching
5731 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5732 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5733 <listitem><para>otherwise, <literal>pat</literal> is matched against
5734 <literal>v</literal></para></listitem>
5736 </para></listitem></itemizedlist>
5737 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5738 Section 3.17.3</ulink>, add a new case (t):
5740 case v of { !pat -> e; _ -> e' }
5741 = v `seq` case v of { pat -> e; _ -> e' }
5744 That leaves let expressions, whose translation is given in
5745 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5747 of the Haskell Report.
5748 In the translation box, first apply
5749 the following transformation: for each pattern <literal>pi</literal> that is of
5750 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5751 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5752 have a bang at the top, apply the rules in the existing box.
5754 <para>The effect of the let rule is to force complete matching of the pattern
5755 <literal>qi</literal> before evaluation of the body is begun. The bang is
5756 retained in the translated form in case <literal>qi</literal> is a variable,
5764 The let-binding can be recursive. However, it is much more common for
5765 the let-binding to be non-recursive, in which case the following law holds:
5766 <literal>(let !p = rhs in body)</literal>
5768 <literal>(case rhs of !p -> body)</literal>
5771 A pattern with a bang at the outermost level is not allowed at the top level of
5777 <!-- ==================== ASSERTIONS ================= -->
5779 <sect1 id="assertions">
5781 <indexterm><primary>Assertions</primary></indexterm>
5785 If you want to make use of assertions in your standard Haskell code, you
5786 could define a function like the following:
5792 assert :: Bool -> a -> a
5793 assert False x = error "assertion failed!"
5800 which works, but gives you back a less than useful error message --
5801 an assertion failed, but which and where?
5805 One way out is to define an extended <function>assert</function> function which also
5806 takes a descriptive string to include in the error message and
5807 perhaps combine this with the use of a pre-processor which inserts
5808 the source location where <function>assert</function> was used.
5812 Ghc offers a helping hand here, doing all of this for you. For every
5813 use of <function>assert</function> in the user's source:
5819 kelvinToC :: Double -> Double
5820 kelvinToC k = assert (k >= 0.0) (k+273.15)
5826 Ghc will rewrite this to also include the source location where the
5833 assert pred val ==> assertError "Main.hs|15" pred val
5839 The rewrite is only performed by the compiler when it spots
5840 applications of <function>Control.Exception.assert</function>, so you
5841 can still define and use your own versions of
5842 <function>assert</function>, should you so wish. If not, import
5843 <literal>Control.Exception</literal> to make use
5844 <function>assert</function> in your code.
5848 GHC ignores assertions when optimisation is turned on with the
5849 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5850 <literal>assert pred e</literal> will be rewritten to
5851 <literal>e</literal>. You can also disable assertions using the
5852 <option>-fignore-asserts</option>
5853 option<indexterm><primary><option>-fignore-asserts</option></primary>
5854 </indexterm>.</para>
5857 Assertion failures can be caught, see the documentation for the
5858 <literal>Control.Exception</literal> library for the details.
5864 <!-- =============================== PRAGMAS =========================== -->
5866 <sect1 id="pragmas">
5867 <title>Pragmas</title>
5869 <indexterm><primary>pragma</primary></indexterm>
5871 <para>GHC supports several pragmas, or instructions to the
5872 compiler placed in the source code. Pragmas don't normally affect
5873 the meaning of the program, but they might affect the efficiency
5874 of the generated code.</para>
5876 <para>Pragmas all take the form
5878 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5880 where <replaceable>word</replaceable> indicates the type of
5881 pragma, and is followed optionally by information specific to that
5882 type of pragma. Case is ignored in
5883 <replaceable>word</replaceable>. The various values for
5884 <replaceable>word</replaceable> that GHC understands are described
5885 in the following sections; any pragma encountered with an
5886 unrecognised <replaceable>word</replaceable> is (silently)
5889 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
5890 pragma must precede the <literal>module</literal> keyword in the file.
5891 There can be as many file-header pragmas as you please, and they can be
5892 preceded or followed by comments.</para>
5894 <sect2 id="language-pragma">
5895 <title>LANGUAGE pragma</title>
5897 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5898 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5900 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
5902 It is the intention that all Haskell compilers support the
5903 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5904 all extensions are supported by all compilers, of
5905 course. The <literal>LANGUAGE</literal> pragma should be used instead
5906 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5908 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5910 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5912 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5914 <para>Every language extension can also be turned into a command-line flag
5915 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
5916 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
5919 <para>A list of all supported language extensions can be obtained by invoking
5920 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
5922 <para>Any extension from the <literal>Extension</literal> type defined in
5924 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
5925 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
5929 <sect2 id="options-pragma">
5930 <title>OPTIONS_GHC pragma</title>
5931 <indexterm><primary>OPTIONS_GHC</primary>
5933 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5936 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5937 additional options that are given to the compiler when compiling
5938 this source file. See <xref linkend="source-file-options"/> for
5941 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5942 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5945 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5947 <sect2 id="include-pragma">
5948 <title>INCLUDE pragma</title>
5950 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5951 of C header files that should be <literal>#include</literal>'d into
5952 the C source code generated by the compiler for the current module (if
5953 compiling via C). For example:</para>
5956 {-# INCLUDE "foo.h" #-}
5957 {-# INCLUDE <stdio.h> #-}</programlisting>
5959 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5961 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5962 to the <option>-#include</option> option (<xref
5963 linkend="options-C-compiler" />), because the
5964 <literal>INCLUDE</literal> pragma is understood by other
5965 compilers. Yet another alternative is to add the include file to each
5966 <literal>foreign import</literal> declaration in your code, but we
5967 don't recommend using this approach with GHC.</para>
5970 <sect2 id="deprecated-pragma">
5971 <title>DEPRECATED pragma</title>
5972 <indexterm><primary>DEPRECATED</primary>
5975 <para>The DEPRECATED pragma lets you specify that a particular
5976 function, class, or type, is deprecated. There are two
5981 <para>You can deprecate an entire module thus:</para>
5983 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5986 <para>When you compile any module that import
5987 <literal>Wibble</literal>, GHC will print the specified
5992 <para>You can deprecate a function, class, type, or data constructor, with the
5993 following top-level declaration:</para>
5995 {-# DEPRECATED f, C, T "Don't use these" #-}
5997 <para>When you compile any module that imports and uses any
5998 of the specified entities, GHC will print the specified
6000 <para> You can only deprecate entities declared at top level in the module
6001 being compiled, and you can only use unqualified names in the list of
6002 entities being deprecated. A capitalised name, such as <literal>T</literal>
6003 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6004 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6005 both are in scope. If both are in scope, there is currently no way to deprecate
6006 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
6009 Any use of the deprecated item, or of anything from a deprecated
6010 module, will be flagged with an appropriate message. However,
6011 deprecations are not reported for
6012 (a) uses of a deprecated function within its defining module, and
6013 (b) uses of a deprecated function in an export list.
6014 The latter reduces spurious complaints within a library
6015 in which one module gathers together and re-exports
6016 the exports of several others.
6018 <para>You can suppress the warnings with the flag
6019 <option>-fno-warn-deprecations</option>.</para>
6022 <sect2 id="inline-noinline-pragma">
6023 <title>INLINE and NOINLINE pragmas</title>
6025 <para>These pragmas control the inlining of function
6028 <sect3 id="inline-pragma">
6029 <title>INLINE pragma</title>
6030 <indexterm><primary>INLINE</primary></indexterm>
6032 <para>GHC (with <option>-O</option>, as always) tries to
6033 inline (or “unfold”) functions/values that are
6034 “small enough,” thus avoiding the call overhead
6035 and possibly exposing other more-wonderful optimisations.
6036 Normally, if GHC decides a function is “too
6037 expensive” to inline, it will not do so, nor will it
6038 export that unfolding for other modules to use.</para>
6040 <para>The sledgehammer you can bring to bear is the
6041 <literal>INLINE</literal><indexterm><primary>INLINE
6042 pragma</primary></indexterm> pragma, used thusly:</para>
6045 key_function :: Int -> String -> (Bool, Double)
6047 #ifdef __GLASGOW_HASKELL__
6048 {-# INLINE key_function #-}
6052 <para>(You don't need to do the C pre-processor carry-on
6053 unless you're going to stick the code through HBC—it
6054 doesn't like <literal>INLINE</literal> pragmas.)</para>
6056 <para>The major effect of an <literal>INLINE</literal> pragma
6057 is to declare a function's “cost” to be very low.
6058 The normal unfolding machinery will then be very keen to
6059 inline it. However, an <literal>INLINE</literal> pragma for a
6060 function "<literal>f</literal>" has a number of other effects:
6063 No funtions are inlined into <literal>f</literal>. Otherwise
6064 GHC might inline a big function into <literal>f</literal>'s right hand side,
6065 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6068 The float-in, float-out, and common-sub-expression transformations are not
6069 applied to the body of <literal>f</literal>.
6072 An INLINE function is not worker/wrappered by strictness analysis.
6073 It's going to be inlined wholesale instead.
6076 All of these effects are aimed at ensuring that what gets inlined is
6077 exactly what you asked for, no more and no less.
6079 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6080 function can be put anywhere its type signature could be
6083 <para><literal>INLINE</literal> pragmas are a particularly
6085 <literal>then</literal>/<literal>return</literal> (or
6086 <literal>bind</literal>/<literal>unit</literal>) functions in
6087 a monad. For example, in GHC's own
6088 <literal>UniqueSupply</literal> monad code, we have:</para>
6091 #ifdef __GLASGOW_HASKELL__
6092 {-# INLINE thenUs #-}
6093 {-# INLINE returnUs #-}
6097 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6098 linkend="noinline-pragma"/>).</para>
6101 <sect3 id="noinline-pragma">
6102 <title>NOINLINE pragma</title>
6104 <indexterm><primary>NOINLINE</primary></indexterm>
6105 <indexterm><primary>NOTINLINE</primary></indexterm>
6107 <para>The <literal>NOINLINE</literal> pragma does exactly what
6108 you'd expect: it stops the named function from being inlined
6109 by the compiler. You shouldn't ever need to do this, unless
6110 you're very cautious about code size.</para>
6112 <para><literal>NOTINLINE</literal> is a synonym for
6113 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6114 specified by Haskell 98 as the standard way to disable
6115 inlining, so it should be used if you want your code to be
6119 <sect3 id="phase-control">
6120 <title>Phase control</title>
6122 <para> Sometimes you want to control exactly when in GHC's
6123 pipeline the INLINE pragma is switched on. Inlining happens
6124 only during runs of the <emphasis>simplifier</emphasis>. Each
6125 run of the simplifier has a different <emphasis>phase
6126 number</emphasis>; the phase number decreases towards zero.
6127 If you use <option>-dverbose-core2core</option> you'll see the
6128 sequence of phase numbers for successive runs of the
6129 simplifier. In an INLINE pragma you can optionally specify a
6133 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6134 <literal>f</literal>
6135 until phase <literal>k</literal>, but from phase
6136 <literal>k</literal> onwards be very keen to inline it.
6139 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6140 <literal>f</literal>
6141 until phase <literal>k</literal>, but from phase
6142 <literal>k</literal> onwards do not inline it.
6145 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6146 <literal>f</literal>
6147 until phase <literal>k</literal>, but from phase
6148 <literal>k</literal> onwards be willing to inline it (as if
6149 there was no pragma).
6152 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
6153 <literal>f</literal>
6154 until phase <literal>k</literal>, but from phase
6155 <literal>k</literal> onwards do not inline it.
6158 The same information is summarised here:
6160 -- Before phase 2 Phase 2 and later
6161 {-# INLINE [2] f #-} -- No Yes
6162 {-# INLINE [~2] f #-} -- Yes No
6163 {-# NOINLINE [2] f #-} -- No Maybe
6164 {-# NOINLINE [~2] f #-} -- Maybe No
6166 {-# INLINE f #-} -- Yes Yes
6167 {-# NOINLINE f #-} -- No No
6169 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6170 function body is small, or it is applied to interesting-looking arguments etc).
6171 Another way to understand the semantics is this:
6173 <listitem><para>For both INLINE and NOINLINE, the phase number says
6174 when inlining is allowed at all.</para></listitem>
6175 <listitem><para>The INLINE pragma has the additional effect of making the
6176 function body look small, so that when inlining is allowed it is very likely to
6181 <para>The same phase-numbering control is available for RULES
6182 (<xref linkend="rewrite-rules"/>).</para>
6186 <sect2 id="line-pragma">
6187 <title>LINE pragma</title>
6189 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6190 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6191 <para>This pragma is similar to C's <literal>#line</literal>
6192 pragma, and is mainly for use in automatically generated Haskell
6193 code. It lets you specify the line number and filename of the
6194 original code; for example</para>
6196 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6198 <para>if you'd generated the current file from something called
6199 <filename>Foo.vhs</filename> and this line corresponds to line
6200 42 in the original. GHC will adjust its error messages to refer
6201 to the line/file named in the <literal>LINE</literal>
6206 <title>RULES pragma</title>
6208 <para>The RULES pragma lets you specify rewrite rules. It is
6209 described in <xref linkend="rewrite-rules"/>.</para>
6212 <sect2 id="specialize-pragma">
6213 <title>SPECIALIZE pragma</title>
6215 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6216 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6217 <indexterm><primary>overloading, death to</primary></indexterm>
6219 <para>(UK spelling also accepted.) For key overloaded
6220 functions, you can create extra versions (NB: more code space)
6221 specialised to particular types. Thus, if you have an
6222 overloaded function:</para>
6225 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6228 <para>If it is heavily used on lists with
6229 <literal>Widget</literal> keys, you could specialise it as
6233 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6236 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6237 be put anywhere its type signature could be put.</para>
6239 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6240 (a) a specialised version of the function and (b) a rewrite rule
6241 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6242 un-specialised function into a call to the specialised one.</para>
6244 <para>The type in a SPECIALIZE pragma can be any type that is less
6245 polymorphic than the type of the original function. In concrete terms,
6246 if the original function is <literal>f</literal> then the pragma
6248 {-# SPECIALIZE f :: <type> #-}
6250 is valid if and only if the definition
6252 f_spec :: <type>
6255 is valid. Here are some examples (where we only give the type signature
6256 for the original function, not its code):
6258 f :: Eq a => a -> b -> b
6259 {-# SPECIALISE f :: Int -> b -> b #-}
6261 g :: (Eq a, Ix b) => a -> b -> b
6262 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6264 h :: Eq a => a -> a -> a
6265 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6267 The last of these examples will generate a
6268 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6269 well. If you use this kind of specialisation, let us know how well it works.
6272 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6273 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6274 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6275 The <literal>INLINE</literal> pragma affects the specialised version of the
6276 function (only), and applies even if the function is recursive. The motivating
6279 -- A GADT for arrays with type-indexed representation
6281 ArrInt :: !Int -> ByteArray# -> Arr Int
6282 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6284 (!:) :: Arr e -> Int -> e
6285 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6286 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6287 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6288 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6290 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6291 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6292 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6293 the specialised function will be inlined. It has two calls to
6294 <literal>(!:)</literal>,
6295 both at type <literal>Int</literal>. Both these calls fire the first
6296 specialisation, whose body is also inlined. The result is a type-based
6297 unrolling of the indexing function.</para>
6298 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6299 on an ordinarily-recursive function.</para>
6301 <para>Note: In earlier versions of GHC, it was possible to provide your own
6302 specialised function for a given type:
6305 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6308 This feature has been removed, as it is now subsumed by the
6309 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6313 <sect2 id="specialize-instance-pragma">
6314 <title>SPECIALIZE instance pragma
6318 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6319 <indexterm><primary>overloading, death to</primary></indexterm>
6320 Same idea, except for instance declarations. For example:
6323 instance (Eq a) => Eq (Foo a) where {
6324 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6328 The pragma must occur inside the <literal>where</literal> part
6329 of the instance declaration.
6332 Compatible with HBC, by the way, except perhaps in the placement
6338 <sect2 id="unpack-pragma">
6339 <title>UNPACK pragma</title>
6341 <indexterm><primary>UNPACK</primary></indexterm>
6343 <para>The <literal>UNPACK</literal> indicates to the compiler
6344 that it should unpack the contents of a constructor field into
6345 the constructor itself, removing a level of indirection. For
6349 data T = T {-# UNPACK #-} !Float
6350 {-# UNPACK #-} !Float
6353 <para>will create a constructor <literal>T</literal> containing
6354 two unboxed floats. This may not always be an optimisation: if
6355 the <function>T</function> constructor is scrutinised and the
6356 floats passed to a non-strict function for example, they will
6357 have to be reboxed (this is done automatically by the
6360 <para>Unpacking constructor fields should only be used in
6361 conjunction with <option>-O</option>, in order to expose
6362 unfoldings to the compiler so the reboxing can be removed as
6363 often as possible. For example:</para>
6367 f (T f1 f2) = f1 + f2
6370 <para>The compiler will avoid reboxing <function>f1</function>
6371 and <function>f2</function> by inlining <function>+</function>
6372 on floats, but only when <option>-O</option> is on.</para>
6374 <para>Any single-constructor data is eligible for unpacking; for
6378 data T = T {-# UNPACK #-} !(Int,Int)
6381 <para>will store the two <literal>Int</literal>s directly in the
6382 <function>T</function> constructor, by flattening the pair.
6383 Multi-level unpacking is also supported:
6386 data T = T {-# UNPACK #-} !S
6387 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6390 will store two unboxed <literal>Int#</literal>s
6391 directly in the <function>T</function> constructor. The
6392 unpacker can see through newtypes, too.</para>
6394 <para>If a field cannot be unpacked, you will not get a warning,
6395 so it might be an idea to check the generated code with
6396 <option>-ddump-simpl</option>.</para>
6398 <para>See also the <option>-funbox-strict-fields</option> flag,
6399 which essentially has the effect of adding
6400 <literal>{-# UNPACK #-}</literal> to every strict
6401 constructor field.</para>
6404 <sect2 id="source-pragma">
6405 <title>SOURCE pragma</title>
6407 <indexterm><primary>SOURCE</primary></indexterm>
6408 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6409 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6415 <!-- ======================= REWRITE RULES ======================== -->
6417 <sect1 id="rewrite-rules">
6418 <title>Rewrite rules
6420 <indexterm><primary>RULES pragma</primary></indexterm>
6421 <indexterm><primary>pragma, RULES</primary></indexterm>
6422 <indexterm><primary>rewrite rules</primary></indexterm></title>
6425 The programmer can specify rewrite rules as part of the source program
6426 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6427 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6428 and (b) the <option>-frules-off</option> flag
6429 (<xref linkend="options-f"/>) is not specified, and (c) the
6430 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6439 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6446 <title>Syntax</title>
6449 From a syntactic point of view:
6455 There may be zero or more rules in a <literal>RULES</literal> pragma.
6462 Each rule has a name, enclosed in double quotes. The name itself has
6463 no significance at all. It is only used when reporting how many times the rule fired.
6469 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6470 immediately after the name of the rule. Thus:
6473 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6476 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6477 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6486 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
6487 is set, so you must lay out your rules starting in the same column as the
6488 enclosing definitions.
6495 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6496 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6497 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6498 by spaces, just like in a type <literal>forall</literal>.
6504 A pattern variable may optionally have a type signature.
6505 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6506 For example, here is the <literal>foldr/build</literal> rule:
6509 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6510 foldr k z (build g) = g k z
6513 Since <function>g</function> has a polymorphic type, it must have a type signature.
6520 The left hand side of a rule must consist of a top-level variable applied
6521 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6524 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6525 "wrong2" forall f. f True = True
6528 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6535 A rule does not need to be in the same module as (any of) the
6536 variables it mentions, though of course they need to be in scope.
6542 Rules are automatically exported from a module, just as instance declarations are.
6553 <title>Semantics</title>
6556 From a semantic point of view:
6562 Rules are only applied if you use the <option>-O</option> flag.
6568 Rules are regarded as left-to-right rewrite rules.
6569 When GHC finds an expression that is a substitution instance of the LHS
6570 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6571 By "a substitution instance" we mean that the LHS can be made equal to the
6572 expression by substituting for the pattern variables.
6579 The LHS and RHS of a rule are typechecked, and must have the
6587 GHC makes absolutely no attempt to verify that the LHS and RHS
6588 of a rule have the same meaning. That is undecidable in general, and
6589 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6596 GHC makes no attempt to make sure that the rules are confluent or
6597 terminating. For example:
6600 "loop" forall x,y. f x y = f y x
6603 This rule will cause the compiler to go into an infinite loop.
6610 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6616 GHC currently uses a very simple, syntactic, matching algorithm
6617 for matching a rule LHS with an expression. It seeks a substitution
6618 which makes the LHS and expression syntactically equal modulo alpha
6619 conversion. The pattern (rule), but not the expression, is eta-expanded if
6620 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6621 But not beta conversion (that's called higher-order matching).
6625 Matching is carried out on GHC's intermediate language, which includes
6626 type abstractions and applications. So a rule only matches if the
6627 types match too. See <xref linkend="rule-spec"/> below.
6633 GHC keeps trying to apply the rules as it optimises the program.
6634 For example, consider:
6643 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6644 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6645 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6646 not be substituted, and the rule would not fire.
6653 In the earlier phases of compilation, GHC inlines <emphasis>nothing
6654 that appears on the LHS of a rule</emphasis>, because once you have substituted
6655 for something you can't match against it (given the simple minded
6656 matching). So if you write the rule
6659 "map/map" forall f,g. map f . map g = map (f.g)
6662 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
6663 It will only match something written with explicit use of ".".
6664 Well, not quite. It <emphasis>will</emphasis> match the expression
6670 where <function>wibble</function> is defined:
6673 wibble f g = map f . map g
6676 because <function>wibble</function> will be inlined (it's small).
6678 Later on in compilation, GHC starts inlining even things on the
6679 LHS of rules, but still leaves the rules enabled. This inlining
6680 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
6687 All rules are implicitly exported from the module, and are therefore
6688 in force in any module that imports the module that defined the rule, directly
6689 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6690 in force when compiling A.) The situation is very similar to that for instance
6702 <title>List fusion</title>
6705 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6706 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6707 intermediate list should be eliminated entirely.
6711 The following are good producers:
6723 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6729 Explicit lists (e.g. <literal>[True, False]</literal>)
6735 The cons constructor (e.g <literal>3:4:[]</literal>)
6741 <function>++</function>
6747 <function>map</function>
6753 <function>take</function>, <function>filter</function>
6759 <function>iterate</function>, <function>repeat</function>
6765 <function>zip</function>, <function>zipWith</function>
6774 The following are good consumers:
6786 <function>array</function> (on its second argument)
6792 <function>++</function> (on its first argument)
6798 <function>foldr</function>
6804 <function>map</function>
6810 <function>take</function>, <function>filter</function>
6816 <function>concat</function>
6822 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6828 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6829 will fuse with one but not the other)
6835 <function>partition</function>
6841 <function>head</function>
6847 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6853 <function>sequence_</function>
6859 <function>msum</function>
6865 <function>sortBy</function>
6874 So, for example, the following should generate no intermediate lists:
6877 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6883 This list could readily be extended; if there are Prelude functions that you use
6884 a lot which are not included, please tell us.
6888 If you want to write your own good consumers or producers, look at the
6889 Prelude definitions of the above functions to see how to do so.
6894 <sect2 id="rule-spec">
6895 <title>Specialisation
6899 Rewrite rules can be used to get the same effect as a feature
6900 present in earlier versions of GHC.
6901 For example, suppose that:
6904 genericLookup :: Ord a => Table a b -> a -> b
6905 intLookup :: Table Int b -> Int -> b
6908 where <function>intLookup</function> is an implementation of
6909 <function>genericLookup</function> that works very fast for
6910 keys of type <literal>Int</literal>. You might wish
6911 to tell GHC to use <function>intLookup</function> instead of
6912 <function>genericLookup</function> whenever the latter was called with
6913 type <literal>Table Int b -> Int -> b</literal>.
6914 It used to be possible to write
6917 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6920 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6923 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6926 This slightly odd-looking rule instructs GHC to replace
6927 <function>genericLookup</function> by <function>intLookup</function>
6928 <emphasis>whenever the types match</emphasis>.
6929 What is more, this rule does not need to be in the same
6930 file as <function>genericLookup</function>, unlike the
6931 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6932 have an original definition available to specialise).
6935 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6936 <function>intLookup</function> really behaves as a specialised version
6937 of <function>genericLookup</function>!!!</para>
6939 <para>An example in which using <literal>RULES</literal> for
6940 specialisation will Win Big:
6943 toDouble :: Real a => a -> Double
6944 toDouble = fromRational . toRational
6946 {-# RULES "toDouble/Int" toDouble = i2d #-}
6947 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6950 The <function>i2d</function> function is virtually one machine
6951 instruction; the default conversion—via an intermediate
6952 <literal>Rational</literal>—is obscenely expensive by
6959 <title>Controlling what's going on</title>
6967 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6973 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6974 If you add <option>-dppr-debug</option> you get a more detailed listing.
6980 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
6983 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6984 {-# INLINE build #-}
6988 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6989 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6990 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6991 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6998 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6999 see how to write rules that will do fusion and yet give an efficient
7000 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7010 <sect2 id="core-pragma">
7011 <title>CORE pragma</title>
7013 <indexterm><primary>CORE pragma</primary></indexterm>
7014 <indexterm><primary>pragma, CORE</primary></indexterm>
7015 <indexterm><primary>core, annotation</primary></indexterm>
7018 The external core format supports <quote>Note</quote> annotations;
7019 the <literal>CORE</literal> pragma gives a way to specify what these
7020 should be in your Haskell source code. Syntactically, core
7021 annotations are attached to expressions and take a Haskell string
7022 literal as an argument. The following function definition shows an
7026 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7029 Semantically, this is equivalent to:
7037 However, when external for is generated (via
7038 <option>-fext-core</option>), there will be Notes attached to the
7039 expressions <function>show</function> and <varname>x</varname>.
7040 The core function declaration for <function>f</function> is:
7044 f :: %forall a . GHCziShow.ZCTShow a ->
7045 a -> GHCziBase.ZMZN GHCziBase.Char =
7046 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7048 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7050 (tpl1::GHCziBase.Int ->
7052 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7054 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7055 (tpl3::GHCziBase.ZMZN a ->
7056 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7064 Here, we can see that the function <function>show</function> (which
7065 has been expanded out to a case expression over the Show dictionary)
7066 has a <literal>%note</literal> attached to it, as does the
7067 expression <varname>eta</varname> (which used to be called
7068 <varname>x</varname>).
7075 <sect1 id="special-ids">
7076 <title>Special built-in functions</title>
7077 <para>GHC has a few built-in functions with special behaviour. These
7078 are now described in the module <ulink
7079 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7080 in the library documentation.</para>
7084 <sect1 id="generic-classes">
7085 <title>Generic classes</title>
7088 The ideas behind this extension are described in detail in "Derivable type classes",
7089 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7090 An example will give the idea:
7098 fromBin :: [Int] -> (a, [Int])
7100 toBin {| Unit |} Unit = []
7101 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7102 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7103 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7105 fromBin {| Unit |} bs = (Unit, bs)
7106 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7107 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7108 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7109 (y,bs'') = fromBin bs'
7112 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7113 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7114 which are defined thus in the library module <literal>Generics</literal>:
7118 data a :+: b = Inl a | Inr b
7119 data a :*: b = a :*: b
7122 Now you can make a data type into an instance of Bin like this:
7124 instance (Bin a, Bin b) => Bin (a,b)
7125 instance Bin a => Bin [a]
7127 That is, just leave off the "where" clause. Of course, you can put in the
7128 where clause and over-ride whichever methods you please.
7132 <title> Using generics </title>
7133 <para>To use generics you need to</para>
7136 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7137 <option>-XGenerics</option> (to generate extra per-data-type code),
7138 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7142 <para>Import the module <literal>Generics</literal> from the
7143 <literal>lang</literal> package. This import brings into
7144 scope the data types <literal>Unit</literal>,
7145 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7146 don't need this import if you don't mention these types
7147 explicitly; for example, if you are simply giving instance
7148 declarations.)</para>
7153 <sect2> <title> Changes wrt the paper </title>
7155 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7156 can be written infix (indeed, you can now use
7157 any operator starting in a colon as an infix type constructor). Also note that
7158 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7159 Finally, note that the syntax of the type patterns in the class declaration
7160 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7161 alone would ambiguous when they appear on right hand sides (an extension we
7162 anticipate wanting).
7166 <sect2> <title>Terminology and restrictions</title>
7168 Terminology. A "generic default method" in a class declaration
7169 is one that is defined using type patterns as above.
7170 A "polymorphic default method" is a default method defined as in Haskell 98.
7171 A "generic class declaration" is a class declaration with at least one
7172 generic default method.
7180 Alas, we do not yet implement the stuff about constructor names and
7187 A generic class can have only one parameter; you can't have a generic
7188 multi-parameter class.
7194 A default method must be defined entirely using type patterns, or entirely
7195 without. So this is illegal:
7198 op :: a -> (a, Bool)
7199 op {| Unit |} Unit = (Unit, True)
7202 However it is perfectly OK for some methods of a generic class to have
7203 generic default methods and others to have polymorphic default methods.
7209 The type variable(s) in the type pattern for a generic method declaration
7210 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:
7214 op {| p :*: q |} (x :*: y) = op (x :: p)
7222 The type patterns in a generic default method must take one of the forms:
7228 where "a" and "b" are type variables. Furthermore, all the type patterns for
7229 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7230 must use the same type variables. So this is illegal:
7234 op {| a :+: b |} (Inl x) = True
7235 op {| p :+: q |} (Inr y) = False
7237 The type patterns must be identical, even in equations for different methods of the class.
7238 So this too is illegal:
7242 op1 {| a :*: b |} (x :*: y) = True
7245 op2 {| p :*: q |} (x :*: y) = False
7247 (The reason for this restriction is that we gather all the equations for a particular type constructor
7248 into a single generic instance declaration.)
7254 A generic method declaration must give a case for each of the three type constructors.
7260 The type for a generic method can be built only from:
7262 <listitem> <para> Function arrows </para> </listitem>
7263 <listitem> <para> Type variables </para> </listitem>
7264 <listitem> <para> Tuples </para> </listitem>
7265 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7267 Here are some example type signatures for generic methods:
7270 op2 :: Bool -> (a,Bool)
7271 op3 :: [Int] -> a -> a
7274 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7278 This restriction is an implementation restriction: we just haven't got around to
7279 implementing the necessary bidirectional maps over arbitrary type constructors.
7280 It would be relatively easy to add specific type constructors, such as Maybe and list,
7281 to the ones that are allowed.</para>
7286 In an instance declaration for a generic class, the idea is that the compiler
7287 will fill in the methods for you, based on the generic templates. However it can only
7292 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7297 No constructor of the instance type has unboxed fields.
7301 (Of course, these things can only arise if you are already using GHC extensions.)
7302 However, you can still give an instance declarations for types which break these rules,
7303 provided you give explicit code to override any generic default methods.
7311 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7312 what the compiler does with generic declarations.
7317 <sect2> <title> Another example </title>
7319 Just to finish with, here's another example I rather like:
7323 nCons {| Unit |} _ = 1
7324 nCons {| a :*: b |} _ = 1
7325 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7328 tag {| Unit |} _ = 1
7329 tag {| a :*: b |} _ = 1
7330 tag {| a :+: b |} (Inl x) = tag x
7331 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7337 <sect1 id="monomorphism">
7338 <title>Control over monomorphism</title>
7340 <para>GHC supports two flags that control the way in which generalisation is
7341 carried out at let and where bindings.
7345 <title>Switching off the dreaded Monomorphism Restriction</title>
7346 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7348 <para>Haskell's monomorphism restriction (see
7349 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7351 of the Haskell Report)
7352 can be completely switched off by
7353 <option>-XNoMonomorphismRestriction</option>.
7358 <title>Monomorphic pattern bindings</title>
7359 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7360 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7362 <para> As an experimental change, we are exploring the possibility of
7363 making pattern bindings monomorphic; that is, not generalised at all.
7364 A pattern binding is a binding whose LHS has no function arguments,
7365 and is not a simple variable. For example:
7367 f x = x -- Not a pattern binding
7368 f = \x -> x -- Not a pattern binding
7369 f :: Int -> Int = \x -> x -- Not a pattern binding
7371 (g,h) = e -- A pattern binding
7372 (f) = e -- A pattern binding
7373 [x] = e -- A pattern binding
7375 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7376 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7385 ;;; Local Variables: ***
7387 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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