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://haskell.cs.yale.edu/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 <!-- ===================== REBINDABLE SYNTAX =================== -->
1064 <sect2 id="rebindable-syntax">
1065 <title>Rebindable syntax</title>
1067 <para>GHC allows most kinds of built-in syntax to be rebound by
1068 the user, to facilitate replacing the <literal>Prelude</literal>
1069 with a home-grown version, for example.</para>
1071 <para>You may want to define your own numeric class
1072 hierarchy. It completely defeats that purpose if the
1073 literal "1" means "<literal>Prelude.fromInteger
1074 1</literal>", which is what the Haskell Report specifies.
1075 So the <option>-XNoImplicitPrelude</option> flag causes
1076 the following pieces of built-in syntax to refer to
1077 <emphasis>whatever is in scope</emphasis>, not the Prelude
1082 <para>An integer literal <literal>368</literal> means
1083 "<literal>fromInteger (368::Integer)</literal>", rather than
1084 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1087 <listitem><para>Fractional literals are handed in just the same way,
1088 except that the translation is
1089 <literal>fromRational (3.68::Rational)</literal>.
1092 <listitem><para>The equality test in an overloaded numeric pattern
1093 uses whatever <literal>(==)</literal> is in scope.
1096 <listitem><para>The subtraction operation, and the
1097 greater-than-or-equal test, in <literal>n+k</literal> patterns
1098 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1102 <para>Negation (e.g. "<literal>- (f x)</literal>")
1103 means "<literal>negate (f x)</literal>", both in numeric
1104 patterns, and expressions.
1108 <para>"Do" notation is translated using whatever
1109 functions <literal>(>>=)</literal>,
1110 <literal>(>>)</literal>, and <literal>fail</literal>,
1111 are in scope (not the Prelude
1112 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1113 comprehensions, are unaffected. </para></listitem>
1117 notation (see <xref linkend="arrow-notation"/>)
1118 uses whatever <literal>arr</literal>,
1119 <literal>(>>>)</literal>, <literal>first</literal>,
1120 <literal>app</literal>, <literal>(|||)</literal> and
1121 <literal>loop</literal> functions are in scope. But unlike the
1122 other constructs, the types of these functions must match the
1123 Prelude types very closely. Details are in flux; if you want
1127 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1128 even if that is a little unexpected. For emample, the
1129 static semantics of the literal <literal>368</literal>
1130 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1131 <literal>fromInteger</literal> to have any of the types:
1133 fromInteger :: Integer -> Integer
1134 fromInteger :: forall a. Foo a => Integer -> a
1135 fromInteger :: Num a => a -> Integer
1136 fromInteger :: Integer -> Bool -> Bool
1140 <para>Be warned: this is an experimental facility, with
1141 fewer checks than usual. Use <literal>-dcore-lint</literal>
1142 to typecheck the desugared program. If Core Lint is happy
1143 you should be all right.</para>
1147 <sect2 id="postfix-operators">
1148 <title>Postfix operators</title>
1151 GHC allows a small extension to the syntax of left operator sections, which
1152 allows you to define postfix operators. The extension is this: the left section
1156 is equivalent (from the point of view of both type checking and execution) to the expression
1160 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1161 The strict Haskell 98 interpretation is that the section is equivalent to
1165 That is, the operator must be a function of two arguments. GHC allows it to
1166 take only one argument, and that in turn allows you to write the function
1169 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1170 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1171 change their behaviour, of course.)
1173 <para>The extension does not extend to the left-hand side of function
1174 definitions; you must define such a function in prefix form.</para>
1178 <sect2 id="disambiguate-fields">
1179 <title>Record field disambiguation</title>
1181 In record construction and record pattern matching
1182 it is entirely unambiguous which field is referred to, even if there are two different
1183 data types in scope with a common field name. For example:
1186 data S = MkS { x :: Int, y :: Bool }
1191 data T = MkT { x :: Int }
1193 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1195 ok2 n = MkT { x = n+1 } -- Unambiguous
1197 bad1 k = k { x = 3 } -- Ambiguous
1198 bad2 k = x k -- Ambiguous
1200 Even though there are two <literal>x</literal>'s in scope,
1201 it is clear that the <literal>x</literal> in the pattern in the
1202 definition of <literal>ok1</literal> can only mean the field
1203 <literal>x</literal> from type <literal>S</literal>. Similarly for
1204 the function <literal>ok2</literal>. However, in the record update
1205 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1206 it is not clear which of the two types is intended.
1209 Haskell 98 regards all four as ambiguous, but with the
1210 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1211 the former two. The rules are precisely the same as those for instance
1212 declarations in Haskell 98, where the method names on the left-hand side
1213 of the method bindings in an instance declaration refer unambiguously
1214 to the method of that class (provided they are in scope at all), even
1215 if there are other variables in scope with the same name.
1216 This reduces the clutter of qualified names when you import two
1217 records from different modules that use the same field name.
1221 <!-- ===================== Record puns =================== -->
1223 <sect2 id="record-puns">
1228 Record puns are enabled by the flag <literal>-XRecordPuns</literal>.
1232 When using records, it is common to write a pattern that binds a
1233 variable with the same name as a record field, such as:
1236 data C = C {a :: Int}
1242 Record punning permits the variable name to be elided, so one can simply
1249 to mean the same pattern as above. That is, in a record pattern, the
1250 pattern <literal>a</literal> expands into the pattern <literal>a =
1251 a</literal> for the same name <literal>a</literal>.
1255 Note that puns and other patterns can be mixed in the same record:
1257 data C = C {a :: Int, b :: Int}
1258 f (C {a, b = 4}) = a
1260 and that puns can be used wherever record patterns occur (e.g. in
1261 <literal>let</literal> bindings or at the top-level).
1265 Record punning can also be used in an expression, writing, for example,
1271 let a = 1 in C {a = a}
1274 Note that this expansion is purely syntactic, so the record pun
1275 expression refers to the nearest enclosing variable that is spelled the
1276 same as the field name.
1281 <!-- ===================== Record wildcards =================== -->
1283 <sect2 id="record-wildcards">
1284 <title>Record wildcards
1288 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1292 For records with many fields, it can be tiresome to write out each field
1293 individually in a record pattern, as in
1295 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1296 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1301 Record wildcard syntax permits a (<literal>..</literal>) in a record
1302 pattern, where each elided field <literal>f</literal> is replaced by the
1303 pattern <literal>f = f</literal>. For example, the above pattern can be
1306 f (C {a = 1, ..}) = b + c + d
1311 Note that wildcards can be mixed with other patterns, including puns
1312 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1313 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1314 wherever record patterns occur, including in <literal>let</literal>
1315 bindings and at the top-level. For example, the top-level binding
1319 defines <literal>b</literal>, <literal>c</literal>, and
1320 <literal>d</literal>.
1324 Record wildcards can also be used in expressions, writing, for example,
1327 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1333 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1336 Note that this expansion is purely syntactic, so the record wildcard
1337 expression refers to the nearest enclosing variables that are spelled
1338 the same as the omitted field names.
1343 <!-- ===================== Local fixity declarations =================== -->
1345 <sect2 id="local-fixity-declarations">
1346 <title>Local Fixity Declarations
1349 <para>A careful reading of the Haskell 98 Report reveals that fixity
1350 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1351 <literal>infixr</literal>) are permitted to appear inside local bindings
1352 such those introduced by <literal>let</literal> and
1353 <literal>where</literal>. However, the Haskell Report does not specify
1354 the semantics of such bindings very precisely.
1357 <para>In GHC, a fixity declaration may accompany a local binding:
1364 and the fixity declaration applies wherever the binding is in scope.
1365 For example, in a <literal>let</literal>, it applies in the right-hand
1366 sides of other <literal>let</literal>-bindings and the body of the
1367 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1368 expressions (<xref linkend="mdo-notation"/>), the local fixity
1369 declarations of aA <literal>let</literal> statement scope over other
1370 statements in the group, just as the bound name does.
1373 Moreover, a local fixity declatation *must* accompany a local binding of
1374 that name: it is not possible to revise the fixity of name bound
1377 let infixr 9 $ in ...
1380 Because local fixity declarations are technically Haskell 98, no flag is
1381 necessary to enable them.
1387 <!-- TYPE SYSTEM EXTENSIONS -->
1388 <sect1 id="data-type-extensions">
1389 <title>Extensions to data types and type synonyms</title>
1391 <sect2 id="nullary-types">
1392 <title>Data types with no constructors</title>
1394 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1395 a data type with no constructors. For example:</para>
1399 data T a -- T :: * -> *
1402 <para>Syntactically, the declaration lacks the "= constrs" part. The
1403 type can be parameterised over types of any kind, but if the kind is
1404 not <literal>*</literal> then an explicit kind annotation must be used
1405 (see <xref linkend="kinding"/>).</para>
1407 <para>Such data types have only one value, namely bottom.
1408 Nevertheless, they can be useful when defining "phantom types".</para>
1411 <sect2 id="infix-tycons">
1412 <title>Infix type constructors, classes, and type variables</title>
1415 GHC allows type constructors, classes, and type variables to be operators, and
1416 to be written infix, very much like expressions. More specifically:
1419 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1420 The lexical syntax is the same as that for data constructors.
1423 Data type and type-synonym declarations can be written infix, parenthesised
1424 if you want further arguments. E.g.
1426 data a :*: b = Foo a b
1427 type a :+: b = Either a b
1428 class a :=: b where ...
1430 data (a :**: b) x = Baz a b x
1431 type (a :++: b) y = Either (a,b) y
1435 Types, and class constraints, can be written infix. For example
1438 f :: (a :=: b) => a -> b
1442 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1443 The lexical syntax is the same as that for variable operators, excluding "(.)",
1444 "(!)", and "(*)". In a binding position, the operator must be
1445 parenthesised. For example:
1447 type T (+) = Int + Int
1451 liftA2 :: Arrow (~>)
1452 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1458 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1459 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1462 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1463 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1464 sets the fixity for a data constructor and the corresponding type constructor. For example:
1468 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1469 and similarly for <literal>:*:</literal>.
1470 <literal>Int `a` Bool</literal>.
1473 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1480 <sect2 id="type-synonyms">
1481 <title>Liberalised type synonyms</title>
1484 Type synonyms are like macros at the type level, and
1485 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1486 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1488 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1489 in a type synonym, thus:
1491 type Discard a = forall b. Show b => a -> b -> (a, String)
1496 g :: Discard Int -> (Int,String) -- A rank-2 type
1503 You can write an unboxed tuple in a type synonym:
1505 type Pr = (# Int, Int #)
1513 You can apply a type synonym to a forall type:
1515 type Foo a = a -> a -> Bool
1517 f :: Foo (forall b. b->b)
1519 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1521 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1526 You can apply a type synonym to a partially applied type synonym:
1528 type Generic i o = forall x. i x -> o x
1531 foo :: Generic Id []
1533 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1535 foo :: forall x. x -> [x]
1543 GHC currently does kind checking before expanding synonyms (though even that
1547 After expanding type synonyms, GHC does validity checking on types, looking for
1548 the following mal-formedness which isn't detected simply by kind checking:
1551 Type constructor applied to a type involving for-alls.
1554 Unboxed tuple on left of an arrow.
1557 Partially-applied type synonym.
1561 this will be rejected:
1563 type Pr = (# Int, Int #)
1568 because GHC does not allow unboxed tuples on the left of a function arrow.
1573 <sect2 id="existential-quantification">
1574 <title>Existentially quantified data constructors
1578 The idea of using existential quantification in data type declarations
1579 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1580 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1581 London, 1991). It was later formalised by Laufer and Odersky
1582 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1583 TOPLAS, 16(5), pp1411-1430, 1994).
1584 It's been in Lennart
1585 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1586 proved very useful. Here's the idea. Consider the declaration:
1592 data Foo = forall a. MkFoo a (a -> Bool)
1599 The data type <literal>Foo</literal> has two constructors with types:
1605 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1612 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1613 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1614 For example, the following expression is fine:
1620 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1626 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1627 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1628 isUpper</function> packages a character with a compatible function. These
1629 two things are each of type <literal>Foo</literal> and can be put in a list.
1633 What can we do with a value of type <literal>Foo</literal>?. In particular,
1634 what happens when we pattern-match on <function>MkFoo</function>?
1640 f (MkFoo val fn) = ???
1646 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1647 are compatible, the only (useful) thing we can do with them is to
1648 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1655 f (MkFoo val fn) = fn val
1661 What this allows us to do is to package heterogenous values
1662 together with a bunch of functions that manipulate them, and then treat
1663 that collection of packages in a uniform manner. You can express
1664 quite a bit of object-oriented-like programming this way.
1667 <sect3 id="existential">
1668 <title>Why existential?
1672 What has this to do with <emphasis>existential</emphasis> quantification?
1673 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1679 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1685 But Haskell programmers can safely think of the ordinary
1686 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1687 adding a new existential quantification construct.
1692 <sect3 id="existential-with-context">
1693 <title>Existentials and type classes</title>
1696 An easy extension is to allow
1697 arbitrary contexts before the constructor. For example:
1703 data Baz = forall a. Eq a => Baz1 a a
1704 | forall b. Show b => Baz2 b (b -> b)
1710 The two constructors have the types you'd expect:
1716 Baz1 :: forall a. Eq a => a -> a -> Baz
1717 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1723 But when pattern matching on <function>Baz1</function> the matched values can be compared
1724 for equality, and when pattern matching on <function>Baz2</function> the first matched
1725 value can be converted to a string (as well as applying the function to it).
1726 So this program is legal:
1733 f (Baz1 p q) | p == q = "Yes"
1735 f (Baz2 v fn) = show (fn v)
1741 Operationally, in a dictionary-passing implementation, the
1742 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1743 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1744 extract it on pattern matching.
1749 <sect3 id="existential-records">
1750 <title>Record Constructors</title>
1753 GHC allows existentials to be used with records syntax as well. For example:
1756 data Counter a = forall self. NewCounter
1758 , _inc :: self -> self
1759 , _display :: self -> IO ()
1763 Here <literal>tag</literal> is a public field, with a well-typed selector
1764 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1765 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1766 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1767 compile-time error. In other words, <emphasis>GHC defines a record selector function
1768 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1769 (This example used an underscore in the fields for which record selectors
1770 will not be defined, but that is only programming style; GHC ignores them.)
1774 To make use of these hidden fields, we need to create some helper functions:
1777 inc :: Counter a -> Counter a
1778 inc (NewCounter x i d t) = NewCounter
1779 { _this = i x, _inc = i, _display = d, tag = t }
1781 display :: Counter a -> IO ()
1782 display NewCounter{ _this = x, _display = d } = d x
1785 Now we can define counters with different underlying implementations:
1788 counterA :: Counter String
1789 counterA = NewCounter
1790 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1792 counterB :: Counter String
1793 counterB = NewCounter
1794 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1797 display (inc counterA) -- prints "1"
1798 display (inc (inc counterB)) -- prints "##"
1801 At the moment, record update syntax is only supported for Haskell 98 data types,
1802 so the following function does <emphasis>not</emphasis> work:
1805 -- This is invalid; use explicit NewCounter instead for now
1806 setTag :: Counter a -> a -> Counter a
1807 setTag obj t = obj{ tag = t }
1816 <title>Restrictions</title>
1819 There are several restrictions on the ways in which existentially-quantified
1820 constructors can be use.
1829 When pattern matching, each pattern match introduces a new,
1830 distinct, type for each existential type variable. These types cannot
1831 be unified with any other type, nor can they escape from the scope of
1832 the pattern match. For example, these fragments are incorrect:
1840 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1841 is the result of <function>f1</function>. One way to see why this is wrong is to
1842 ask what type <function>f1</function> has:
1846 f1 :: Foo -> a -- Weird!
1850 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1855 f1 :: forall a. Foo -> a -- Wrong!
1859 The original program is just plain wrong. Here's another sort of error
1863 f2 (Baz1 a b) (Baz1 p q) = a==q
1867 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1868 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1869 from the two <function>Baz1</function> constructors.
1877 You can't pattern-match on an existentially quantified
1878 constructor in a <literal>let</literal> or <literal>where</literal> group of
1879 bindings. So this is illegal:
1883 f3 x = a==b where { Baz1 a b = x }
1886 Instead, use a <literal>case</literal> expression:
1889 f3 x = case x of Baz1 a b -> a==b
1892 In general, you can only pattern-match
1893 on an existentially-quantified constructor in a <literal>case</literal> expression or
1894 in the patterns of a function definition.
1896 The reason for this restriction is really an implementation one.
1897 Type-checking binding groups is already a nightmare without
1898 existentials complicating the picture. Also an existential pattern
1899 binding at the top level of a module doesn't make sense, because it's
1900 not clear how to prevent the existentially-quantified type "escaping".
1901 So for now, there's a simple-to-state restriction. We'll see how
1909 You can't use existential quantification for <literal>newtype</literal>
1910 declarations. So this is illegal:
1914 newtype T = forall a. Ord a => MkT a
1918 Reason: a value of type <literal>T</literal> must be represented as a
1919 pair of a dictionary for <literal>Ord t</literal> and a value of type
1920 <literal>t</literal>. That contradicts the idea that
1921 <literal>newtype</literal> should have no concrete representation.
1922 You can get just the same efficiency and effect by using
1923 <literal>data</literal> instead of <literal>newtype</literal>. If
1924 there is no overloading involved, then there is more of a case for
1925 allowing an existentially-quantified <literal>newtype</literal>,
1926 because the <literal>data</literal> version does carry an
1927 implementation cost, but single-field existentially quantified
1928 constructors aren't much use. So the simple restriction (no
1929 existential stuff on <literal>newtype</literal>) stands, unless there
1930 are convincing reasons to change it.
1938 You can't use <literal>deriving</literal> to define instances of a
1939 data type with existentially quantified data constructors.
1941 Reason: in most cases it would not make sense. For example:;
1944 data T = forall a. MkT [a] deriving( Eq )
1947 To derive <literal>Eq</literal> in the standard way we would need to have equality
1948 between the single component of two <function>MkT</function> constructors:
1952 (MkT a) == (MkT b) = ???
1955 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1956 It's just about possible to imagine examples in which the derived instance
1957 would make sense, but it seems altogether simpler simply to prohibit such
1958 declarations. Define your own instances!
1969 <!-- ====================== Generalised algebraic data types ======================= -->
1971 <sect2 id="gadt-style">
1972 <title>Declaring data types with explicit constructor signatures</title>
1974 <para>GHC allows you to declare an algebraic data type by
1975 giving the type signatures of constructors explicitly. For example:
1979 Just :: a -> Maybe a
1981 The form is called a "GADT-style declaration"
1982 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1983 can only be declared using this form.</para>
1984 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1985 For example, these two declarations are equivalent:
1987 data Foo = forall a. MkFoo a (a -> Bool)
1988 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1991 <para>Any data type that can be declared in standard Haskell-98 syntax
1992 can also be declared using GADT-style syntax.
1993 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1994 they treat class constraints on the data constructors differently.
1995 Specifically, if the constructor is given a type-class context, that
1996 context is made available by pattern matching. For example:
1999 MkSet :: Eq a => [a] -> Set a
2001 makeSet :: Eq a => [a] -> Set a
2002 makeSet xs = MkSet (nub xs)
2004 insert :: a -> Set a -> Set a
2005 insert a (MkSet as) | a `elem` as = MkSet as
2006 | otherwise = MkSet (a:as)
2008 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2009 gives rise to a <literal>(Eq a)</literal>
2010 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2011 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2012 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2013 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2014 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2015 In the example, the equality dictionary is used to satisfy the equality constraint
2016 generated by the call to <literal>elem</literal>, so that the type of
2017 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2020 For example, one possible application is to reify dictionaries:
2022 data NumInst a where
2023 MkNumInst :: Num a => NumInst a
2025 intInst :: NumInst Int
2028 plus :: NumInst a -> a -> a -> a
2029 plus MkNumInst p q = p + q
2031 Here, a value of type <literal>NumInst a</literal> is equivalent
2032 to an explicit <literal>(Num a)</literal> dictionary.
2035 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2036 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2040 = Num a => MkNumInst (NumInst a)
2042 Notice that, unlike the situation when declaring an existental, there is
2043 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2044 data type's univerally quantified type variable <literal>a</literal>.
2045 A constructor may have both universal and existential type variables: for example,
2046 the following two declarations are equivalent:
2049 = forall b. (Num a, Eq b) => MkT1 a b
2051 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2054 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2055 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2056 In Haskell 98 the definition
2058 data Eq a => Set' a = MkSet' [a]
2060 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2061 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2062 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2063 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2064 GHC's behaviour is much more useful, as well as much more intuitive.
2068 The rest of this section gives further details about GADT-style data
2073 The result type of each data constructor must begin with the type constructor being defined.
2074 If the result type of all constructors
2075 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2076 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2077 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2081 The type signature of
2082 each constructor is independent, and is implicitly universally quantified as usual.
2083 Different constructors may have different universally-quantified type variables
2084 and different type-class constraints.
2085 For example, this is fine:
2088 T1 :: Eq b => b -> T b
2089 T2 :: (Show c, Ix c) => c -> [c] -> T c
2094 Unlike a Haskell-98-style
2095 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2096 have no scope. Indeed, one can write a kind signature instead:
2098 data Set :: * -> * where ...
2100 or even a mixture of the two:
2102 data Foo a :: (* -> *) -> * where ...
2104 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2107 data Foo a (b :: * -> *) where ...
2113 You can use strictness annotations, in the obvious places
2114 in the constructor type:
2117 Lit :: !Int -> Term Int
2118 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2119 Pair :: Term a -> Term b -> Term (a,b)
2124 You can use a <literal>deriving</literal> clause on a GADT-style data type
2125 declaration. For example, these two declarations are equivalent
2127 data Maybe1 a where {
2128 Nothing1 :: Maybe1 a ;
2129 Just1 :: a -> Maybe1 a
2130 } deriving( Eq, Ord )
2132 data Maybe2 a = Nothing2 | Just2 a
2138 You can use record syntax on a GADT-style data type declaration:
2142 Adult { name :: String, children :: [Person] } :: Person
2143 Child { name :: String } :: Person
2145 As usual, for every constructor that has a field <literal>f</literal>, the type of
2146 field <literal>f</literal> must be the same (modulo alpha conversion).
2149 At the moment, record updates are not yet possible with GADT-style declarations,
2150 so support is limited to record construction, selection and pattern matching.
2153 aPerson = Adult { name = "Fred", children = [] }
2155 shortName :: Person -> Bool
2156 hasChildren (Adult { children = kids }) = not (null kids)
2157 hasChildren (Child {}) = False
2162 As in the case of existentials declared using the Haskell-98-like record syntax
2163 (<xref linkend="existential-records"/>),
2164 record-selector functions are generated only for those fields that have well-typed
2166 Here is the example of that section, in GADT-style syntax:
2168 data Counter a where
2169 NewCounter { _this :: self
2170 , _inc :: self -> self
2171 , _display :: self -> IO ()
2176 As before, only one selector function is generated here, that for <literal>tag</literal>.
2177 Nevertheless, you can still use all the field names in pattern matching and record construction.
2179 </itemizedlist></para>
2183 <title>Generalised Algebraic Data Types (GADTs)</title>
2185 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2186 by allowing constructors to have richer return types. Here is an example:
2189 Lit :: Int -> Term Int
2190 Succ :: Term Int -> Term Int
2191 IsZero :: Term Int -> Term Bool
2192 If :: Term Bool -> Term a -> Term a -> Term a
2193 Pair :: Term a -> Term b -> Term (a,b)
2195 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2196 case with ordinary data types. This generality allows us to
2197 write a well-typed <literal>eval</literal> function
2198 for these <literal>Terms</literal>:
2202 eval (Succ t) = 1 + eval t
2203 eval (IsZero t) = eval t == 0
2204 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2205 eval (Pair e1 e2) = (eval e1, eval e2)
2207 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2208 For example, in the right hand side of the equation
2213 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2214 A precise specification of the type rules is beyond what this user manual aspires to,
2215 but the design closely follows that described in
2217 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
2218 unification-based type inference for GADTs</ulink>,
2220 The general principle is this: <emphasis>type refinement is only carried out
2221 based on user-supplied type annotations</emphasis>.
2222 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2223 and lots of obscure error messages will
2224 occur. However, the refinement is quite general. For example, if we had:
2226 eval :: Term a -> a -> a
2227 eval (Lit i) j = i+j
2229 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2230 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2231 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2234 These and many other examples are given in papers by Hongwei Xi, and
2235 Tim Sheard. There is a longer introduction
2236 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2238 <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
2239 may use different notation to that implemented in GHC.
2242 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2243 <option>-XGADTs</option>.
2246 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2247 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2248 The result type of each constructor must begin with the type constructor being defined,
2249 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2250 For example, in the <literal>Term</literal> data
2251 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2252 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
2257 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2258 an ordinary data type.
2262 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2266 Lit { val :: Int } :: Term Int
2267 Succ { num :: Term Int } :: Term Int
2268 Pred { num :: Term Int } :: Term Int
2269 IsZero { arg :: Term Int } :: Term Bool
2270 Pair { arg1 :: Term a
2273 If { cnd :: Term Bool
2278 However, for GADTs there is the following additional constraint:
2279 every constructor that has a field <literal>f</literal> must have
2280 the same result type (modulo alpha conversion)
2281 Hence, in the above example, we cannot merge the <literal>num</literal>
2282 and <literal>arg</literal> fields above into a
2283 single name. Although their field types are both <literal>Term Int</literal>,
2284 their selector functions actually have different types:
2287 num :: Term Int -> Term Int
2288 arg :: Term Bool -> Term Int
2298 <!-- ====================== End of Generalised algebraic data types ======================= -->
2300 <sect1 id="deriving">
2301 <title>Extensions to the "deriving" mechanism</title>
2303 <sect2 id="deriving-inferred">
2304 <title>Inferred context for deriving clauses</title>
2307 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2310 data T0 f a = MkT0 a deriving( Eq )
2311 data T1 f a = MkT1 (f a) deriving( Eq )
2312 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2314 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2316 instance Eq a => Eq (T0 f a) where ...
2317 instance Eq (f a) => Eq (T1 f a) where ...
2318 instance Eq (f (f a)) => Eq (T2 f a) where ...
2320 The first of these is obviously fine. The second is still fine, although less obviously.
2321 The third is not Haskell 98, and risks losing termination of instances.
2324 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2325 each constraint in the inferred instance context must consist only of type variables,
2326 with no repetitions.
2329 This rule is applied regardless of flags. If you want a more exotic context, you can write
2330 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2334 <sect2 id="stand-alone-deriving">
2335 <title>Stand-alone deriving declarations</title>
2338 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2340 data Foo a = Bar a | Baz String
2342 deriving instance Eq a => Eq (Foo a)
2344 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2345 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2346 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2347 exactly as you would in an ordinary instance declaration.
2348 (In contrast the context is inferred in a <literal>deriving</literal> clause
2349 attached to a data type declaration.) These <literal>deriving instance</literal>
2350 rules obey the same rules concerning form and termination as ordinary instance declarations,
2351 controlled by the same flags; see <xref linkend="instance-decls"/>. </para>
2353 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2354 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2357 newtype Foo a = MkFoo (State Int a)
2359 deriving instance MonadState Int Foo
2361 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2362 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2368 <sect2 id="deriving-typeable">
2369 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2372 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2373 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2374 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2375 classes <literal>Eq</literal>, <literal>Ord</literal>,
2376 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2379 GHC extends this list with two more classes that may be automatically derived
2380 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2381 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2382 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2383 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2385 <para>An instance of <literal>Typeable</literal> can only be derived if the
2386 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2387 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2389 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2390 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2392 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2393 are used, and only <literal>Typeable1</literal> up to
2394 <literal>Typeable7</literal> are provided in the library.)
2395 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2396 class, whose kind suits that of the data type constructor, and
2397 then writing the data type instance by hand.
2401 <sect2 id="newtype-deriving">
2402 <title>Generalised derived instances for newtypes</title>
2405 When you define an abstract type using <literal>newtype</literal>, you may want
2406 the new type to inherit some instances from its representation. In
2407 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2408 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2409 other classes you have to write an explicit instance declaration. For
2410 example, if you define
2413 newtype Dollars = Dollars Int
2416 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2417 explicitly define an instance of <literal>Num</literal>:
2420 instance Num Dollars where
2421 Dollars a + Dollars b = Dollars (a+b)
2424 All the instance does is apply and remove the <literal>newtype</literal>
2425 constructor. It is particularly galling that, since the constructor
2426 doesn't appear at run-time, this instance declaration defines a
2427 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2428 dictionary, only slower!
2432 <sect3> <title> Generalising the deriving clause </title>
2434 GHC now permits such instances to be derived instead,
2435 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2438 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2441 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2442 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2443 derives an instance declaration of the form
2446 instance Num Int => Num Dollars
2449 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2453 We can also derive instances of constructor classes in a similar
2454 way. For example, suppose we have implemented state and failure monad
2455 transformers, such that
2458 instance Monad m => Monad (State s m)
2459 instance Monad m => Monad (Failure m)
2461 In Haskell 98, we can define a parsing monad by
2463 type Parser tok m a = State [tok] (Failure m) a
2466 which is automatically a monad thanks to the instance declarations
2467 above. With the extension, we can make the parser type abstract,
2468 without needing to write an instance of class <literal>Monad</literal>, via
2471 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2474 In this case the derived instance declaration is of the form
2476 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2479 Notice that, since <literal>Monad</literal> is a constructor class, the
2480 instance is a <emphasis>partial application</emphasis> of the new type, not the
2481 entire left hand side. We can imagine that the type declaration is
2482 "eta-converted" to generate the context of the instance
2487 We can even derive instances of multi-parameter classes, provided the
2488 newtype is the last class parameter. In this case, a ``partial
2489 application'' of the class appears in the <literal>deriving</literal>
2490 clause. For example, given the class
2493 class StateMonad s m | m -> s where ...
2494 instance Monad m => StateMonad s (State s m) where ...
2496 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2498 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2499 deriving (Monad, StateMonad [tok])
2502 The derived instance is obtained by completing the application of the
2503 class to the new type:
2506 instance StateMonad [tok] (State [tok] (Failure m)) =>
2507 StateMonad [tok] (Parser tok m)
2512 As a result of this extension, all derived instances in newtype
2513 declarations are treated uniformly (and implemented just by reusing
2514 the dictionary for the representation type), <emphasis>except</emphasis>
2515 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2516 the newtype and its representation.
2520 <sect3> <title> A more precise specification </title>
2522 Derived instance declarations are constructed as follows. Consider the
2523 declaration (after expansion of any type synonyms)
2526 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2532 The <literal>ci</literal> are partial applications of
2533 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2534 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2537 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2540 The type <literal>t</literal> is an arbitrary type.
2543 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2544 nor in the <literal>ci</literal>, and
2547 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2548 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2549 should not "look through" the type or its constructor. You can still
2550 derive these classes for a newtype, but it happens in the usual way, not
2551 via this new mechanism.
2554 Then, for each <literal>ci</literal>, the derived instance
2557 instance ci t => ci (T v1...vk)
2559 As an example which does <emphasis>not</emphasis> work, consider
2561 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2563 Here we cannot derive the instance
2565 instance Monad (State s m) => Monad (NonMonad m)
2568 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2569 and so cannot be "eta-converted" away. It is a good thing that this
2570 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2571 not, in fact, a monad --- for the same reason. Try defining
2572 <literal>>>=</literal> with the correct type: you won't be able to.
2576 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2577 important, since we can only derive instances for the last one. If the
2578 <literal>StateMonad</literal> class above were instead defined as
2581 class StateMonad m s | m -> s where ...
2584 then we would not have been able to derive an instance for the
2585 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2586 classes usually have one "main" parameter for which deriving new
2587 instances is most interesting.
2589 <para>Lastly, all of this applies only for classes other than
2590 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2591 and <literal>Data</literal>, for which the built-in derivation applies (section
2592 4.3.3. of the Haskell Report).
2593 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2594 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2595 the standard method is used or the one described here.)
2602 <!-- TYPE SYSTEM EXTENSIONS -->
2603 <sect1 id="type-class-extensions">
2604 <title>Class and instances declarations</title>
2606 <sect2 id="multi-param-type-classes">
2607 <title>Class declarations</title>
2610 This section, and the next one, documents GHC's type-class extensions.
2611 There's lots of background in the paper <ulink
2612 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2613 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2614 Jones, Erik Meijer).
2617 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2621 <title>Multi-parameter type classes</title>
2623 Multi-parameter type classes are permitted. For example:
2627 class Collection c a where
2628 union :: c a -> c a -> c a
2636 <title>The superclasses of a class declaration</title>
2639 There are no restrictions on the context in a class declaration
2640 (which introduces superclasses), except that the class hierarchy must
2641 be acyclic. So these class declarations are OK:
2645 class Functor (m k) => FiniteMap m k where
2648 class (Monad m, Monad (t m)) => Transform t m where
2649 lift :: m a -> (t m) a
2655 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2656 of "acyclic" involves only the superclass relationships. For example,
2662 op :: D b => a -> b -> b
2665 class C a => D a where { ... }
2669 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2670 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2671 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2678 <sect3 id="class-method-types">
2679 <title>Class method types</title>
2682 Haskell 98 prohibits class method types to mention constraints on the
2683 class type variable, thus:
2686 fromList :: [a] -> s a
2687 elem :: Eq a => a -> s a -> Bool
2689 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2690 contains the constraint <literal>Eq a</literal>, constrains only the
2691 class type variable (in this case <literal>a</literal>).
2692 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2699 <sect2 id="functional-dependencies">
2700 <title>Functional dependencies
2703 <para> Functional dependencies are implemented as described by Mark Jones
2704 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2705 In Proceedings of the 9th European Symposium on Programming,
2706 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2710 Functional dependencies are introduced by a vertical bar in the syntax of a
2711 class declaration; e.g.
2713 class (Monad m) => MonadState s m | m -> s where ...
2715 class Foo a b c | a b -> c where ...
2717 There should be more documentation, but there isn't (yet). Yell if you need it.
2720 <sect3><title>Rules for functional dependencies </title>
2722 In a class declaration, all of the class type variables must be reachable (in the sense
2723 mentioned in <xref linkend="type-restrictions"/>)
2724 from the free variables of each method type.
2728 class Coll s a where
2730 insert :: s -> a -> s
2733 is not OK, because the type of <literal>empty</literal> doesn't mention
2734 <literal>a</literal>. Functional dependencies can make the type variable
2737 class Coll s a | s -> a where
2739 insert :: s -> a -> s
2742 Alternatively <literal>Coll</literal> might be rewritten
2745 class Coll s a where
2747 insert :: s a -> a -> s a
2751 which makes the connection between the type of a collection of
2752 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2753 Occasionally this really doesn't work, in which case you can split the
2761 class CollE s => Coll s a where
2762 insert :: s -> a -> s
2769 <title>Background on functional dependencies</title>
2771 <para>The following description of the motivation and use of functional dependencies is taken
2772 from the Hugs user manual, reproduced here (with minor changes) by kind
2773 permission of Mark Jones.
2776 Consider the following class, intended as part of a
2777 library for collection types:
2779 class Collects e ce where
2781 insert :: e -> ce -> ce
2782 member :: e -> ce -> Bool
2784 The type variable e used here represents the element type, while ce is the type
2785 of the container itself. Within this framework, we might want to define
2786 instances of this class for lists or characteristic functions (both of which
2787 can be used to represent collections of any equality type), bit sets (which can
2788 be used to represent collections of characters), or hash tables (which can be
2789 used to represent any collection whose elements have a hash function). Omitting
2790 standard implementation details, this would lead to the following declarations:
2792 instance Eq e => Collects e [e] where ...
2793 instance Eq e => Collects e (e -> Bool) where ...
2794 instance Collects Char BitSet where ...
2795 instance (Hashable e, Collects a ce)
2796 => Collects e (Array Int ce) where ...
2798 All this looks quite promising; we have a class and a range of interesting
2799 implementations. Unfortunately, there are some serious problems with the class
2800 declaration. First, the empty function has an ambiguous type:
2802 empty :: Collects e ce => ce
2804 By "ambiguous" we mean that there is a type variable e that appears on the left
2805 of the <literal>=></literal> symbol, but not on the right. The problem with
2806 this is that, according to the theoretical foundations of Haskell overloading,
2807 we cannot guarantee a well-defined semantics for any term with an ambiguous
2811 We can sidestep this specific problem by removing the empty member from the
2812 class declaration. However, although the remaining members, insert and member,
2813 do not have ambiguous types, we still run into problems when we try to use
2814 them. For example, consider the following two functions:
2816 f x y = insert x . insert y
2819 for which GHC infers the following types:
2821 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2822 g :: (Collects Bool c, Collects Char c) => c -> c
2824 Notice that the type for f allows the two parameters x and y to be assigned
2825 different types, even though it attempts to insert each of the two values, one
2826 after the other, into the same collection. If we're trying to model collections
2827 that contain only one type of value, then this is clearly an inaccurate
2828 type. Worse still, the definition for g is accepted, without causing a type
2829 error. As a result, the error in this code will not be flagged at the point
2830 where it appears. Instead, it will show up only when we try to use g, which
2831 might even be in a different module.
2834 <sect4><title>An attempt to use constructor classes</title>
2837 Faced with the problems described above, some Haskell programmers might be
2838 tempted to use something like the following version of the class declaration:
2840 class Collects e c where
2842 insert :: e -> c e -> c e
2843 member :: e -> c e -> Bool
2845 The key difference here is that we abstract over the type constructor c that is
2846 used to form the collection type c e, and not over that collection type itself,
2847 represented by ce in the original class declaration. This avoids the immediate
2848 problems that we mentioned above: empty has type <literal>Collects e c => c
2849 e</literal>, which is not ambiguous.
2852 The function f from the previous section has a more accurate type:
2854 f :: (Collects e c) => e -> e -> c e -> c e
2856 The function g from the previous section is now rejected with a type error as
2857 we would hope because the type of f does not allow the two arguments to have
2859 This, then, is an example of a multiple parameter class that does actually work
2860 quite well in practice, without ambiguity problems.
2861 There is, however, a catch. This version of the Collects class is nowhere near
2862 as general as the original class seemed to be: only one of the four instances
2863 for <literal>Collects</literal>
2864 given above can be used with this version of Collects because only one of
2865 them---the instance for lists---has a collection type that can be written in
2866 the form c e, for some type constructor c, and element type e.
2870 <sect4><title>Adding functional dependencies</title>
2873 To get a more useful version of the Collects class, Hugs provides a mechanism
2874 that allows programmers to specify dependencies between the parameters of a
2875 multiple parameter class (For readers with an interest in theoretical
2876 foundations and previous work: The use of dependency information can be seen
2877 both as a generalization of the proposal for `parametric type classes' that was
2878 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2879 later framework for "improvement" of qualified types. The
2880 underlying ideas are also discussed in a more theoretical and abstract setting
2881 in a manuscript [implparam], where they are identified as one point in a
2882 general design space for systems of implicit parameterization.).
2884 To start with an abstract example, consider a declaration such as:
2886 class C a b where ...
2888 which tells us simply that C can be thought of as a binary relation on types
2889 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2890 included in the definition of classes to add information about dependencies
2891 between parameters, as in the following examples:
2893 class D a b | a -> b where ...
2894 class E a b | a -> b, b -> a where ...
2896 The notation <literal>a -> b</literal> used here between the | and where
2897 symbols --- not to be
2898 confused with a function type --- indicates that the a parameter uniquely
2899 determines the b parameter, and might be read as "a determines b." Thus D is
2900 not just a relation, but actually a (partial) function. Similarly, from the two
2901 dependencies that are included in the definition of E, we can see that E
2902 represents a (partial) one-one mapping between types.
2905 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2906 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2907 m>=0, meaning that the y parameters are uniquely determined by the x
2908 parameters. Spaces can be used as separators if more than one variable appears
2909 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2910 annotated with multiple dependencies using commas as separators, as in the
2911 definition of E above. Some dependencies that we can write in this notation are
2912 redundant, and will be rejected because they don't serve any useful
2913 purpose, and may instead indicate an error in the program. Examples of
2914 dependencies like this include <literal>a -> a </literal>,
2915 <literal>a -> a a </literal>,
2916 <literal>a -> </literal>, etc. There can also be
2917 some redundancy if multiple dependencies are given, as in
2918 <literal>a->b</literal>,
2919 <literal>b->c </literal>, <literal>a->c </literal>, and
2920 in which some subset implies the remaining dependencies. Examples like this are
2921 not treated as errors. Note that dependencies appear only in class
2922 declarations, and not in any other part of the language. In particular, the
2923 syntax for instance declarations, class constraints, and types is completely
2927 By including dependencies in a class declaration, we provide a mechanism for
2928 the programmer to specify each multiple parameter class more precisely. The
2929 compiler, on the other hand, is responsible for ensuring that the set of
2930 instances that are in scope at any given point in the program is consistent
2931 with any declared dependencies. For example, the following pair of instance
2932 declarations cannot appear together in the same scope because they violate the
2933 dependency for D, even though either one on its own would be acceptable:
2935 instance D Bool Int where ...
2936 instance D Bool Char where ...
2938 Note also that the following declaration is not allowed, even by itself:
2940 instance D [a] b where ...
2942 The problem here is that this instance would allow one particular choice of [a]
2943 to be associated with more than one choice for b, which contradicts the
2944 dependency specified in the definition of D. More generally, this means that,
2945 in any instance of the form:
2947 instance D t s where ...
2949 for some particular types t and s, the only variables that can appear in s are
2950 the ones that appear in t, and hence, if the type t is known, then s will be
2951 uniquely determined.
2954 The benefit of including dependency information is that it allows us to define
2955 more general multiple parameter classes, without ambiguity problems, and with
2956 the benefit of more accurate types. To illustrate this, we return to the
2957 collection class example, and annotate the original definition of <literal>Collects</literal>
2958 with a simple dependency:
2960 class Collects e ce | ce -> e where
2962 insert :: e -> ce -> ce
2963 member :: e -> ce -> Bool
2965 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2966 determined by the type of the collection ce. Note that both parameters of
2967 Collects are of kind *; there are no constructor classes here. Note too that
2968 all of the instances of Collects that we gave earlier can be used
2969 together with this new definition.
2972 What about the ambiguity problems that we encountered with the original
2973 definition? The empty function still has type Collects e ce => ce, but it is no
2974 longer necessary to regard that as an ambiguous type: Although the variable e
2975 does not appear on the right of the => symbol, the dependency for class
2976 Collects tells us that it is uniquely determined by ce, which does appear on
2977 the right of the => symbol. Hence the context in which empty is used can still
2978 give enough information to determine types for both ce and e, without
2979 ambiguity. More generally, we need only regard a type as ambiguous if it
2980 contains a variable on the left of the => that is not uniquely determined
2981 (either directly or indirectly) by the variables on the right.
2984 Dependencies also help to produce more accurate types for user defined
2985 functions, and hence to provide earlier detection of errors, and less cluttered
2986 types for programmers to work with. Recall the previous definition for a
2989 f x y = insert x y = insert x . insert y
2991 for which we originally obtained a type:
2993 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2995 Given the dependency information that we have for Collects, however, we can
2996 deduce that a and b must be equal because they both appear as the second
2997 parameter in a Collects constraint with the same first parameter c. Hence we
2998 can infer a shorter and more accurate type for f:
3000 f :: (Collects a c) => a -> a -> c -> c
3002 In a similar way, the earlier definition of g will now be flagged as a type error.
3005 Although we have given only a few examples here, it should be clear that the
3006 addition of dependency information can help to make multiple parameter classes
3007 more useful in practice, avoiding ambiguity problems, and allowing more general
3008 sets of instance declarations.
3014 <sect2 id="instance-decls">
3015 <title>Instance declarations</title>
3017 <sect3 id="instance-rules">
3018 <title>Relaxed rules for instance declarations</title>
3020 <para>An instance declaration has the form
3022 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 ...
3024 The part before the "<literal>=></literal>" is the
3025 <emphasis>context</emphasis>, while the part after the
3026 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3030 In Haskell 98 the head of an instance declaration
3031 must be of the form <literal>C (T a1 ... an)</literal>, where
3032 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3033 and the <literal>a1 ... an</literal> are distinct type variables.
3034 Furthermore, the assertions in the context of the instance declaration
3035 must be of the form <literal>C a</literal> where <literal>a</literal>
3036 is a type variable that occurs in the head.
3039 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3040 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3041 the context and head of the instance declaration can each consist of arbitrary
3042 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3046 The Paterson Conditions: for each assertion in the context
3048 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3049 <listitem><para>The assertion has fewer constructors and variables (taken together
3050 and counting repetitions) than the head</para></listitem>
3054 <listitem><para>The Coverage Condition. For each functional dependency,
3055 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3056 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3057 every type variable in
3058 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3059 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3060 substitution mapping each type variable in the class declaration to the
3061 corresponding type in the instance declaration.
3064 These restrictions ensure that context reduction terminates: each reduction
3065 step makes the problem smaller by at least one
3066 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3067 if you give the <option>-fallow-undecidable-instances</option>
3068 flag (<xref linkend="undecidable-instances"/>).
3069 You can find lots of background material about the reason for these
3070 restrictions in the paper <ulink
3071 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3072 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3075 For example, these are OK:
3077 instance C Int [a] -- Multiple parameters
3078 instance Eq (S [a]) -- Structured type in head
3080 -- Repeated type variable in head
3081 instance C4 a a => C4 [a] [a]
3082 instance Stateful (ST s) (MutVar s)
3084 -- Head can consist of type variables only
3086 instance (Eq a, Show b) => C2 a b
3088 -- Non-type variables in context
3089 instance Show (s a) => Show (Sized s a)
3090 instance C2 Int a => C3 Bool [a]
3091 instance C2 Int a => C3 [a] b
3095 -- Context assertion no smaller than head
3096 instance C a => C a where ...
3097 -- (C b b) has more more occurrences of b than the head
3098 instance C b b => Foo [b] where ...
3103 The same restrictions apply to instances generated by
3104 <literal>deriving</literal> clauses. Thus the following is accepted:
3106 data MinHeap h a = H a (h a)
3109 because the derived instance
3111 instance (Show a, Show (h a)) => Show (MinHeap h a)
3113 conforms to the above rules.
3117 A useful idiom permitted by the above rules is as follows.
3118 If one allows overlapping instance declarations then it's quite
3119 convenient to have a "default instance" declaration that applies if
3120 something more specific does not:
3128 <sect3 id="undecidable-instances">
3129 <title>Undecidable instances</title>
3132 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3133 For example, sometimes you might want to use the following to get the
3134 effect of a "class synonym":
3136 class (C1 a, C2 a, C3 a) => C a where { }
3138 instance (C1 a, C2 a, C3 a) => C a where { }
3140 This allows you to write shorter signatures:
3146 f :: (C1 a, C2 a, C3 a) => ...
3148 The restrictions on functional dependencies (<xref
3149 linkend="functional-dependencies"/>) are particularly troublesome.
3150 It is tempting to introduce type variables in the context that do not appear in
3151 the head, something that is excluded by the normal rules. For example:
3153 class HasConverter a b | a -> b where
3156 data Foo a = MkFoo a
3158 instance (HasConverter a b,Show b) => Show (Foo a) where
3159 show (MkFoo value) = show (convert value)
3161 This is dangerous territory, however. Here, for example, is a program that would make the
3166 instance F [a] [[a]]
3167 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3169 Similarly, it can be tempting to lift the coverage condition:
3171 class Mul a b c | a b -> c where
3172 (.*.) :: a -> b -> c
3174 instance Mul Int Int Int where (.*.) = (*)
3175 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3176 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3178 The third instance declaration does not obey the coverage condition;
3179 and indeed the (somewhat strange) definition:
3181 f = \ b x y -> if b then x .*. [y] else y
3183 makes instance inference go into a loop, because it requires the constraint
3184 <literal>(Mul a [b] b)</literal>.
3187 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3188 the experimental flag <option>-XUndecidableInstances</option>
3189 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3190 both the Paterson Conditions and the Coverage Condition
3191 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3192 fixed-depth recursion stack. If you exceed the stack depth you get a
3193 sort of backtrace, and the opportunity to increase the stack depth
3194 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3200 <sect3 id="instance-overlap">
3201 <title>Overlapping instances</title>
3203 In general, <emphasis>GHC requires that that it be unambiguous which instance
3205 should be used to resolve a type-class constraint</emphasis>. This behaviour
3206 can be modified by two flags: <option>-XOverlappingInstances</option>
3207 <indexterm><primary>-XOverlappingInstances
3208 </primary></indexterm>
3209 and <option>-XIncoherentInstances</option>
3210 <indexterm><primary>-XIncoherentInstances
3211 </primary></indexterm>, as this section discusses. Both these
3212 flags are dynamic flags, and can be set on a per-module basis, using
3213 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3215 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3216 it tries to match every instance declaration against the
3218 by instantiating the head of the instance declaration. For example, consider
3221 instance context1 => C Int a where ... -- (A)
3222 instance context2 => C a Bool where ... -- (B)
3223 instance context3 => C Int [a] where ... -- (C)
3224 instance context4 => C Int [Int] where ... -- (D)
3226 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3227 but (C) and (D) do not. When matching, GHC takes
3228 no account of the context of the instance declaration
3229 (<literal>context1</literal> etc).
3230 GHC's default behaviour is that <emphasis>exactly one instance must match the
3231 constraint it is trying to resolve</emphasis>.
3232 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3233 including both declarations (A) and (B), say); an error is only reported if a
3234 particular constraint matches more than one.
3238 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3239 more than one instance to match, provided there is a most specific one. For
3240 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3241 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3242 most-specific match, the program is rejected.
3245 However, GHC is conservative about committing to an overlapping instance. For example:
3250 Suppose that from the RHS of <literal>f</literal> we get the constraint
3251 <literal>C Int [b]</literal>. But
3252 GHC does not commit to instance (C), because in a particular
3253 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3254 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3255 So GHC rejects the program.
3256 (If you add the flag <option>-XIncoherentInstances</option>,
3257 GHC will instead pick (C), without complaining about
3258 the problem of subsequent instantiations.)
3261 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3262 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3263 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3264 it instead. In this case, GHC will refrain from
3265 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3266 as before) but, rather than rejecting the program, it will infer the type
3268 f :: C Int b => [b] -> [b]
3270 That postpones the question of which instance to pick to the
3271 call site for <literal>f</literal>
3272 by which time more is known about the type <literal>b</literal>.
3275 The willingness to be overlapped or incoherent is a property of
3276 the <emphasis>instance declaration</emphasis> itself, controlled by the
3277 presence or otherwise of the <option>-XOverlappingInstances</option>
3278 and <option>-XIncoherentInstances</option> flags when that module is
3279 being defined. Neither flag is required in a module that imports and uses the
3280 instance declaration. Specifically, during the lookup process:
3283 An instance declaration is ignored during the lookup process if (a) a more specific
3284 match is found, and (b) the instance declaration was compiled with
3285 <option>-XOverlappingInstances</option>. The flag setting for the
3286 more-specific instance does not matter.
3289 Suppose an instance declaration does not match the constraint being looked up, but
3290 does unify with it, so that it might match when the constraint is further
3291 instantiated. Usually GHC will regard this as a reason for not committing to
3292 some other constraint. But if the instance declaration was compiled with
3293 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3294 check for that declaration.
3297 These rules make it possible for a library author to design a library that relies on
3298 overlapping instances without the library client having to know.
3301 If an instance declaration is compiled without
3302 <option>-XOverlappingInstances</option>,
3303 then that instance can never be overlapped. This could perhaps be
3304 inconvenient. Perhaps the rule should instead say that the
3305 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3306 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3307 at a usage site should be permitted regardless of how the instance declarations
3308 are compiled, if the <option>-XOverlappingInstances</option> flag is
3309 used at the usage site. (Mind you, the exact usage site can occasionally be
3310 hard to pin down.) We are interested to receive feedback on these points.
3312 <para>The <option>-XIncoherentInstances</option> flag implies the
3313 <option>-XOverlappingInstances</option> flag, but not vice versa.
3318 <title>Type synonyms in the instance head</title>
3321 <emphasis>Unlike Haskell 98, instance heads may use type
3322 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3323 As always, using a type synonym is just shorthand for
3324 writing the RHS of the type synonym definition. For example:
3328 type Point = (Int,Int)
3329 instance C Point where ...
3330 instance C [Point] where ...
3334 is legal. However, if you added
3338 instance C (Int,Int) where ...
3342 as well, then the compiler will complain about the overlapping
3343 (actually, identical) instance declarations. As always, type synonyms
3344 must be fully applied. You cannot, for example, write:
3349 instance Monad P where ...
3353 This design decision is independent of all the others, and easily
3354 reversed, but it makes sense to me.
3362 <sect2 id="overloaded-strings">
3363 <title>Overloaded string literals
3367 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3368 string literal has type <literal>String</literal>, but with overloaded string
3369 literals enabled (with <literal>-XOverloadedStrings</literal>)
3370 a string literal has type <literal>(IsString a) => a</literal>.
3373 This means that the usual string syntax can be used, e.g., for packed strings
3374 and other variations of string like types. String literals behave very much
3375 like integer literals, i.e., they can be used in both expressions and patterns.
3376 If used in a pattern the literal with be replaced by an equality test, in the same
3377 way as an integer literal is.
3380 The class <literal>IsString</literal> is defined as:
3382 class IsString a where
3383 fromString :: String -> a
3385 The only predefined instance is the obvious one to make strings work as usual:
3387 instance IsString [Char] where
3390 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3391 it explicitly (for example, to give an instance declaration for it), you can import it
3392 from module <literal>GHC.Exts</literal>.
3395 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3399 Each type in a default declaration must be an
3400 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3404 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3405 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3406 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3407 <emphasis>or</emphasis> <literal>IsString</literal>.
3416 import GHC.Exts( IsString(..) )
3418 newtype MyString = MyString String deriving (Eq, Show)
3419 instance IsString MyString where
3420 fromString = MyString
3422 greet :: MyString -> MyString
3423 greet "hello" = "world"
3427 print $ greet "hello"
3428 print $ greet "fool"
3432 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3433 to work since it gets translated into an equality comparison.
3439 <sect1 id="other-type-extensions">
3440 <title>Other type system extensions</title>
3442 <sect2 id="type-restrictions">
3443 <title>Type signatures</title>
3445 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3447 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3448 the form <emphasis>(class type-variable)</emphasis> or
3449 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3450 these type signatures are perfectly OK
3453 g :: Ord (T a ()) => ...
3457 GHC imposes the following restrictions on the constraints in a type signature.
3461 forall tv1..tvn (c1, ...,cn) => type
3464 (Here, we write the "foralls" explicitly, although the Haskell source
3465 language omits them; in Haskell 98, all the free type variables of an
3466 explicit source-language type signature are universally quantified,
3467 except for the class type variables in a class declaration. However,
3468 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3477 <emphasis>Each universally quantified type variable
3478 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3480 A type variable <literal>a</literal> is "reachable" if it it appears
3481 in the same constraint as either a type variable free in in
3482 <literal>type</literal>, or another reachable type variable.
3483 A value with a type that does not obey
3484 this reachability restriction cannot be used without introducing
3485 ambiguity; that is why the type is rejected.
3486 Here, for example, is an illegal type:
3490 forall a. Eq a => Int
3494 When a value with this type was used, the constraint <literal>Eq tv</literal>
3495 would be introduced where <literal>tv</literal> is a fresh type variable, and
3496 (in the dictionary-translation implementation) the value would be
3497 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3498 can never know which instance of <literal>Eq</literal> to use because we never
3499 get any more information about <literal>tv</literal>.
3503 that the reachability condition is weaker than saying that <literal>a</literal> is
3504 functionally dependent on a type variable free in
3505 <literal>type</literal> (see <xref
3506 linkend="functional-dependencies"/>). The reason for this is there
3507 might be a "hidden" dependency, in a superclass perhaps. So
3508 "reachable" is a conservative approximation to "functionally dependent".
3509 For example, consider:
3511 class C a b | a -> b where ...
3512 class C a b => D a b where ...
3513 f :: forall a b. D a b => a -> a
3515 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3516 but that is not immediately apparent from <literal>f</literal>'s type.
3522 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3523 universally quantified type variables <literal>tvi</literal></emphasis>.
3525 For example, this type is OK because <literal>C a b</literal> mentions the
3526 universally quantified type variable <literal>b</literal>:
3530 forall a. C a b => burble
3534 The next type is illegal because the constraint <literal>Eq b</literal> does not
3535 mention <literal>a</literal>:
3539 forall a. Eq b => burble
3543 The reason for this restriction is milder than the other one. The
3544 excluded types are never useful or necessary (because the offending
3545 context doesn't need to be witnessed at this point; it can be floated
3546 out). Furthermore, floating them out increases sharing. Lastly,
3547 excluding them is a conservative choice; it leaves a patch of
3548 territory free in case we need it later.
3562 <sect2 id="implicit-parameters">
3563 <title>Implicit parameters</title>
3565 <para> Implicit parameters are implemented as described in
3566 "Implicit parameters: dynamic scoping with static types",
3567 J Lewis, MB Shields, E Meijer, J Launchbury,
3568 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3572 <para>(Most of the following, still rather incomplete, documentation is
3573 due to Jeff Lewis.)</para>
3575 <para>Implicit parameter support is enabled with the option
3576 <option>-XImplicitParams</option>.</para>
3579 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3580 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3581 context. In Haskell, all variables are statically bound. Dynamic
3582 binding of variables is a notion that goes back to Lisp, but was later
3583 discarded in more modern incarnations, such as Scheme. Dynamic binding
3584 can be very confusing in an untyped language, and unfortunately, typed
3585 languages, in particular Hindley-Milner typed languages like Haskell,
3586 only support static scoping of variables.
3589 However, by a simple extension to the type class system of Haskell, we
3590 can support dynamic binding. Basically, we express the use of a
3591 dynamically bound variable as a constraint on the type. These
3592 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3593 function uses a dynamically-bound variable <literal>?x</literal>
3594 of type <literal>t'</literal>". For
3595 example, the following expresses the type of a sort function,
3596 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3598 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3600 The dynamic binding constraints are just a new form of predicate in the type class system.
3603 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3604 where <literal>x</literal> is
3605 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3606 Use of this construct also introduces a new
3607 dynamic-binding constraint in the type of the expression.
3608 For example, the following definition
3609 shows how we can define an implicitly parameterized sort function in
3610 terms of an explicitly parameterized <literal>sortBy</literal> function:
3612 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3614 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3620 <title>Implicit-parameter type constraints</title>
3622 Dynamic binding constraints behave just like other type class
3623 constraints in that they are automatically propagated. Thus, when a
3624 function is used, its implicit parameters are inherited by the
3625 function that called it. For example, our <literal>sort</literal> function might be used
3626 to pick out the least value in a list:
3628 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3629 least xs = head (sort xs)
3631 Without lifting a finger, the <literal>?cmp</literal> parameter is
3632 propagated to become a parameter of <literal>least</literal> as well. With explicit
3633 parameters, the default is that parameters must always be explicit
3634 propagated. With implicit parameters, the default is to always
3638 An implicit-parameter type constraint differs from other type class constraints in the
3639 following way: All uses of a particular implicit parameter must have
3640 the same type. This means that the type of <literal>(?x, ?x)</literal>
3641 is <literal>(?x::a) => (a,a)</literal>, and not
3642 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3646 <para> You can't have an implicit parameter in the context of a class or instance
3647 declaration. For example, both these declarations are illegal:
3649 class (?x::Int) => C a where ...
3650 instance (?x::a) => Foo [a] where ...
3652 Reason: exactly which implicit parameter you pick up depends on exactly where
3653 you invoke a function. But the ``invocation'' of instance declarations is done
3654 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3655 Easiest thing is to outlaw the offending types.</para>
3657 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3659 f :: (?x :: [a]) => Int -> Int
3662 g :: (Read a, Show a) => String -> String
3665 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3666 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3667 quite unambiguous, and fixes the type <literal>a</literal>.
3672 <title>Implicit-parameter bindings</title>
3675 An implicit parameter is <emphasis>bound</emphasis> using the standard
3676 <literal>let</literal> or <literal>where</literal> binding forms.
3677 For example, we define the <literal>min</literal> function by binding
3678 <literal>cmp</literal>.
3681 min = let ?cmp = (<=) in least
3685 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3686 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3687 (including in a list comprehension, or do-notation, or pattern guards),
3688 or a <literal>where</literal> clause.
3689 Note the following points:
3692 An implicit-parameter binding group must be a
3693 collection of simple bindings to implicit-style variables (no
3694 function-style bindings, and no type signatures); these bindings are
3695 neither polymorphic or recursive.
3698 You may not mix implicit-parameter bindings with ordinary bindings in a
3699 single <literal>let</literal>
3700 expression; use two nested <literal>let</literal>s instead.
3701 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3705 You may put multiple implicit-parameter bindings in a
3706 single binding group; but they are <emphasis>not</emphasis> treated
3707 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3708 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3709 parameter. The bindings are not nested, and may be re-ordered without changing
3710 the meaning of the program.
3711 For example, consider:
3713 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3715 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3716 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3718 f :: (?x::Int) => Int -> Int
3726 <sect3><title>Implicit parameters and polymorphic recursion</title>
3729 Consider these two definitions:
3732 len1 xs = let ?acc = 0 in len_acc1 xs
3735 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3740 len2 xs = let ?acc = 0 in len_acc2 xs
3742 len_acc2 :: (?acc :: Int) => [a] -> Int
3744 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3746 The only difference between the two groups is that in the second group
3747 <literal>len_acc</literal> is given a type signature.
3748 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3749 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3750 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3751 has a type signature, the recursive call is made to the
3752 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3753 as an implicit parameter. So we get the following results in GHCi:
3760 Adding a type signature dramatically changes the result! This is a rather
3761 counter-intuitive phenomenon, worth watching out for.
3765 <sect3><title>Implicit parameters and monomorphism</title>
3767 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3768 Haskell Report) to implicit parameters. For example, consider:
3776 Since the binding for <literal>y</literal> falls under the Monomorphism
3777 Restriction it is not generalised, so the type of <literal>y</literal> is
3778 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3779 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3780 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3781 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3782 <literal>y</literal> in the body of the <literal>let</literal> will see the
3783 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3784 <literal>14</literal>.
3789 <!-- ======================= COMMENTED OUT ========================
3791 We intend to remove linear implicit parameters, so I'm at least removing
3792 them from the 6.6 user manual
3794 <sect2 id="linear-implicit-parameters">
3795 <title>Linear implicit parameters</title>
3797 Linear implicit parameters are an idea developed by Koen Claessen,
3798 Mark Shields, and Simon PJ. They address the long-standing
3799 problem that monads seem over-kill for certain sorts of problem, notably:
3802 <listitem> <para> distributing a supply of unique names </para> </listitem>
3803 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3804 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3808 Linear implicit parameters are just like ordinary implicit parameters,
3809 except that they are "linear"; that is, they cannot be copied, and
3810 must be explicitly "split" instead. Linear implicit parameters are
3811 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3812 (The '/' in the '%' suggests the split!)
3817 import GHC.Exts( Splittable )
3819 data NameSupply = ...
3821 splitNS :: NameSupply -> (NameSupply, NameSupply)
3822 newName :: NameSupply -> Name
3824 instance Splittable NameSupply where
3828 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3829 f env (Lam x e) = Lam x' (f env e)
3832 env' = extend env x x'
3833 ...more equations for f...
3835 Notice that the implicit parameter %ns is consumed
3837 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3838 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3842 So the translation done by the type checker makes
3843 the parameter explicit:
3845 f :: NameSupply -> Env -> Expr -> Expr
3846 f ns env (Lam x e) = Lam x' (f ns1 env e)
3848 (ns1,ns2) = splitNS ns
3850 env = extend env x x'
3852 Notice the call to 'split' introduced by the type checker.
3853 How did it know to use 'splitNS'? Because what it really did
3854 was to introduce a call to the overloaded function 'split',
3855 defined by the class <literal>Splittable</literal>:
3857 class Splittable a where
3860 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3861 split for name supplies. But we can simply write
3867 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3869 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3870 <literal>GHC.Exts</literal>.
3875 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3876 are entirely distinct implicit parameters: you
3877 can use them together and they won't interfere with each other. </para>
3880 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3882 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3883 in the context of a class or instance declaration. </para></listitem>
3887 <sect3><title>Warnings</title>
3890 The monomorphism restriction is even more important than usual.
3891 Consider the example above:
3893 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3894 f env (Lam x e) = Lam x' (f env e)
3897 env' = extend env x x'
3899 If we replaced the two occurrences of x' by (newName %ns), which is
3900 usually a harmless thing to do, we get:
3902 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3903 f env (Lam x e) = Lam (newName %ns) (f env e)
3905 env' = extend env x (newName %ns)
3907 But now the name supply is consumed in <emphasis>three</emphasis> places
3908 (the two calls to newName,and the recursive call to f), so
3909 the result is utterly different. Urk! We don't even have
3913 Well, this is an experimental change. With implicit
3914 parameters we have already lost beta reduction anyway, and
3915 (as John Launchbury puts it) we can't sensibly reason about
3916 Haskell programs without knowing their typing.
3921 <sect3><title>Recursive functions</title>
3922 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3925 foo :: %x::T => Int -> [Int]
3927 foo n = %x : foo (n-1)
3929 where T is some type in class Splittable.</para>
3931 Do you get a list of all the same T's or all different T's
3932 (assuming that split gives two distinct T's back)?
3934 If you supply the type signature, taking advantage of polymorphic
3935 recursion, you get what you'd probably expect. Here's the
3936 translated term, where the implicit param is made explicit:
3939 foo x n = let (x1,x2) = split x
3940 in x1 : foo x2 (n-1)
3942 But if you don't supply a type signature, GHC uses the Hindley
3943 Milner trick of using a single monomorphic instance of the function
3944 for the recursive calls. That is what makes Hindley Milner type inference
3945 work. So the translation becomes
3949 foom n = x : foom (n-1)
3953 Result: 'x' is not split, and you get a list of identical T's. So the
3954 semantics of the program depends on whether or not foo has a type signature.
3957 You may say that this is a good reason to dislike linear implicit parameters
3958 and you'd be right. That is why they are an experimental feature.
3964 ================ END OF Linear Implicit Parameters commented out -->
3966 <sect2 id="kinding">
3967 <title>Explicitly-kinded quantification</title>
3970 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3971 to give the kind explicitly as (machine-checked) documentation,
3972 just as it is nice to give a type signature for a function. On some occasions,
3973 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3974 John Hughes had to define the data type:
3976 data Set cxt a = Set [a]
3977 | Unused (cxt a -> ())
3979 The only use for the <literal>Unused</literal> constructor was to force the correct
3980 kind for the type variable <literal>cxt</literal>.
3983 GHC now instead allows you to specify the kind of a type variable directly, wherever
3984 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
3987 This flag enables kind signatures in the following places:
3989 <listitem><para><literal>data</literal> declarations:
3991 data Set (cxt :: * -> *) a = Set [a]
3992 </screen></para></listitem>
3993 <listitem><para><literal>type</literal> declarations:
3995 type T (f :: * -> *) = f Int
3996 </screen></para></listitem>
3997 <listitem><para><literal>class</literal> declarations:
3999 class (Eq a) => C (f :: * -> *) a where ...
4000 </screen></para></listitem>
4001 <listitem><para><literal>forall</literal>'s in type signatures:
4003 f :: forall (cxt :: * -> *). Set cxt Int
4004 </screen></para></listitem>
4009 The parentheses are required. Some of the spaces are required too, to
4010 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4011 will get a parse error, because "<literal>::*->*</literal>" is a
4012 single lexeme in Haskell.
4016 As part of the same extension, you can put kind annotations in types
4019 f :: (Int :: *) -> Int
4020 g :: forall a. a -> (a :: *)
4024 atype ::= '(' ctype '::' kind ')
4026 The parentheses are required.
4031 <sect2 id="universal-quantification">
4032 <title>Arbitrary-rank polymorphism
4036 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4037 allows us to say exactly what this means. For example:
4045 g :: forall b. (b -> b)
4047 The two are treated identically.
4051 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4052 explicit universal quantification in
4054 For example, all the following types are legal:
4056 f1 :: forall a b. a -> b -> a
4057 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4059 f2 :: (forall a. a->a) -> Int -> Int
4060 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4062 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4064 f4 :: Int -> (forall a. a -> a)
4066 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4067 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4068 The <literal>forall</literal> makes explicit the universal quantification that
4069 is implicitly added by Haskell.
4072 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4073 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4074 shows, the polymorphic type on the left of the function arrow can be overloaded.
4077 The function <literal>f3</literal> has a rank-3 type;
4078 it has rank-2 types on the left of a function arrow.
4081 GHC has three flags to control higher-rank types:
4084 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argment types.
4087 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4090 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4091 That is, you can nest <literal>forall</literal>s
4092 arbitrarily deep in function arrows.
4093 In particular, a forall-type (also called a "type scheme"),
4094 including an operational type class context, is legal:
4096 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4097 of a function arrow </para> </listitem>
4098 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4099 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4100 field type signatures.</para> </listitem>
4101 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4102 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4106 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4107 a type variable any more!
4116 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4117 the types of the constructor arguments. Here are several examples:
4123 data T a = T1 (forall b. b -> b -> b) a
4125 data MonadT m = MkMonad { return :: forall a. a -> m a,
4126 bind :: forall a b. m a -> (a -> m b) -> m b
4129 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4135 The constructors have rank-2 types:
4141 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4142 MkMonad :: forall m. (forall a. a -> m a)
4143 -> (forall a b. m a -> (a -> m b) -> m b)
4145 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4151 Notice that you don't need to use a <literal>forall</literal> if there's an
4152 explicit context. For example in the first argument of the
4153 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4154 prefixed to the argument type. The implicit <literal>forall</literal>
4155 quantifies all type variables that are not already in scope, and are
4156 mentioned in the type quantified over.
4160 As for type signatures, implicit quantification happens for non-overloaded
4161 types too. So if you write this:
4164 data T a = MkT (Either a b) (b -> b)
4167 it's just as if you had written this:
4170 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4173 That is, since the type variable <literal>b</literal> isn't in scope, it's
4174 implicitly universally quantified. (Arguably, it would be better
4175 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4176 where that is what is wanted. Feedback welcomed.)
4180 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4181 the constructor to suitable values, just as usual. For example,
4192 a3 = MkSwizzle reverse
4195 a4 = let r x = Just x
4202 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4203 mkTs f x y = [T1 f x, T1 f y]
4209 The type of the argument can, as usual, be more general than the type
4210 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4211 does not need the <literal>Ord</literal> constraint.)
4215 When you use pattern matching, the bound variables may now have
4216 polymorphic types. For example:
4222 f :: T a -> a -> (a, Char)
4223 f (T1 w k) x = (w k x, w 'c' 'd')
4225 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4226 g (MkSwizzle s) xs f = s (map f (s xs))
4228 h :: MonadT m -> [m a] -> m [a]
4229 h m [] = return m []
4230 h m (x:xs) = bind m x $ \y ->
4231 bind m (h m xs) $ \ys ->
4238 In the function <function>h</function> we use the record selectors <literal>return</literal>
4239 and <literal>bind</literal> to extract the polymorphic bind and return functions
4240 from the <literal>MonadT</literal> data structure, rather than using pattern
4246 <title>Type inference</title>
4249 In general, type inference for arbitrary-rank types is undecidable.
4250 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4251 to get a decidable algorithm by requiring some help from the programmer.
4252 We do not yet have a formal specification of "some help" but the rule is this:
4255 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4256 provides an explicit polymorphic type for x, or GHC's type inference will assume
4257 that x's type has no foralls in it</emphasis>.
4260 What does it mean to "provide" an explicit type for x? You can do that by
4261 giving a type signature for x directly, using a pattern type signature
4262 (<xref linkend="scoped-type-variables"/>), thus:
4264 \ f :: (forall a. a->a) -> (f True, f 'c')
4266 Alternatively, you can give a type signature to the enclosing
4267 context, which GHC can "push down" to find the type for the variable:
4269 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4271 Here the type signature on the expression can be pushed inwards
4272 to give a type signature for f. Similarly, and more commonly,
4273 one can give a type signature for the function itself:
4275 h :: (forall a. a->a) -> (Bool,Char)
4276 h f = (f True, f 'c')
4278 You don't need to give a type signature if the lambda bound variable
4279 is a constructor argument. Here is an example we saw earlier:
4281 f :: T a -> a -> (a, Char)
4282 f (T1 w k) x = (w k x, w 'c' 'd')
4284 Here we do not need to give a type signature to <literal>w</literal>, because
4285 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4292 <sect3 id="implicit-quant">
4293 <title>Implicit quantification</title>
4296 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4297 user-written types, if and only if there is no explicit <literal>forall</literal>,
4298 GHC finds all the type variables mentioned in the type that are not already
4299 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4303 f :: forall a. a -> a
4310 h :: forall b. a -> b -> b
4316 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4319 f :: (a -> a) -> Int
4321 f :: forall a. (a -> a) -> Int
4323 f :: (forall a. a -> a) -> Int
4326 g :: (Ord a => a -> a) -> Int
4327 -- MEANS the illegal type
4328 g :: forall a. (Ord a => a -> a) -> Int
4330 g :: (forall a. Ord a => a -> a) -> Int
4332 The latter produces an illegal type, which you might think is silly,
4333 but at least the rule is simple. If you want the latter type, you
4334 can write your for-alls explicitly. Indeed, doing so is strongly advised
4341 <sect2 id="impredicative-polymorphism">
4342 <title>Impredicative polymorphism
4344 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
4345 that you can call a polymorphic function at a polymorphic type, and
4346 parameterise data structures over polymorphic types. For example:
4348 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4349 f (Just g) = Just (g [3], g "hello")
4352 Notice here that the <literal>Maybe</literal> type is parameterised by the
4353 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4356 <para>The technical details of this extension are described in the paper
4357 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
4358 type inference for higher-rank types and impredicativity</ulink>,
4359 which appeared at ICFP 2006.
4363 <sect2 id="scoped-type-variables">
4364 <title>Lexically scoped type variables
4368 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4369 which some type signatures are simply impossible to write. For example:
4371 f :: forall a. [a] -> [a]
4377 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4378 the entire definition of <literal>f</literal>.
4379 In particular, it is in scope at the type signature for <varname>ys</varname>.
4380 In Haskell 98 it is not possible to declare
4381 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4382 it becomes possible to do so.
4384 <para>Lexically-scoped type variables are enabled by
4385 <option>-fglasgow-exts</option>.
4387 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4388 variables work, compared to earlier releases. Read this section
4392 <title>Overview</title>
4394 <para>The design follows the following principles
4396 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4397 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4398 design.)</para></listitem>
4399 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4400 type variables. This means that every programmer-written type signature
4401 (including one that contains free scoped type variables) denotes a
4402 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4403 checker, and no inference is involved.</para></listitem>
4404 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4405 changing the program.</para></listitem>
4409 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4411 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4412 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4413 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4414 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4418 In Haskell, a programmer-written type signature is implicitly quantified over
4419 its free type variables (<ulink
4420 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
4422 of the Haskel Report).
4423 Lexically scoped type variables affect this implicit quantification rules
4424 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4425 quantified. For example, if type variable <literal>a</literal> is in scope,
4428 (e :: a -> a) means (e :: a -> a)
4429 (e :: b -> b) means (e :: forall b. b->b)
4430 (e :: a -> b) means (e :: forall b. a->b)
4438 <sect3 id="decl-type-sigs">
4439 <title>Declaration type signatures</title>
4440 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4441 quantification (using <literal>forall</literal>) brings into scope the
4442 explicitly-quantified
4443 type variables, in the definition of the named function(s). For example:
4445 f :: forall a. [a] -> [a]
4446 f (x:xs) = xs ++ [ x :: a ]
4448 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4449 the definition of "<literal>f</literal>".
4451 <para>This only happens if the quantification in <literal>f</literal>'s type
4452 signature is explicit. For example:
4455 g (x:xs) = xs ++ [ x :: a ]
4457 This program will be rejected, because "<literal>a</literal>" does not scope
4458 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4459 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4460 quantification rules.
4464 <sect3 id="exp-type-sigs">
4465 <title>Expression type signatures</title>
4467 <para>An expression type signature that has <emphasis>explicit</emphasis>
4468 quantification (using <literal>forall</literal>) brings into scope the
4469 explicitly-quantified
4470 type variables, in the annotated expression. For example:
4472 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4474 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4475 type variable <literal>s</literal> into scope, in the annotated expression
4476 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4481 <sect3 id="pattern-type-sigs">
4482 <title>Pattern type signatures</title>
4484 A type signature may occur in any pattern; this is a <emphasis>pattern type
4485 signature</emphasis>.
4488 -- f and g assume that 'a' is already in scope
4489 f = \(x::Int, y::a) -> x
4491 h ((x,y) :: (Int,Bool)) = (y,x)
4493 In the case where all the type variables in the pattern type signature are
4494 already in scope (i.e. bound by the enclosing context), matters are simple: the
4495 signature simply constrains the type of the pattern in the obvious way.
4498 Unlike expression and declaration type signatures, pattern type signatures are not implictly generalised.
4499 The pattern in a <emphasis>patterm binding</emphasis> may only mention type variables
4500 that are already in scope. For example:
4502 f :: forall a. [a] -> (Int, [a])
4505 (ys::[a], n) = (reverse xs, length xs) -- OK
4506 zs::[a] = xs ++ ys -- OK
4508 Just (v::b) = ... -- Not OK; b is not in scope
4510 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4511 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4515 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4516 type signature may mention a type variable that is not in scope; in this case,
4517 <emphasis>the signature brings that type variable into scope</emphasis>.
4518 This is particularly important for existential data constructors. For example:
4520 data T = forall a. MkT [a]
4523 k (MkT [t::a]) = MkT t3
4527 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4528 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4529 because it is bound by the pattern match. GHC's rule is that in this situation
4530 (and only then), a pattern type signature can mention a type variable that is
4531 not already in scope; the effect is to bring it into scope, standing for the
4532 existentially-bound type variable.
4535 When a pattern type signature binds a type variable in this way, GHC insists that the
4536 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4537 This means that any user-written type signature always stands for a completely known type.
4540 If all this seems a little odd, we think so too. But we must have
4541 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4542 could not name existentially-bound type variables in subsequent type signatures.
4545 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4546 signature is allowed to mention a lexical variable that is not already in
4548 For example, both <literal>f</literal> and <literal>g</literal> would be
4549 illegal if <literal>a</literal> was not already in scope.
4555 <!-- ==================== Commented out part about result type signatures
4557 <sect3 id="result-type-sigs">
4558 <title>Result type signatures</title>
4561 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4564 {- f assumes that 'a' is already in scope -}
4565 f x y :: [a] = [x,y,x]
4567 g = \ x :: [Int] -> [3,4]
4569 h :: forall a. [a] -> a
4573 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4574 the result of the function. Similarly, the body of the lambda in the RHS of
4575 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4576 alternative in <literal>h</literal> is <literal>a</literal>.
4578 <para> A result type signature never brings new type variables into scope.</para>
4580 There are a couple of syntactic wrinkles. First, notice that all three
4581 examples would parse quite differently with parentheses:
4583 {- f assumes that 'a' is already in scope -}
4584 f x (y :: [a]) = [x,y,x]
4586 g = \ (x :: [Int]) -> [3,4]
4588 h :: forall a. [a] -> a
4592 Now the signature is on the <emphasis>pattern</emphasis>; and
4593 <literal>h</literal> would certainly be ill-typed (since the pattern
4594 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4596 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4597 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4598 token or a parenthesised type of some sort). To see why,
4599 consider how one would parse this:
4608 <sect3 id="cls-inst-scoped-tyvars">
4609 <title>Class and instance declarations</title>
4612 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4613 scope over the methods defined in the <literal>where</literal> part. For example:
4631 <sect2 id="typing-binds">
4632 <title>Generalised typing of mutually recursive bindings</title>
4635 The Haskell Report specifies that a group of bindings (at top level, or in a
4636 <literal>let</literal> or <literal>where</literal>) should be sorted into
4637 strongly-connected components, and then type-checked in dependency order
4638 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4639 Report, Section 4.5.1</ulink>).
4640 As each group is type-checked, any binders of the group that
4642 an explicit type signature are put in the type environment with the specified
4644 and all others are monomorphic until the group is generalised
4645 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4648 <para>Following a suggestion of Mark Jones, in his paper
4649 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4651 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4653 <emphasis>the dependency analysis ignores references to variables that have an explicit
4654 type signature</emphasis>.
4655 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4656 typecheck. For example, consider:
4658 f :: Eq a => a -> Bool
4659 f x = (x == x) || g True || g "Yes"
4661 g y = (y <= y) || f True
4663 This is rejected by Haskell 98, but under Jones's scheme the definition for
4664 <literal>g</literal> is typechecked first, separately from that for
4665 <literal>f</literal>,
4666 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4667 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4668 type is generalised, to get
4670 g :: Ord a => a -> Bool
4672 Now, the definition for <literal>f</literal> is typechecked, with this type for
4673 <literal>g</literal> in the type environment.
4677 The same refined dependency analysis also allows the type signatures of
4678 mutually-recursive functions to have different contexts, something that is illegal in
4679 Haskell 98 (Section 4.5.2, last sentence). With
4680 <option>-XRelaxedPolyRec</option>
4681 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4682 type signatures; in practice this means that only variables bound by the same
4683 pattern binding must have the same context. For example, this is fine:
4685 f :: Eq a => a -> Bool
4686 f x = (x == x) || g True
4688 g :: Ord a => a -> Bool
4689 g y = (y <= y) || f True
4694 <sect2 id="type-families">
4695 <title>Type families
4699 GHC supports the definition of type families indexed by types. They may be
4700 seen as an extension of Haskell 98's class-based overloading of values to
4701 types. When type families are declared in classes, they are also known as
4705 There are two forms of type families: data families and type synonym families.
4706 Currently, only the former are fully implemented, while we are still working
4707 on the latter. As a result, the specification of the language extension is
4708 also still to some degree in flux. Hence, a more detailed description of
4709 the language extension and its use is currently available
4710 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4711 wiki page on type families</ulink>. The material will be moved to this user's
4712 guide when it has stabilised.
4715 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4722 <!-- ==================== End of type system extensions ================= -->
4724 <!-- ====================== TEMPLATE HASKELL ======================= -->
4726 <sect1 id="template-haskell">
4727 <title>Template Haskell</title>
4729 <para>Template Haskell allows you to do compile-time meta-programming in
4732 the main technical innovations is discussed in "<ulink
4733 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4734 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4737 There is a Wiki page about
4738 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4739 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4743 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4744 Haskell library reference material</ulink>
4745 (look for module <literal>Language.Haskell.TH</literal>).
4746 Many changes to the original design are described in
4747 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4748 Notes on Template Haskell version 2</ulink>.
4749 Not all of these changes are in GHC, however.
4752 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4753 as a worked example to help get you started.
4757 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4758 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4763 <title>Syntax</title>
4765 <para> Template Haskell has the following new syntactic
4766 constructions. You need to use the flag
4767 <option>-XTemplateHaskell</option>
4768 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4769 </indexterm>to switch these syntactic extensions on
4770 (<option>-XTemplateHaskell</option> is no longer implied by
4771 <option>-fglasgow-exts</option>).</para>
4775 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4776 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4777 There must be no space between the "$" and the identifier or parenthesis. This use
4778 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4779 of "." as an infix operator. If you want the infix operator, put spaces around it.
4781 <para> A splice can occur in place of
4783 <listitem><para> an expression; the spliced expression must
4784 have type <literal>Q Exp</literal></para></listitem>
4785 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4788 Inside a splice you can can only call functions defined in imported modules,
4789 not functions defined elsewhere in the same module.</listitem>
4793 A expression quotation is written in Oxford brackets, thus:
4795 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4796 the quotation has type <literal>Q Exp</literal>.</para></listitem>
4797 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4798 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4799 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4800 the quotation has type <literal>Q Typ</literal>.</para></listitem>
4801 </itemizedlist></para></listitem>
4804 A name can be quoted with either one or two prefix single quotes:
4806 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
4807 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
4808 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
4810 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
4811 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
4814 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, delarations etc. They
4815 may also be given as an argument to the <literal>reify</literal> function.
4821 (Compared to the original paper, there are many differnces of detail.
4822 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
4823 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
4824 Type splices are not implemented, and neither are pattern splices or quotations.
4828 <sect2> <title> Using Template Haskell </title>
4832 The data types and monadic constructor functions for Template Haskell are in the library
4833 <literal>Language.Haskell.THSyntax</literal>.
4837 You can only run a function at compile time if it is imported from another module. That is,
4838 you can't define a function in a module, and call it from within a splice in the same module.
4839 (It would make sense to do so, but it's hard to implement.)
4843 Furthermore, you can only run a function at compile time if it is imported
4844 from another module <emphasis>that is not part of a mutually-recursive group of modules
4845 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4846 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4847 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4851 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4854 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4855 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4856 compiles and runs a program, and then looks at the result. So it's important that
4857 the program it compiles produces results whose representations are identical to
4858 those of the compiler itself.
4862 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4863 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4868 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
4869 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4870 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4877 -- Import our template "pr"
4878 import Printf ( pr )
4880 -- The splice operator $ takes the Haskell source code
4881 -- generated at compile time by "pr" and splices it into
4882 -- the argument of "putStrLn".
4883 main = putStrLn ( $(pr "Hello") )
4889 -- Skeletal printf from the paper.
4890 -- It needs to be in a separate module to the one where
4891 -- you intend to use it.
4893 -- Import some Template Haskell syntax
4894 import Language.Haskell.TH
4896 -- Describe a format string
4897 data Format = D | S | L String
4899 -- Parse a format string. This is left largely to you
4900 -- as we are here interested in building our first ever
4901 -- Template Haskell program and not in building printf.
4902 parse :: String -> [Format]
4905 -- Generate Haskell source code from a parsed representation
4906 -- of the format string. This code will be spliced into
4907 -- the module which calls "pr", at compile time.
4908 gen :: [Format] -> Q Exp
4909 gen [D] = [| \n -> show n |]
4910 gen [S] = [| \s -> s |]
4911 gen [L s] = stringE s
4913 -- Here we generate the Haskell code for the splice
4914 -- from an input format string.
4915 pr :: String -> Q Exp
4916 pr s = gen (parse s)
4919 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4922 $ ghc --make -XTemplateHaskell main.hs -o main.exe
4925 <para>Run "main.exe" and here is your output:</para>
4935 <title>Using Template Haskell with Profiling</title>
4936 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4938 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4939 interpreter to run the splice expressions. The bytecode interpreter
4940 runs the compiled expression on top of the same runtime on which GHC
4941 itself is running; this means that the compiled code referred to by
4942 the interpreted expression must be compatible with this runtime, and
4943 in particular this means that object code that is compiled for
4944 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4945 expression, because profiled object code is only compatible with the
4946 profiling version of the runtime.</para>
4948 <para>This causes difficulties if you have a multi-module program
4949 containing Template Haskell code and you need to compile it for
4950 profiling, because GHC cannot load the profiled object code and use it
4951 when executing the splices. Fortunately GHC provides a workaround.
4952 The basic idea is to compile the program twice:</para>
4956 <para>Compile the program or library first the normal way, without
4957 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4960 <para>Then compile it again with <option>-prof</option>, and
4961 additionally use <option>-osuf
4962 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4963 to name the object files differently (you can choose any suffix
4964 that isn't the normal object suffix here). GHC will automatically
4965 load the object files built in the first step when executing splice
4966 expressions. If you omit the <option>-osuf</option> flag when
4967 building with <option>-prof</option> and Template Haskell is used,
4968 GHC will emit an error message. </para>
4975 <!-- ===================== Arrow notation =================== -->
4977 <sect1 id="arrow-notation">
4978 <title>Arrow notation
4981 <para>Arrows are a generalization of monads introduced by John Hughes.
4982 For more details, see
4987 “Generalising Monads to Arrows”,
4988 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4989 pp67–111, May 2000.
4995 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4996 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5002 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5003 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5009 and the arrows web page at
5010 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5011 With the <option>-XArrows</option> flag, GHC supports the arrow
5012 notation described in the second of these papers.
5013 What follows is a brief introduction to the notation;
5014 it won't make much sense unless you've read Hughes's paper.
5015 This notation is translated to ordinary Haskell,
5016 using combinators from the
5017 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5021 <para>The extension adds a new kind of expression for defining arrows:
5023 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5024 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5026 where <literal>proc</literal> is a new keyword.
5027 The variables of the pattern are bound in the body of the
5028 <literal>proc</literal>-expression,
5029 which is a new sort of thing called a <firstterm>command</firstterm>.
5030 The syntax of commands is as follows:
5032 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5033 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5034 | <replaceable>cmd</replaceable><superscript>0</superscript>
5036 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5037 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5038 infix operators as for expressions, and
5040 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5041 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5042 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5043 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5044 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5045 | <replaceable>fcmd</replaceable>
5047 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5048 | ( <replaceable>cmd</replaceable> )
5049 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5051 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5052 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5053 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5054 | <replaceable>cmd</replaceable>
5056 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5057 except that the bodies are commands instead of expressions.
5061 Commands produce values, but (like monadic computations)
5062 may yield more than one value,
5063 or none, and may do other things as well.
5064 For the most part, familiarity with monadic notation is a good guide to
5066 However the values of expressions, even monadic ones,
5067 are determined by the values of the variables they contain;
5068 this is not necessarily the case for commands.
5072 A simple example of the new notation is the expression
5074 proc x -> f -< x+1
5076 We call this a <firstterm>procedure</firstterm> or
5077 <firstterm>arrow abstraction</firstterm>.
5078 As with a lambda expression, the variable <literal>x</literal>
5079 is a new variable bound within the <literal>proc</literal>-expression.
5080 It refers to the input to the arrow.
5081 In the above example, <literal>-<</literal> is not an identifier but an
5082 new reserved symbol used for building commands from an expression of arrow
5083 type and an expression to be fed as input to that arrow.
5084 (The weird look will make more sense later.)
5085 It may be read as analogue of application for arrows.
5086 The above example is equivalent to the Haskell expression
5088 arr (\ x -> x+1) >>> f
5090 That would make no sense if the expression to the left of
5091 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5092 More generally, the expression to the left of <literal>-<</literal>
5093 may not involve any <firstterm>local variable</firstterm>,
5094 i.e. a variable bound in the current arrow abstraction.
5095 For such a situation there is a variant <literal>-<<</literal>, as in
5097 proc x -> f x -<< x+1
5099 which is equivalent to
5101 arr (\ x -> (f x, x+1)) >>> app
5103 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5105 Such an arrow is equivalent to a monad, so if you're using this form
5106 you may find a monadic formulation more convenient.
5110 <title>do-notation for commands</title>
5113 Another form of command is a form of <literal>do</literal>-notation.
5114 For example, you can write
5123 You can read this much like ordinary <literal>do</literal>-notation,
5124 but with commands in place of monadic expressions.
5125 The first line sends the value of <literal>x+1</literal> as an input to
5126 the arrow <literal>f</literal>, and matches its output against
5127 <literal>y</literal>.
5128 In the next line, the output is discarded.
5129 The arrow <function>returnA</function> is defined in the
5130 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5131 module as <literal>arr id</literal>.
5132 The above example is treated as an abbreviation for
5134 arr (\ x -> (x, x)) >>>
5135 first (arr (\ x -> x+1) >>> f) >>>
5136 arr (\ (y, x) -> (y, (x, y))) >>>
5137 first (arr (\ y -> 2*y) >>> g) >>>
5139 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5140 first (arr (\ (x, z) -> x*z) >>> h) >>>
5141 arr (\ (t, z) -> t+z) >>>
5144 Note that variables not used later in the composition are projected out.
5145 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5147 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5148 module, this reduces to
5150 arr (\ x -> (x+1, x)) >>>
5152 arr (\ (y, x) -> (2*y, (x, y))) >>>
5154 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5156 arr (\ (t, z) -> t+z)
5158 which is what you might have written by hand.
5159 With arrow notation, GHC keeps track of all those tuples of variables for you.
5163 Note that although the above translation suggests that
5164 <literal>let</literal>-bound variables like <literal>z</literal> must be
5165 monomorphic, the actual translation produces Core,
5166 so polymorphic variables are allowed.
5170 It's also possible to have mutually recursive bindings,
5171 using the new <literal>rec</literal> keyword, as in the following example:
5173 counter :: ArrowCircuit a => a Bool Int
5174 counter = proc reset -> do
5175 rec output <- returnA -< if reset then 0 else next
5176 next <- delay 0 -< output+1
5177 returnA -< output
5179 The translation of such forms uses the <function>loop</function> combinator,
5180 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5186 <title>Conditional commands</title>
5189 In the previous example, we used a conditional expression to construct the
5191 Sometimes we want to conditionally execute different commands, as in
5198 which is translated to
5200 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5201 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5203 Since the translation uses <function>|||</function>,
5204 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5208 There are also <literal>case</literal> commands, like
5214 y <- h -< (x1, x2)
5218 The syntax is the same as for <literal>case</literal> expressions,
5219 except that the bodies of the alternatives are commands rather than expressions.
5220 The translation is similar to that of <literal>if</literal> commands.
5226 <title>Defining your own control structures</title>
5229 As we're seen, arrow notation provides constructs,
5230 modelled on those for expressions,
5231 for sequencing, value recursion and conditionals.
5232 But suitable combinators,
5233 which you can define in ordinary Haskell,
5234 may also be used to build new commands out of existing ones.
5235 The basic idea is that a command defines an arrow from environments to values.
5236 These environments assign values to the free local variables of the command.
5237 Thus combinators that produce arrows from arrows
5238 may also be used to build commands from commands.
5239 For example, the <literal>ArrowChoice</literal> class includes a combinator
5241 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5243 so we can use it to build commands:
5245 expr' = proc x -> do
5248 symbol Plus -< ()
5249 y <- term -< ()
5252 symbol Minus -< ()
5253 y <- term -< ()
5256 (The <literal>do</literal> on the first line is needed to prevent the first
5257 <literal><+> ...</literal> from being interpreted as part of the
5258 expression on the previous line.)
5259 This is equivalent to
5261 expr' = (proc x -> returnA -< x)
5262 <+> (proc x -> do
5263 symbol Plus -< ()
5264 y <- term -< ()
5266 <+> (proc x -> do
5267 symbol Minus -< ()
5268 y <- term -< ()
5271 It is essential that this operator be polymorphic in <literal>e</literal>
5272 (representing the environment input to the command
5273 and thence to its subcommands)
5274 and satisfy the corresponding naturality property
5276 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5278 at least for strict <literal>k</literal>.
5279 (This should be automatic if you're not using <function>seq</function>.)
5280 This ensures that environments seen by the subcommands are environments
5281 of the whole command,
5282 and also allows the translation to safely trim these environments.
5283 The operator must also not use any variable defined within the current
5288 We could define our own operator
5290 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5291 untilA body cond = proc x ->
5292 if cond x then returnA -< ()
5295 untilA body cond -< x
5297 and use it in the same way.
5298 Of course this infix syntax only makes sense for binary operators;
5299 there is also a more general syntax involving special brackets:
5303 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5310 <title>Primitive constructs</title>
5313 Some operators will need to pass additional inputs to their subcommands.
5314 For example, in an arrow type supporting exceptions,
5315 the operator that attaches an exception handler will wish to pass the
5316 exception that occurred to the handler.
5317 Such an operator might have a type
5319 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5321 where <literal>Ex</literal> is the type of exceptions handled.
5322 You could then use this with arrow notation by writing a command
5324 body `handleA` \ ex -> handler
5326 so that if an exception is raised in the command <literal>body</literal>,
5327 the variable <literal>ex</literal> is bound to the value of the exception
5328 and the command <literal>handler</literal>,
5329 which typically refers to <literal>ex</literal>, is entered.
5330 Though the syntax here looks like a functional lambda,
5331 we are talking about commands, and something different is going on.
5332 The input to the arrow represented by a command consists of values for
5333 the free local variables in the command, plus a stack of anonymous values.
5334 In all the prior examples, this stack was empty.
5335 In the second argument to <function>handleA</function>,
5336 this stack consists of one value, the value of the exception.
5337 The command form of lambda merely gives this value a name.
5342 the values on the stack are paired to the right of the environment.
5343 So operators like <function>handleA</function> that pass
5344 extra inputs to their subcommands can be designed for use with the notation
5345 by pairing the values with the environment in this way.
5346 More precisely, the type of each argument of the operator (and its result)
5347 should have the form
5349 a (...(e,t1), ... tn) t
5351 where <replaceable>e</replaceable> is a polymorphic variable
5352 (representing the environment)
5353 and <replaceable>ti</replaceable> are the types of the values on the stack,
5354 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5355 The polymorphic variable <replaceable>e</replaceable> must not occur in
5356 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5357 <replaceable>t</replaceable>.
5358 However the arrows involved need not be the same.
5359 Here are some more examples of suitable operators:
5361 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5362 runReader :: ... => a e c -> a' (e,State) c
5363 runState :: ... => a e c -> a' (e,State) (c,State)
5365 We can supply the extra input required by commands built with the last two
5366 by applying them to ordinary expressions, as in
5370 (|runReader (do { ... })|) s
5372 which adds <literal>s</literal> to the stack of inputs to the command
5373 built using <function>runReader</function>.
5377 The command versions of lambda abstraction and application are analogous to
5378 the expression versions.
5379 In particular, the beta and eta rules describe equivalences of commands.
5380 These three features (operators, lambda abstraction and application)
5381 are the core of the notation; everything else can be built using them,
5382 though the results would be somewhat clumsy.
5383 For example, we could simulate <literal>do</literal>-notation by defining
5385 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5386 u `bind` f = returnA &&& u >>> f
5388 bind_ :: Arrow a => a e b -> a e c -> a e c
5389 u `bind_` f = u `bind` (arr fst >>> f)
5391 We could simulate <literal>if</literal> by defining
5393 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5394 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5401 <title>Differences with the paper</title>
5406 <para>Instead of a single form of arrow application (arrow tail) with two
5407 translations, the implementation provides two forms
5408 <quote><literal>-<</literal></quote> (first-order)
5409 and <quote><literal>-<<</literal></quote> (higher-order).
5414 <para>User-defined operators are flagged with banana brackets instead of
5415 a new <literal>form</literal> keyword.
5424 <title>Portability</title>
5427 Although only GHC implements arrow notation directly,
5428 there is also a preprocessor
5430 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5431 that translates arrow notation into Haskell 98
5432 for use with other Haskell systems.
5433 You would still want to check arrow programs with GHC;
5434 tracing type errors in the preprocessor output is not easy.
5435 Modules intended for both GHC and the preprocessor must observe some
5436 additional restrictions:
5441 The module must import
5442 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5448 The preprocessor cannot cope with other Haskell extensions.
5449 These would have to go in separate modules.
5455 Because the preprocessor targets Haskell (rather than Core),
5456 <literal>let</literal>-bound variables are monomorphic.
5467 <!-- ==================== BANG PATTERNS ================= -->
5469 <sect1 id="bang-patterns">
5470 <title>Bang patterns
5471 <indexterm><primary>Bang patterns</primary></indexterm>
5473 <para>GHC supports an extension of pattern matching called <emphasis>bang
5474 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5476 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5477 prime feature description</ulink> contains more discussion and examples
5478 than the material below.
5481 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5484 <sect2 id="bang-patterns-informal">
5485 <title>Informal description of bang patterns
5488 The main idea is to add a single new production to the syntax of patterns:
5492 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5493 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5498 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5499 whereas without the bang it would be lazy.
5500 Bang patterns can be nested of course:
5504 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5505 <literal>y</literal>.
5506 A bang only really has an effect if it precedes a variable or wild-card pattern:
5511 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5512 forces evaluation anyway does nothing.
5514 Bang patterns work in <literal>case</literal> expressions too, of course:
5516 g5 x = let y = f x in body
5517 g6 x = case f x of { y -> body }
5518 g7 x = case f x of { !y -> body }
5520 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5521 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5522 result, and then evaluates <literal>body</literal>.
5524 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5525 definitions too. For example:
5529 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5530 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5531 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5532 in a function argument <literal>![x,y]</literal> means the
5533 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5534 is part of the syntax of <literal>let</literal> bindings.
5539 <sect2 id="bang-patterns-sem">
5540 <title>Syntax and semantics
5544 We add a single new production to the syntax of patterns:
5548 There is one problem with syntactic ambiguity. Consider:
5552 Is this a definition of the infix function "<literal>(!)</literal>",
5553 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5554 ambiguity in favour of the latter. If you want to define
5555 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5560 The semantics of Haskell pattern matching is described in <ulink
5561 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5562 Section 3.17.2</ulink> of the Haskell Report. To this description add
5563 one extra item 10, saying:
5564 <itemizedlist><listitem><para>Matching
5565 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5566 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5567 <listitem><para>otherwise, <literal>pat</literal> is matched against
5568 <literal>v</literal></para></listitem>
5570 </para></listitem></itemizedlist>
5571 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5572 Section 3.17.3</ulink>, add a new case (t):
5574 case v of { !pat -> e; _ -> e' }
5575 = v `seq` case v of { pat -> e; _ -> e' }
5578 That leaves let expressions, whose translation is given in
5579 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5581 of the Haskell Report.
5582 In the translation box, first apply
5583 the following transformation: for each pattern <literal>pi</literal> that is of
5584 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5585 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5586 have a bang at the top, apply the rules in the existing box.
5588 <para>The effect of the let rule is to force complete matching of the pattern
5589 <literal>qi</literal> before evaluation of the body is begun. The bang is
5590 retained in the translated form in case <literal>qi</literal> is a variable,
5598 The let-binding can be recursive. However, it is much more common for
5599 the let-binding to be non-recursive, in which case the following law holds:
5600 <literal>(let !p = rhs in body)</literal>
5602 <literal>(case rhs of !p -> body)</literal>
5605 A pattern with a bang at the outermost level is not allowed at the top level of
5611 <!-- ==================== ASSERTIONS ================= -->
5613 <sect1 id="assertions">
5615 <indexterm><primary>Assertions</primary></indexterm>
5619 If you want to make use of assertions in your standard Haskell code, you
5620 could define a function like the following:
5626 assert :: Bool -> a -> a
5627 assert False x = error "assertion failed!"
5634 which works, but gives you back a less than useful error message --
5635 an assertion failed, but which and where?
5639 One way out is to define an extended <function>assert</function> function which also
5640 takes a descriptive string to include in the error message and
5641 perhaps combine this with the use of a pre-processor which inserts
5642 the source location where <function>assert</function> was used.
5646 Ghc offers a helping hand here, doing all of this for you. For every
5647 use of <function>assert</function> in the user's source:
5653 kelvinToC :: Double -> Double
5654 kelvinToC k = assert (k >= 0.0) (k+273.15)
5660 Ghc will rewrite this to also include the source location where the
5667 assert pred val ==> assertError "Main.hs|15" pred val
5673 The rewrite is only performed by the compiler when it spots
5674 applications of <function>Control.Exception.assert</function>, so you
5675 can still define and use your own versions of
5676 <function>assert</function>, should you so wish. If not, import
5677 <literal>Control.Exception</literal> to make use
5678 <function>assert</function> in your code.
5682 GHC ignores assertions when optimisation is turned on with the
5683 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5684 <literal>assert pred e</literal> will be rewritten to
5685 <literal>e</literal>. You can also disable assertions using the
5686 <option>-fignore-asserts</option>
5687 option<indexterm><primary><option>-fignore-asserts</option></primary>
5688 </indexterm>.</para>
5691 Assertion failures can be caught, see the documentation for the
5692 <literal>Control.Exception</literal> library for the details.
5698 <!-- =============================== PRAGMAS =========================== -->
5700 <sect1 id="pragmas">
5701 <title>Pragmas</title>
5703 <indexterm><primary>pragma</primary></indexterm>
5705 <para>GHC supports several pragmas, or instructions to the
5706 compiler placed in the source code. Pragmas don't normally affect
5707 the meaning of the program, but they might affect the efficiency
5708 of the generated code.</para>
5710 <para>Pragmas all take the form
5712 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5714 where <replaceable>word</replaceable> indicates the type of
5715 pragma, and is followed optionally by information specific to that
5716 type of pragma. Case is ignored in
5717 <replaceable>word</replaceable>. The various values for
5718 <replaceable>word</replaceable> that GHC understands are described
5719 in the following sections; any pragma encountered with an
5720 unrecognised <replaceable>word</replaceable> is (silently)
5723 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
5724 pragma must precede the <literal>module</literal> keyword in the file.
5725 There can be as many file-header pragmas as you please, and they can be
5726 preceded or followed by comments.</para>
5728 <sect2 id="language-pragma">
5729 <title>LANGUAGE pragma</title>
5731 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5732 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5734 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
5736 It is the intention that all Haskell compilers support the
5737 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5738 all extensions are supported by all compilers, of
5739 course. The <literal>LANGUAGE</literal> pragma should be used instead
5740 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5742 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5744 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5746 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5748 <para>Every language extension can also be turned into a command-line flag
5749 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
5750 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
5753 <para>A list of all supported language extensions can be obtained by invoking
5754 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
5756 <para>Any extension from the <literal>Extension</literal> type defined in
5758 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
5759 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
5763 <sect2 id="options-pragma">
5764 <title>OPTIONS_GHC pragma</title>
5765 <indexterm><primary>OPTIONS_GHC</primary>
5767 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5770 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5771 additional options that are given to the compiler when compiling
5772 this source file. See <xref linkend="source-file-options"/> for
5775 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5776 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5779 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5781 <sect2 id="include-pragma">
5782 <title>INCLUDE pragma</title>
5784 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5785 of C header files that should be <literal>#include</literal>'d into
5786 the C source code generated by the compiler for the current module (if
5787 compiling via C). For example:</para>
5790 {-# INCLUDE "foo.h" #-}
5791 {-# INCLUDE <stdio.h> #-}</programlisting>
5793 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5795 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5796 to the <option>-#include</option> option (<xref
5797 linkend="options-C-compiler" />), because the
5798 <literal>INCLUDE</literal> pragma is understood by other
5799 compilers. Yet another alternative is to add the include file to each
5800 <literal>foreign import</literal> declaration in your code, but we
5801 don't recommend using this approach with GHC.</para>
5804 <sect2 id="deprecated-pragma">
5805 <title>DEPRECATED pragma</title>
5806 <indexterm><primary>DEPRECATED</primary>
5809 <para>The DEPRECATED pragma lets you specify that a particular
5810 function, class, or type, is deprecated. There are two
5815 <para>You can deprecate an entire module thus:</para>
5817 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5820 <para>When you compile any module that import
5821 <literal>Wibble</literal>, GHC will print the specified
5826 <para>You can deprecate a function, class, type, or data constructor, with the
5827 following top-level declaration:</para>
5829 {-# DEPRECATED f, C, T "Don't use these" #-}
5831 <para>When you compile any module that imports and uses any
5832 of the specified entities, GHC will print the specified
5834 <para> You can only deprecate entities declared at top level in the module
5835 being compiled, and you can only use unqualified names in the list of
5836 entities being deprecated. A capitalised name, such as <literal>T</literal>
5837 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5838 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5839 both are in scope. If both are in scope, there is currently no way to deprecate
5840 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5843 Any use of the deprecated item, or of anything from a deprecated
5844 module, will be flagged with an appropriate message. However,
5845 deprecations are not reported for
5846 (a) uses of a deprecated function within its defining module, and
5847 (b) uses of a deprecated function in an export list.
5848 The latter reduces spurious complaints within a library
5849 in which one module gathers together and re-exports
5850 the exports of several others.
5852 <para>You can suppress the warnings with the flag
5853 <option>-fno-warn-deprecations</option>.</para>
5856 <sect2 id="inline-noinline-pragma">
5857 <title>INLINE and NOINLINE pragmas</title>
5859 <para>These pragmas control the inlining of function
5862 <sect3 id="inline-pragma">
5863 <title>INLINE pragma</title>
5864 <indexterm><primary>INLINE</primary></indexterm>
5866 <para>GHC (with <option>-O</option>, as always) tries to
5867 inline (or “unfold”) functions/values that are
5868 “small enough,” thus avoiding the call overhead
5869 and possibly exposing other more-wonderful optimisations.
5870 Normally, if GHC decides a function is “too
5871 expensive” to inline, it will not do so, nor will it
5872 export that unfolding for other modules to use.</para>
5874 <para>The sledgehammer you can bring to bear is the
5875 <literal>INLINE</literal><indexterm><primary>INLINE
5876 pragma</primary></indexterm> pragma, used thusly:</para>
5879 key_function :: Int -> String -> (Bool, Double)
5881 #ifdef __GLASGOW_HASKELL__
5882 {-# INLINE key_function #-}
5886 <para>(You don't need to do the C pre-processor carry-on
5887 unless you're going to stick the code through HBC—it
5888 doesn't like <literal>INLINE</literal> pragmas.)</para>
5890 <para>The major effect of an <literal>INLINE</literal> pragma
5891 is to declare a function's “cost” to be very low.
5892 The normal unfolding machinery will then be very keen to
5893 inline it. However, an <literal>INLINE</literal> pragma for a
5894 function "<literal>f</literal>" has a number of other effects:
5897 No funtions are inlined into <literal>f</literal>. Otherwise
5898 GHC might inline a big function into <literal>f</literal>'s right hand side,
5899 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
5902 The float-in, float-out, and common-sub-expression transformations are not
5903 applied to the body of <literal>f</literal>.
5906 An INLINE function is not worker/wrappered by strictness analysis.
5907 It's going to be inlined wholesale instead.
5910 All of these effects are aimed at ensuring that what gets inlined is
5911 exactly what you asked for, no more and no less.
5913 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5914 function can be put anywhere its type signature could be
5917 <para><literal>INLINE</literal> pragmas are a particularly
5919 <literal>then</literal>/<literal>return</literal> (or
5920 <literal>bind</literal>/<literal>unit</literal>) functions in
5921 a monad. For example, in GHC's own
5922 <literal>UniqueSupply</literal> monad code, we have:</para>
5925 #ifdef __GLASGOW_HASKELL__
5926 {-# INLINE thenUs #-}
5927 {-# INLINE returnUs #-}
5931 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5932 linkend="noinline-pragma"/>).</para>
5935 <sect3 id="noinline-pragma">
5936 <title>NOINLINE pragma</title>
5938 <indexterm><primary>NOINLINE</primary></indexterm>
5939 <indexterm><primary>NOTINLINE</primary></indexterm>
5941 <para>The <literal>NOINLINE</literal> pragma does exactly what
5942 you'd expect: it stops the named function from being inlined
5943 by the compiler. You shouldn't ever need to do this, unless
5944 you're very cautious about code size.</para>
5946 <para><literal>NOTINLINE</literal> is a synonym for
5947 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5948 specified by Haskell 98 as the standard way to disable
5949 inlining, so it should be used if you want your code to be
5953 <sect3 id="phase-control">
5954 <title>Phase control</title>
5956 <para> Sometimes you want to control exactly when in GHC's
5957 pipeline the INLINE pragma is switched on. Inlining happens
5958 only during runs of the <emphasis>simplifier</emphasis>. Each
5959 run of the simplifier has a different <emphasis>phase
5960 number</emphasis>; the phase number decreases towards zero.
5961 If you use <option>-dverbose-core2core</option> you'll see the
5962 sequence of phase numbers for successive runs of the
5963 simplifier. In an INLINE pragma you can optionally specify a
5967 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5968 <literal>f</literal>
5969 until phase <literal>k</literal>, but from phase
5970 <literal>k</literal> onwards be very keen to inline it.
5973 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5974 <literal>f</literal>
5975 until phase <literal>k</literal>, but from phase
5976 <literal>k</literal> onwards do not inline it.
5979 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5980 <literal>f</literal>
5981 until phase <literal>k</literal>, but from phase
5982 <literal>k</literal> onwards be willing to inline it (as if
5983 there was no pragma).
5986 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5987 <literal>f</literal>
5988 until phase <literal>k</literal>, but from phase
5989 <literal>k</literal> onwards do not inline it.
5992 The same information is summarised here:
5994 -- Before phase 2 Phase 2 and later
5995 {-# INLINE [2] f #-} -- No Yes
5996 {-# INLINE [~2] f #-} -- Yes No
5997 {-# NOINLINE [2] f #-} -- No Maybe
5998 {-# NOINLINE [~2] f #-} -- Maybe No
6000 {-# INLINE f #-} -- Yes Yes
6001 {-# NOINLINE f #-} -- No No
6003 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6004 function body is small, or it is applied to interesting-looking arguments etc).
6005 Another way to understand the semantics is this:
6007 <listitem><para>For both INLINE and NOINLINE, the phase number says
6008 when inlining is allowed at all.</para></listitem>
6009 <listitem><para>The INLINE pragma has the additional effect of making the
6010 function body look small, so that when inlining is allowed it is very likely to
6015 <para>The same phase-numbering control is available for RULES
6016 (<xref linkend="rewrite-rules"/>).</para>
6020 <sect2 id="line-pragma">
6021 <title>LINE pragma</title>
6023 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6024 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6025 <para>This pragma is similar to C's <literal>#line</literal>
6026 pragma, and is mainly for use in automatically generated Haskell
6027 code. It lets you specify the line number and filename of the
6028 original code; for example</para>
6030 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6032 <para>if you'd generated the current file from something called
6033 <filename>Foo.vhs</filename> and this line corresponds to line
6034 42 in the original. GHC will adjust its error messages to refer
6035 to the line/file named in the <literal>LINE</literal>
6040 <title>RULES pragma</title>
6042 <para>The RULES pragma lets you specify rewrite rules. It is
6043 described in <xref linkend="rewrite-rules"/>.</para>
6046 <sect2 id="specialize-pragma">
6047 <title>SPECIALIZE pragma</title>
6049 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6050 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6051 <indexterm><primary>overloading, death to</primary></indexterm>
6053 <para>(UK spelling also accepted.) For key overloaded
6054 functions, you can create extra versions (NB: more code space)
6055 specialised to particular types. Thus, if you have an
6056 overloaded function:</para>
6059 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6062 <para>If it is heavily used on lists with
6063 <literal>Widget</literal> keys, you could specialise it as
6067 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6070 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6071 be put anywhere its type signature could be put.</para>
6073 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6074 (a) a specialised version of the function and (b) a rewrite rule
6075 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6076 un-specialised function into a call to the specialised one.</para>
6078 <para>The type in a SPECIALIZE pragma can be any type that is less
6079 polymorphic than the type of the original function. In concrete terms,
6080 if the original function is <literal>f</literal> then the pragma
6082 {-# SPECIALIZE f :: <type> #-}
6084 is valid if and only if the definition
6086 f_spec :: <type>
6089 is valid. Here are some examples (where we only give the type signature
6090 for the original function, not its code):
6092 f :: Eq a => a -> b -> b
6093 {-# SPECIALISE f :: Int -> b -> b #-}
6095 g :: (Eq a, Ix b) => a -> b -> b
6096 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6098 h :: Eq a => a -> a -> a
6099 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6101 The last of these examples will generate a
6102 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6103 well. If you use this kind of specialisation, let us know how well it works.
6106 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6107 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6108 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6109 The <literal>INLINE</literal> pragma affects the specialised version of the
6110 function (only), and applies even if the function is recursive. The motivating
6113 -- A GADT for arrays with type-indexed representation
6115 ArrInt :: !Int -> ByteArray# -> Arr Int
6116 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6118 (!:) :: Arr e -> Int -> e
6119 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6120 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6121 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6122 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6124 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6125 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6126 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6127 the specialised function will be inlined. It has two calls to
6128 <literal>(!:)</literal>,
6129 both at type <literal>Int</literal>. Both these calls fire the first
6130 specialisation, whose body is also inlined. The result is a type-based
6131 unrolling of the indexing function.</para>
6132 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6133 on an ordinarily-recursive function.</para>
6135 <para>Note: In earlier versions of GHC, it was possible to provide your own
6136 specialised function for a given type:
6139 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6142 This feature has been removed, as it is now subsumed by the
6143 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6147 <sect2 id="specialize-instance-pragma">
6148 <title>SPECIALIZE instance pragma
6152 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6153 <indexterm><primary>overloading, death to</primary></indexterm>
6154 Same idea, except for instance declarations. For example:
6157 instance (Eq a) => Eq (Foo a) where {
6158 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6162 The pragma must occur inside the <literal>where</literal> part
6163 of the instance declaration.
6166 Compatible with HBC, by the way, except perhaps in the placement
6172 <sect2 id="unpack-pragma">
6173 <title>UNPACK pragma</title>
6175 <indexterm><primary>UNPACK</primary></indexterm>
6177 <para>The <literal>UNPACK</literal> indicates to the compiler
6178 that it should unpack the contents of a constructor field into
6179 the constructor itself, removing a level of indirection. For
6183 data T = T {-# UNPACK #-} !Float
6184 {-# UNPACK #-} !Float
6187 <para>will create a constructor <literal>T</literal> containing
6188 two unboxed floats. This may not always be an optimisation: if
6189 the <function>T</function> constructor is scrutinised and the
6190 floats passed to a non-strict function for example, they will
6191 have to be reboxed (this is done automatically by the
6194 <para>Unpacking constructor fields should only be used in
6195 conjunction with <option>-O</option>, in order to expose
6196 unfoldings to the compiler so the reboxing can be removed as
6197 often as possible. For example:</para>
6201 f (T f1 f2) = f1 + f2
6204 <para>The compiler will avoid reboxing <function>f1</function>
6205 and <function>f2</function> by inlining <function>+</function>
6206 on floats, but only when <option>-O</option> is on.</para>
6208 <para>Any single-constructor data is eligible for unpacking; for
6212 data T = T {-# UNPACK #-} !(Int,Int)
6215 <para>will store the two <literal>Int</literal>s directly in the
6216 <function>T</function> constructor, by flattening the pair.
6217 Multi-level unpacking is also supported:</para>
6220 data T = T {-# UNPACK #-} !S
6221 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6224 <para>will store two unboxed <literal>Int#</literal>s
6225 directly in the <function>T</function> constructor. The
6226 unpacker can see through newtypes, too.</para>
6228 <para>If a field cannot be unpacked, you will not get a warning,
6229 so it might be an idea to check the generated code with
6230 <option>-ddump-simpl</option>.</para>
6232 <para>See also the <option>-funbox-strict-fields</option> flag,
6233 which essentially has the effect of adding
6234 <literal>{-# UNPACK #-}</literal> to every strict
6235 constructor field.</para>
6240 <!-- ======================= REWRITE RULES ======================== -->
6242 <sect1 id="rewrite-rules">
6243 <title>Rewrite rules
6245 <indexterm><primary>RULES pragma</primary></indexterm>
6246 <indexterm><primary>pragma, RULES</primary></indexterm>
6247 <indexterm><primary>rewrite rules</primary></indexterm></title>
6250 The programmer can specify rewrite rules as part of the source program
6251 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6252 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6253 and (b) the <option>-frules-off</option> flag
6254 (<xref linkend="options-f"/>) is not specified, and (c) the
6255 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6264 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6271 <title>Syntax</title>
6274 From a syntactic point of view:
6280 There may be zero or more rules in a <literal>RULES</literal> pragma.
6287 Each rule has a name, enclosed in double quotes. The name itself has
6288 no significance at all. It is only used when reporting how many times the rule fired.
6294 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6295 immediately after the name of the rule. Thus:
6298 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6301 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6302 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6311 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
6312 is set, so you must lay out your rules starting in the same column as the
6313 enclosing definitions.
6320 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6321 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6322 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6323 by spaces, just like in a type <literal>forall</literal>.
6329 A pattern variable may optionally have a type signature.
6330 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6331 For example, here is the <literal>foldr/build</literal> rule:
6334 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6335 foldr k z (build g) = g k z
6338 Since <function>g</function> has a polymorphic type, it must have a type signature.
6345 The left hand side of a rule must consist of a top-level variable applied
6346 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6349 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6350 "wrong2" forall f. f True = True
6353 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6360 A rule does not need to be in the same module as (any of) the
6361 variables it mentions, though of course they need to be in scope.
6367 Rules are automatically exported from a module, just as instance declarations are.
6378 <title>Semantics</title>
6381 From a semantic point of view:
6387 Rules are only applied if you use the <option>-O</option> flag.
6393 Rules are regarded as left-to-right rewrite rules.
6394 When GHC finds an expression that is a substitution instance of the LHS
6395 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6396 By "a substitution instance" we mean that the LHS can be made equal to the
6397 expression by substituting for the pattern variables.
6404 The LHS and RHS of a rule are typechecked, and must have the
6412 GHC makes absolutely no attempt to verify that the LHS and RHS
6413 of a rule have the same meaning. That is undecidable in general, and
6414 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6421 GHC makes no attempt to make sure that the rules are confluent or
6422 terminating. For example:
6425 "loop" forall x,y. f x y = f y x
6428 This rule will cause the compiler to go into an infinite loop.
6435 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6441 GHC currently uses a very simple, syntactic, matching algorithm
6442 for matching a rule LHS with an expression. It seeks a substitution
6443 which makes the LHS and expression syntactically equal modulo alpha
6444 conversion. The pattern (rule), but not the expression, is eta-expanded if
6445 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6446 But not beta conversion (that's called higher-order matching).
6450 Matching is carried out on GHC's intermediate language, which includes
6451 type abstractions and applications. So a rule only matches if the
6452 types match too. See <xref linkend="rule-spec"/> below.
6458 GHC keeps trying to apply the rules as it optimises the program.
6459 For example, consider:
6468 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6469 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6470 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6471 not be substituted, and the rule would not fire.
6478 In the earlier phases of compilation, GHC inlines <emphasis>nothing
6479 that appears on the LHS of a rule</emphasis>, because once you have substituted
6480 for something you can't match against it (given the simple minded
6481 matching). So if you write the rule
6484 "map/map" forall f,g. map f . map g = map (f.g)
6487 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
6488 It will only match something written with explicit use of ".".
6489 Well, not quite. It <emphasis>will</emphasis> match the expression
6495 where <function>wibble</function> is defined:
6498 wibble f g = map f . map g
6501 because <function>wibble</function> will be inlined (it's small).
6503 Later on in compilation, GHC starts inlining even things on the
6504 LHS of rules, but still leaves the rules enabled. This inlining
6505 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
6512 All rules are implicitly exported from the module, and are therefore
6513 in force in any module that imports the module that defined the rule, directly
6514 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6515 in force when compiling A.) The situation is very similar to that for instance
6527 <title>List fusion</title>
6530 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6531 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6532 intermediate list should be eliminated entirely.
6536 The following are good producers:
6548 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6554 Explicit lists (e.g. <literal>[True, False]</literal>)
6560 The cons constructor (e.g <literal>3:4:[]</literal>)
6566 <function>++</function>
6572 <function>map</function>
6578 <function>take</function>, <function>filter</function>
6584 <function>iterate</function>, <function>repeat</function>
6590 <function>zip</function>, <function>zipWith</function>
6599 The following are good consumers:
6611 <function>array</function> (on its second argument)
6617 <function>++</function> (on its first argument)
6623 <function>foldr</function>
6629 <function>map</function>
6635 <function>take</function>, <function>filter</function>
6641 <function>concat</function>
6647 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6653 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6654 will fuse with one but not the other)
6660 <function>partition</function>
6666 <function>head</function>
6672 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6678 <function>sequence_</function>
6684 <function>msum</function>
6690 <function>sortBy</function>
6699 So, for example, the following should generate no intermediate lists:
6702 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6708 This list could readily be extended; if there are Prelude functions that you use
6709 a lot which are not included, please tell us.
6713 If you want to write your own good consumers or producers, look at the
6714 Prelude definitions of the above functions to see how to do so.
6719 <sect2 id="rule-spec">
6720 <title>Specialisation
6724 Rewrite rules can be used to get the same effect as a feature
6725 present in earlier versions of GHC.
6726 For example, suppose that:
6729 genericLookup :: Ord a => Table a b -> a -> b
6730 intLookup :: Table Int b -> Int -> b
6733 where <function>intLookup</function> is an implementation of
6734 <function>genericLookup</function> that works very fast for
6735 keys of type <literal>Int</literal>. You might wish
6736 to tell GHC to use <function>intLookup</function> instead of
6737 <function>genericLookup</function> whenever the latter was called with
6738 type <literal>Table Int b -> Int -> b</literal>.
6739 It used to be possible to write
6742 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6745 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6748 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6751 This slightly odd-looking rule instructs GHC to replace
6752 <function>genericLookup</function> by <function>intLookup</function>
6753 <emphasis>whenever the types match</emphasis>.
6754 What is more, this rule does not need to be in the same
6755 file as <function>genericLookup</function>, unlike the
6756 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6757 have an original definition available to specialise).
6760 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6761 <function>intLookup</function> really behaves as a specialised version
6762 of <function>genericLookup</function>!!!</para>
6764 <para>An example in which using <literal>RULES</literal> for
6765 specialisation will Win Big:
6768 toDouble :: Real a => a -> Double
6769 toDouble = fromRational . toRational
6771 {-# RULES "toDouble/Int" toDouble = i2d #-}
6772 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6775 The <function>i2d</function> function is virtually one machine
6776 instruction; the default conversion—via an intermediate
6777 <literal>Rational</literal>—is obscenely expensive by
6784 <title>Controlling what's going on</title>
6792 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6798 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6799 If you add <option>-dppr-debug</option> you get a more detailed listing.
6805 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
6808 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6809 {-# INLINE build #-}
6813 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6814 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6815 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6816 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6823 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6824 see how to write rules that will do fusion and yet give an efficient
6825 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6835 <sect2 id="core-pragma">
6836 <title>CORE pragma</title>
6838 <indexterm><primary>CORE pragma</primary></indexterm>
6839 <indexterm><primary>pragma, CORE</primary></indexterm>
6840 <indexterm><primary>core, annotation</primary></indexterm>
6843 The external core format supports <quote>Note</quote> annotations;
6844 the <literal>CORE</literal> pragma gives a way to specify what these
6845 should be in your Haskell source code. Syntactically, core
6846 annotations are attached to expressions and take a Haskell string
6847 literal as an argument. The following function definition shows an
6851 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6854 Semantically, this is equivalent to:
6862 However, when external for is generated (via
6863 <option>-fext-core</option>), there will be Notes attached to the
6864 expressions <function>show</function> and <varname>x</varname>.
6865 The core function declaration for <function>f</function> is:
6869 f :: %forall a . GHCziShow.ZCTShow a ->
6870 a -> GHCziBase.ZMZN GHCziBase.Char =
6871 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6873 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6875 (tpl1::GHCziBase.Int ->
6877 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6879 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6880 (tpl3::GHCziBase.ZMZN a ->
6881 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6889 Here, we can see that the function <function>show</function> (which
6890 has been expanded out to a case expression over the Show dictionary)
6891 has a <literal>%note</literal> attached to it, as does the
6892 expression <varname>eta</varname> (which used to be called
6893 <varname>x</varname>).
6900 <sect1 id="special-ids">
6901 <title>Special built-in functions</title>
6902 <para>GHC has a few built-in functions with special behaviour. These
6903 are now described in the module <ulink
6904 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
6905 in the library documentation.</para>
6909 <sect1 id="generic-classes">
6910 <title>Generic classes</title>
6913 The ideas behind this extension are described in detail in "Derivable type classes",
6914 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6915 An example will give the idea:
6923 fromBin :: [Int] -> (a, [Int])
6925 toBin {| Unit |} Unit = []
6926 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6927 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6928 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6930 fromBin {| Unit |} bs = (Unit, bs)
6931 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6932 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6933 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6934 (y,bs'') = fromBin bs'
6937 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6938 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6939 which are defined thus in the library module <literal>Generics</literal>:
6943 data a :+: b = Inl a | Inr b
6944 data a :*: b = a :*: b
6947 Now you can make a data type into an instance of Bin like this:
6949 instance (Bin a, Bin b) => Bin (a,b)
6950 instance Bin a => Bin [a]
6952 That is, just leave off the "where" clause. Of course, you can put in the
6953 where clause and over-ride whichever methods you please.
6957 <title> Using generics </title>
6958 <para>To use generics you need to</para>
6961 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6962 <option>-XGenerics</option> (to generate extra per-data-type code),
6963 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6967 <para>Import the module <literal>Generics</literal> from the
6968 <literal>lang</literal> package. This import brings into
6969 scope the data types <literal>Unit</literal>,
6970 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6971 don't need this import if you don't mention these types
6972 explicitly; for example, if you are simply giving instance
6973 declarations.)</para>
6978 <sect2> <title> Changes wrt the paper </title>
6980 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6981 can be written infix (indeed, you can now use
6982 any operator starting in a colon as an infix type constructor). Also note that
6983 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6984 Finally, note that the syntax of the type patterns in the class declaration
6985 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6986 alone would ambiguous when they appear on right hand sides (an extension we
6987 anticipate wanting).
6991 <sect2> <title>Terminology and restrictions</title>
6993 Terminology. A "generic default method" in a class declaration
6994 is one that is defined using type patterns as above.
6995 A "polymorphic default method" is a default method defined as in Haskell 98.
6996 A "generic class declaration" is a class declaration with at least one
6997 generic default method.
7005 Alas, we do not yet implement the stuff about constructor names and
7012 A generic class can have only one parameter; you can't have a generic
7013 multi-parameter class.
7019 A default method must be defined entirely using type patterns, or entirely
7020 without. So this is illegal:
7023 op :: a -> (a, Bool)
7024 op {| Unit |} Unit = (Unit, True)
7027 However it is perfectly OK for some methods of a generic class to have
7028 generic default methods and others to have polymorphic default methods.
7034 The type variable(s) in the type pattern for a generic method declaration
7035 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:
7039 op {| p :*: q |} (x :*: y) = op (x :: p)
7047 The type patterns in a generic default method must take one of the forms:
7053 where "a" and "b" are type variables. Furthermore, all the type patterns for
7054 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7055 must use the same type variables. So this is illegal:
7059 op {| a :+: b |} (Inl x) = True
7060 op {| p :+: q |} (Inr y) = False
7062 The type patterns must be identical, even in equations for different methods of the class.
7063 So this too is illegal:
7067 op1 {| a :*: b |} (x :*: y) = True
7070 op2 {| p :*: q |} (x :*: y) = False
7072 (The reason for this restriction is that we gather all the equations for a particular type constructor
7073 into a single generic instance declaration.)
7079 A generic method declaration must give a case for each of the three type constructors.
7085 The type for a generic method can be built only from:
7087 <listitem> <para> Function arrows </para> </listitem>
7088 <listitem> <para> Type variables </para> </listitem>
7089 <listitem> <para> Tuples </para> </listitem>
7090 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7092 Here are some example type signatures for generic methods:
7095 op2 :: Bool -> (a,Bool)
7096 op3 :: [Int] -> a -> a
7099 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7103 This restriction is an implementation restriction: we just haven't got around to
7104 implementing the necessary bidirectional maps over arbitrary type constructors.
7105 It would be relatively easy to add specific type constructors, such as Maybe and list,
7106 to the ones that are allowed.</para>
7111 In an instance declaration for a generic class, the idea is that the compiler
7112 will fill in the methods for you, based on the generic templates. However it can only
7117 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7122 No constructor of the instance type has unboxed fields.
7126 (Of course, these things can only arise if you are already using GHC extensions.)
7127 However, you can still give an instance declarations for types which break these rules,
7128 provided you give explicit code to override any generic default methods.
7136 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7137 what the compiler does with generic declarations.
7142 <sect2> <title> Another example </title>
7144 Just to finish with, here's another example I rather like:
7148 nCons {| Unit |} _ = 1
7149 nCons {| a :*: b |} _ = 1
7150 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7153 tag {| Unit |} _ = 1
7154 tag {| a :*: b |} _ = 1
7155 tag {| a :+: b |} (Inl x) = tag x
7156 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7162 <sect1 id="monomorphism">
7163 <title>Control over monomorphism</title>
7165 <para>GHC supports two flags that control the way in which generalisation is
7166 carried out at let and where bindings.
7170 <title>Switching off the dreaded Monomorphism Restriction</title>
7171 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7173 <para>Haskell's monomorphism restriction (see
7174 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
7176 of the Haskell Report)
7177 can be completely switched off by
7178 <option>-XNoMonomorphismRestriction</option>.
7183 <title>Monomorphic pattern bindings</title>
7184 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7185 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7187 <para> As an experimental change, we are exploring the possibility of
7188 making pattern bindings monomorphic; that is, not generalised at all.
7189 A pattern binding is a binding whose LHS has no function arguments,
7190 and is not a simple variable. For example:
7192 f x = x -- Not a pattern binding
7193 f = \x -> x -- Not a pattern binding
7194 f :: Int -> Int = \x -> x -- Not a pattern binding
7196 (g,h) = e -- A pattern binding
7197 (f) = e -- A pattern binding
7198 [x] = e -- A pattern binding
7200 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7201 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
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