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 individually.</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>
294 <term><option>-XQuasiQuotes</option></term>
296 <para>Enables quasiquotation (see <xref
297 linkend="th-quasiquotation"/>).</para>
300 <literal>[:<replaceable>varid</replaceable>|</literal>.</para>
307 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
308 <sect1 id="primitives">
309 <title>Unboxed types and primitive operations</title>
311 <para>GHC is built on a raft of primitive data types and operations.
312 While you really can use this stuff to write fast code,
313 we generally find it a lot less painful, and more satisfying in the
314 long run, to use higher-level language features and libraries. With
315 any luck, the code you write will be optimised to the efficient
316 unboxed version in any case. And if it isn't, we'd like to know
319 <para>We do not currently have good, up-to-date documentation about the
320 primitives, perhaps because they are mainly intended for internal use.
321 There used to be a long section about them here in the User Guide, but it
322 became out of date, and wrong information is worse than none.</para>
324 <para>The Real Truth about what primitive types there are, and what operations
325 work over those types, is held in the file
326 <filename>compiler/prelude/primops.txt.pp</filename>.
327 This file is used directly to generate GHC's primitive-operation definitions, so
328 it is always correct! It is also intended for processing into text.</para>
331 the result of such processing is part of the description of the
333 url="http://www.haskell.org/ghc/docs/papers/core.ps.gz">External
334 Core language</ulink>.
335 So that document is a good place to look for a type-set version.
336 We would be very happy if someone wanted to volunteer to produce an XML
337 back end to the program that processes <filename>primops.txt</filename> so that
338 we could include the results here in the User Guide.</para>
340 <para>What follows here is a brief summary of some main points.</para>
342 <sect2 id="glasgow-unboxed">
347 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
350 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
351 that values of that type are represented by a pointer to a heap
352 object. The representation of a Haskell <literal>Int</literal>, for
353 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
354 type, however, is represented by the value itself, no pointers or heap
355 allocation are involved.
359 Unboxed types correspond to the “raw machine” types you
360 would use in C: <literal>Int#</literal> (long int),
361 <literal>Double#</literal> (double), <literal>Addr#</literal>
362 (void *), etc. The <emphasis>primitive operations</emphasis>
363 (PrimOps) on these types are what you might expect; e.g.,
364 <literal>(+#)</literal> is addition on
365 <literal>Int#</literal>s, and is the machine-addition that we all
366 know and love—usually one instruction.
369 <para> For some primitive types we have special syntax for literals.
370 Anything that would be an integer lexeme followed by a
371 <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
372 <literal>32#</literal> and <literal>-0x3A#</literal>. Likewise,
373 any non-negative integer literal followed by
374 <literal>##</literal> is a <literal>Word#</literal> literal.
375 Likewise, any floating point literal followed by a
376 <literal>#</literal> is a <literal>Float#</literal> literal, and
377 followed by <literal>##</literal> is a
378 <literal>Double#</literal>. Finally, a string literal followed by a
379 <literal>#</literal>, e.g. <literal>"foo"#</literal>,
380 is a <literal>Addr#</literal> literal.
384 Primitive (unboxed) types cannot be defined in Haskell, and are
385 therefore built into the language and compiler. Primitive types are
386 always unlifted; that is, a value of a primitive type cannot be
387 bottom. We use the convention that primitive types, values, and
388 operations have a <literal>#</literal> suffix.
392 Primitive values are often represented by a simple bit-pattern, such
393 as <literal>Int#</literal>, <literal>Float#</literal>,
394 <literal>Double#</literal>. But this is not necessarily the case:
395 a primitive value might be represented by a pointer to a
396 heap-allocated object. Examples include
397 <literal>Array#</literal>, the type of primitive arrays. A
398 primitive array is heap-allocated because it is too big a value to fit
399 in a register, and would be too expensive to copy around; in a sense,
400 it is accidental that it is represented by a pointer. If a pointer
401 represents a primitive value, then it really does point to that value:
402 no unevaluated thunks, no indirections…nothing can be at the
403 other end of the pointer than the primitive value.
404 A numerically-intensive program using unboxed types can
405 go a <emphasis>lot</emphasis> faster than its “standard”
406 counterpart—we saw a threefold speedup on one example.
410 There are some restrictions on the use of primitive types:
412 <listitem><para>The main restriction
413 is that you can't pass a primitive value to a polymorphic
414 function or store one in a polymorphic data type. This rules out
415 things like <literal>[Int#]</literal> (i.e. lists of primitive
416 integers). The reason for this restriction is that polymorphic
417 arguments and constructor fields are assumed to be pointers: if an
418 unboxed integer is stored in one of these, the garbage collector would
419 attempt to follow it, leading to unpredictable space leaks. Or a
420 <function>seq</function> operation on the polymorphic component may
421 attempt to dereference the pointer, with disastrous results. Even
422 worse, the unboxed value might be larger than a pointer
423 (<literal>Double#</literal> for instance).
426 <listitem><para> You cannot define a newtype whose representation type
427 (the argument type of the data constructor) is an unboxed type. Thus,
433 <listitem><para> You cannot bind a variable with an unboxed type
434 in a <emphasis>top-level</emphasis> binding.
436 <listitem><para> You cannot bind a variable with an unboxed type
437 in a <emphasis>recursive</emphasis> binding.
439 <listitem><para> You may bind unboxed variables in a (non-recursive,
440 non-top-level) pattern binding, but any such variable causes the entire
442 to become strict. For example:
444 data Foo = Foo Int Int#
446 f x = let (Foo a b, w) = ..rhs.. in ..body..
448 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
450 is strict, and the program behaves as if you had written
452 data Foo = Foo Int Int#
454 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
463 <sect2 id="unboxed-tuples">
464 <title>Unboxed Tuples
468 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
469 they're available by default with <option>-fglasgow-exts</option>. An
470 unboxed tuple looks like this:
482 where <literal>e_1..e_n</literal> are expressions of any
483 type (primitive or non-primitive). The type of an unboxed tuple looks
488 Unboxed tuples are used for functions that need to return multiple
489 values, but they avoid the heap allocation normally associated with
490 using fully-fledged tuples. When an unboxed tuple is returned, the
491 components are put directly into registers or on the stack; the
492 unboxed tuple itself does not have a composite representation. Many
493 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
495 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
496 tuples to avoid unnecessary allocation during sequences of operations.
500 There are some pretty stringent restrictions on the use of unboxed tuples:
505 Values of unboxed tuple types are subject to the same restrictions as
506 other unboxed types; i.e. they may not be stored in polymorphic data
507 structures or passed to polymorphic functions.
514 No variable can have an unboxed tuple type, nor may a constructor or function
515 argument have an unboxed tuple type. The following are all illegal:
519 data Foo = Foo (# Int, Int #)
521 f :: (# Int, Int #) -> (# Int, Int #)
524 g :: (# Int, Int #) -> Int
527 h x = let y = (# x,x #) in ...
534 The typical use of unboxed tuples is simply to return multiple values,
535 binding those multiple results with a <literal>case</literal> expression, thus:
537 f x y = (# x+1, y-1 #)
538 g x = case f x x of { (# a, b #) -> a + b }
540 You can have an unboxed tuple in a pattern binding, thus
542 f x = let (# p,q #) = h x in ..body..
544 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
545 the resulting binding is lazy like any other Haskell pattern binding. The
546 above example desugars like this:
548 f x = let t = case h x o f{ (# p,q #) -> (p,q)
553 Indeed, the bindings can even be recursive.
560 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
562 <sect1 id="syntax-extns">
563 <title>Syntactic extensions</title>
565 <!-- ====================== HIERARCHICAL MODULES ======================= -->
567 <sect2 id="hierarchical-modules">
568 <title>Hierarchical Modules</title>
570 <para>GHC supports a small extension to the syntax of module
571 names: a module name is allowed to contain a dot
572 <literal>‘.’</literal>. This is also known as the
573 “hierarchical module namespace” extension, because
574 it extends the normally flat Haskell module namespace into a
575 more flexible hierarchy of modules.</para>
577 <para>This extension has very little impact on the language
578 itself; modules names are <emphasis>always</emphasis> fully
579 qualified, so you can just think of the fully qualified module
580 name as <quote>the module name</quote>. In particular, this
581 means that the full module name must be given after the
582 <literal>module</literal> keyword at the beginning of the
583 module; for example, the module <literal>A.B.C</literal> must
586 <programlisting>module A.B.C</programlisting>
589 <para>It is a common strategy to use the <literal>as</literal>
590 keyword to save some typing when using qualified names with
591 hierarchical modules. For example:</para>
594 import qualified Control.Monad.ST.Strict as ST
597 <para>For details on how GHC searches for source and interface
598 files in the presence of hierarchical modules, see <xref
599 linkend="search-path"/>.</para>
601 <para>GHC comes with a large collection of libraries arranged
602 hierarchically; see the accompanying <ulink
603 url="../libraries/index.html">library
604 documentation</ulink>. More libraries to install are available
606 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
609 <!-- ====================== PATTERN GUARDS ======================= -->
611 <sect2 id="pattern-guards">
612 <title>Pattern guards</title>
615 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
616 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.)
620 Suppose we have an abstract data type of finite maps, with a
624 lookup :: FiniteMap -> Int -> Maybe Int
627 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
628 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
632 clunky env var1 var2 | ok1 && ok2 = val1 + val2
633 | otherwise = var1 + var2
644 The auxiliary functions are
648 maybeToBool :: Maybe a -> Bool
649 maybeToBool (Just x) = True
650 maybeToBool Nothing = False
652 expectJust :: Maybe a -> a
653 expectJust (Just x) = x
654 expectJust Nothing = error "Unexpected Nothing"
658 What is <function>clunky</function> doing? The guard <literal>ok1 &&
659 ok2</literal> checks that both lookups succeed, using
660 <function>maybeToBool</function> to convert the <function>Maybe</function>
661 types to booleans. The (lazily evaluated) <function>expectJust</function>
662 calls extract the values from the results of the lookups, and binds the
663 returned values to <varname>val1</varname> and <varname>val2</varname>
664 respectively. If either lookup fails, then clunky takes the
665 <literal>otherwise</literal> case and returns the sum of its arguments.
669 This is certainly legal Haskell, but it is a tremendously verbose and
670 un-obvious way to achieve the desired effect. Arguably, a more direct way
671 to write clunky would be to use case expressions:
675 clunky env var1 var2 = case lookup env var1 of
677 Just val1 -> case lookup env var2 of
679 Just val2 -> val1 + val2
685 This is a bit shorter, but hardly better. Of course, we can rewrite any set
686 of pattern-matching, guarded equations as case expressions; that is
687 precisely what the compiler does when compiling equations! The reason that
688 Haskell provides guarded equations is because they allow us to write down
689 the cases we want to consider, one at a time, independently of each other.
690 This structure is hidden in the case version. Two of the right-hand sides
691 are really the same (<function>fail</function>), and the whole expression
692 tends to become more and more indented.
696 Here is how I would write clunky:
701 | Just val1 <- lookup env var1
702 , Just val2 <- lookup env var2
704 ...other equations for clunky...
708 The semantics should be clear enough. The qualifiers are matched in order.
709 For a <literal><-</literal> qualifier, which I call a pattern guard, the
710 right hand side is evaluated and matched against the pattern on the left.
711 If the match fails then the whole guard fails and the next equation is
712 tried. If it succeeds, then the appropriate binding takes place, and the
713 next qualifier is matched, in the augmented environment. Unlike list
714 comprehensions, however, the type of the expression to the right of the
715 <literal><-</literal> is the same as the type of the pattern to its
716 left. The bindings introduced by pattern guards scope over all the
717 remaining guard qualifiers, and over the right hand side of the equation.
721 Just as with list comprehensions, boolean expressions can be freely mixed
722 with among the pattern guards. For example:
733 Haskell's current guards therefore emerge as a special case, in which the
734 qualifier list has just one element, a boolean expression.
738 <!-- ===================== View patterns =================== -->
740 <sect2 id="view-patterns">
745 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
746 More information and examples of view patterns can be found on the
747 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
752 View patterns are somewhat like pattern guards that can be nested inside
753 of other patterns. They are a convenient way of pattern-matching
754 against values of abstract types. For example, in a programming language
755 implementation, we might represent the syntax of the types of the
764 view :: Type -> TypeView
766 -- additional operations for constructing Typ's ...
769 The representation of Typ is held abstract, permitting implementations
770 to use a fancy representation (e.g., hash-consing to manage sharing).
772 Without view patterns, using this signature a little inconvenient:
774 size :: Typ -> Integer
775 size t = case view t of
777 Arrow t1 t2 -> size t1 + size t2
780 It is necessary to iterate the case, rather than using an equational
781 function definition. And the situation is even worse when the matching
782 against <literal>t</literal> is buried deep inside another pattern.
786 View patterns permit calling the view function inside the pattern and
787 matching against the result:
789 size (view -> Unit) = 1
790 size (view -> Arrow t1 t2) = size t1 + size t2
793 That is, we add a new form of pattern, written
794 <replaceable>expression</replaceable> <literal>-></literal>
795 <replaceable>pattern</replaceable> that means "apply the expression to
796 whatever we're trying to match against, and then match the result of
797 that application against the pattern". The expression can be any Haskell
798 expression of function type, and view patterns can be used wherever
803 The semantics of a pattern <literal>(</literal>
804 <replaceable>exp</replaceable> <literal>-></literal>
805 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
811 <para>The variables bound by the view pattern are the variables bound by
812 <replaceable>pat</replaceable>.
816 Any variables in <replaceable>exp</replaceable> are bound occurrences,
817 but variables bound "to the left" in a pattern are in scope. This
818 feature permits, for example, one argument to a function to be used in
819 the view of another argument. For example, the function
820 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
821 written using view patterns as follows:
824 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
825 ...other equations for clunky...
830 More precisely, the scoping rules are:
834 In a single pattern, variables bound by patterns to the left of a view
835 pattern expression are in scope. For example:
837 example :: Maybe ((String -> Integer,Integer), String) -> Bool
838 example Just ((f,_), f -> 4) = True
841 Additionally, in function definitions, variables bound by matching earlier curried
842 arguments may be used in view pattern expressions in later arguments:
844 example :: (String -> Integer) -> String -> Bool
845 example f (f -> 4) = True
847 That is, the scoping is the same as it would be if the curried arguments
848 were collected into a tuple.
854 In mutually recursive bindings, such as <literal>let</literal>,
855 <literal>where</literal>, or the top level, view patterns in one
856 declaration may not mention variables bound by other declarations. That
857 is, each declaration must be self-contained. For example, the following
858 program is not allowed:
865 restriction in the future; the only cost is that type checking patterns
866 would get a little more complicated.)
876 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
877 <replaceable>T1</replaceable> <literal>-></literal>
878 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
879 a <replaceable>T2</replaceable>, then the whole view pattern matches a
880 <replaceable>T1</replaceable>.
883 <listitem><para> Matching: To the equations in Section 3.17.3 of the
884 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
885 Report</ulink>, add the following:
887 case v of { (e -> p) -> e1 ; _ -> e2 }
889 case (e v) of { p -> e1 ; _ -> e2 }
891 That is, to match a variable <replaceable>v</replaceable> against a pattern
892 <literal>(</literal> <replaceable>exp</replaceable>
893 <literal>-></literal> <replaceable>pat</replaceable>
894 <literal>)</literal>, evaluate <literal>(</literal>
895 <replaceable>exp</replaceable> <replaceable> v</replaceable>
896 <literal>)</literal> and match the result against
897 <replaceable>pat</replaceable>.
900 <listitem><para> Efficiency: When the same view function is applied in
901 multiple branches of a function definition or a case expression (e.g.,
902 in <literal>size</literal> above), GHC makes an attempt to collect these
903 applications into a single nested case expression, so that the view
904 function is only applied once. Pattern compilation in GHC follows the
905 matrix algorithm described in Chapter 4 of <ulink
906 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
907 Implementation of Functional Programming Languages</ulink>. When the
908 top rows of the first column of a matrix are all view patterns with the
909 "same" expression, these patterns are transformed into a single nested
910 case. This includes, for example, adjacent view patterns that line up
913 f ((view -> A, p1), p2) = e1
914 f ((view -> B, p3), p4) = e2
918 <para> The current notion of when two view pattern expressions are "the
919 same" is very restricted: it is not even full syntactic equality.
920 However, it does include variables, literals, applications, and tuples;
921 e.g., two instances of <literal>view ("hi", "there")</literal> will be
922 collected. However, the current implementation does not compare up to
923 alpha-equivalence, so two instances of <literal>(x, view x ->
924 y)</literal> will not be coalesced.
934 <!-- ===================== Recursive do-notation =================== -->
936 <sect2 id="mdo-notation">
937 <title>The recursive do-notation
940 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
941 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
942 by Levent Erkok, John Launchbury,
943 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
944 This paper is essential reading for anyone making non-trivial use of mdo-notation,
945 and we do not repeat it here.
948 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
949 that is, the variables bound in a do-expression are visible only in the textually following
950 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
951 group. It turns out that several applications can benefit from recursive bindings in
952 the do-notation, and this extension provides the necessary syntactic support.
955 Here is a simple (yet contrived) example:
958 import Control.Monad.Fix
960 justOnes = mdo xs <- Just (1:xs)
964 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
968 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
971 class Monad m => MonadFix m where
972 mfix :: (a -> m a) -> m a
975 The function <literal>mfix</literal>
976 dictates how the required recursion operation should be performed. For example,
977 <literal>justOnes</literal> desugars as follows:
979 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
981 For full details of the way in which mdo is typechecked and desugared, see
982 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
983 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
986 If recursive bindings are required for a monad,
987 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
988 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
989 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
990 for Haskell's internal state monad (strict and lazy, respectively).
993 Here are some important points in using the recursive-do notation:
996 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
997 than <literal>do</literal>).
1001 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
1002 <literal>-fglasgow-exts</literal>.
1006 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
1007 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
1008 be distinct (Section 3.3 of the paper).
1012 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
1013 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
1014 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
1015 and improve termination (Section 3.2 of the paper).
1021 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb/">http://www.cse.ogi.edu/PacSoft/projects/rmb/</ulink>
1022 contains up to date information on recursive monadic bindings.
1026 Historical note: The old implementation of the mdo-notation (and most
1027 of the existing documents) used the name
1028 <literal>MonadRec</literal> for the class and the corresponding library.
1029 This name is not supported by GHC.
1035 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1037 <sect2 id="parallel-list-comprehensions">
1038 <title>Parallel List Comprehensions</title>
1039 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1041 <indexterm><primary>parallel list comprehensions</primary>
1044 <para>Parallel list comprehensions are a natural extension to list
1045 comprehensions. List comprehensions can be thought of as a nice
1046 syntax for writing maps and filters. Parallel comprehensions
1047 extend this to include the zipWith family.</para>
1049 <para>A parallel list comprehension has multiple independent
1050 branches of qualifier lists, each separated by a `|' symbol. For
1051 example, the following zips together two lists:</para>
1054 [ (x, y) | x <- xs | y <- ys ]
1057 <para>The behavior of parallel list comprehensions follows that of
1058 zip, in that the resulting list will have the same length as the
1059 shortest branch.</para>
1061 <para>We can define parallel list comprehensions by translation to
1062 regular comprehensions. Here's the basic idea:</para>
1064 <para>Given a parallel comprehension of the form: </para>
1067 [ e | p1 <- e11, p2 <- e12, ...
1068 | q1 <- e21, q2 <- e22, ...
1073 <para>This will be translated to: </para>
1076 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1077 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1082 <para>where `zipN' is the appropriate zip for the given number of
1087 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1089 <sect2 id="generalised-list-comprehensions">
1090 <title>Generalised (SQL-Like) List Comprehensions</title>
1091 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1093 <indexterm><primary>extended list comprehensions</primary>
1095 <indexterm><primary>group</primary></indexterm>
1096 <indexterm><primary>sql</primary></indexterm>
1099 <para>Generalised list comprehensions are a further enhancement to the
1100 list comprehension syntatic sugar to allow operations such as sorting
1101 and grouping which are familiar from SQL. They are fully described in the
1102 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1103 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1104 except that the syntax we use differs slightly from the paper.</para>
1105 <para>Here is an example:
1107 employees = [ ("Simon", "MS", 80)
1108 , ("Erik", "MS", 100)
1109 , ("Phil", "Ed", 40)
1110 , ("Gordon", "Ed", 45)
1111 , ("Paul", "Yale", 60)]
1113 output = [ (the dept, sum salary)
1114 | (name, dept, salary) <- employees
1115 , then group by dept
1116 , then sortWith by (sum salary)
1119 In this example, the list <literal>output</literal> would take on
1123 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1126 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1127 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1128 function that is exported by <literal>GHC.Exts</literal>.)</para>
1130 <para>There are five new forms of comprehension qualifier,
1131 all introduced by the (existing) keyword <literal>then</literal>:
1139 This statement requires that <literal>f</literal> have the type <literal>
1140 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1141 motivating example, as this form is used to apply <literal>take 5</literal>.
1152 This form is similar to the previous one, but allows you to create a function
1153 which will be passed as the first argument to f. As a consequence f must have
1154 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1155 from the type, this function lets f "project out" some information
1156 from the elements of the list it is transforming.</para>
1158 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1159 is supplied with a function that lets it find out the <literal>sum salary</literal>
1160 for any item in the list comprehension it transforms.</para>
1168 then group by e using f
1171 <para>This is the most general of the grouping-type statements. In this form,
1172 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1173 As with the <literal>then f by e</literal> case above, the first argument
1174 is a function supplied to f by the compiler which lets it compute e on every
1175 element of the list being transformed. However, unlike the non-grouping case,
1176 f additionally partitions the list into a number of sublists: this means that
1177 at every point after this statement, binders occurring before it in the comprehension
1178 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1179 this, let's look at an example:</para>
1182 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1183 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1184 groupRuns f = groupBy (\x y -> f x == f y)
1186 output = [ (the x, y)
1187 | x <- ([1..3] ++ [1..2])
1189 , then group by x using groupRuns ]
1192 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1195 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1198 <para>Note that we have used the <literal>the</literal> function to change the type
1199 of x from a list to its original numeric type. The variable y, in contrast, is left
1200 unchanged from the list form introduced by the grouping.</para>
1210 <para>This form of grouping is essentially the same as the one described above. However,
1211 since no function to use for the grouping has been supplied it will fall back on the
1212 <literal>groupWith</literal> function defined in
1213 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1214 is the form of the group statement that we made use of in the opening example.</para>
1225 <para>With this form of the group statement, f is required to simply have the type
1226 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1227 comprehension so far directly. An example of this form is as follows:</para>
1233 , then group using inits]
1236 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1239 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1247 <!-- ===================== REBINDABLE SYNTAX =================== -->
1249 <sect2 id="rebindable-syntax">
1250 <title>Rebindable syntax</title>
1252 <para>GHC allows most kinds of built-in syntax to be rebound by
1253 the user, to facilitate replacing the <literal>Prelude</literal>
1254 with a home-grown version, for example.</para>
1256 <para>You may want to define your own numeric class
1257 hierarchy. It completely defeats that purpose if the
1258 literal "1" means "<literal>Prelude.fromInteger
1259 1</literal>", which is what the Haskell Report specifies.
1260 So the <option>-XNoImplicitPrelude</option> flag causes
1261 the following pieces of built-in syntax to refer to
1262 <emphasis>whatever is in scope</emphasis>, not the Prelude
1267 <para>An integer literal <literal>368</literal> means
1268 "<literal>fromInteger (368::Integer)</literal>", rather than
1269 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1272 <listitem><para>Fractional literals are handed in just the same way,
1273 except that the translation is
1274 <literal>fromRational (3.68::Rational)</literal>.
1277 <listitem><para>The equality test in an overloaded numeric pattern
1278 uses whatever <literal>(==)</literal> is in scope.
1281 <listitem><para>The subtraction operation, and the
1282 greater-than-or-equal test, in <literal>n+k</literal> patterns
1283 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1287 <para>Negation (e.g. "<literal>- (f x)</literal>")
1288 means "<literal>negate (f x)</literal>", both in numeric
1289 patterns, and expressions.
1293 <para>"Do" notation is translated using whatever
1294 functions <literal>(>>=)</literal>,
1295 <literal>(>>)</literal>, and <literal>fail</literal>,
1296 are in scope (not the Prelude
1297 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1298 comprehensions, are unaffected. </para></listitem>
1302 notation (see <xref linkend="arrow-notation"/>)
1303 uses whatever <literal>arr</literal>,
1304 <literal>(>>>)</literal>, <literal>first</literal>,
1305 <literal>app</literal>, <literal>(|||)</literal> and
1306 <literal>loop</literal> functions are in scope. But unlike the
1307 other constructs, the types of these functions must match the
1308 Prelude types very closely. Details are in flux; if you want
1312 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1313 even if that is a little unexpected. For example, the
1314 static semantics of the literal <literal>368</literal>
1315 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1316 <literal>fromInteger</literal> to have any of the types:
1318 fromInteger :: Integer -> Integer
1319 fromInteger :: forall a. Foo a => Integer -> a
1320 fromInteger :: Num a => a -> Integer
1321 fromInteger :: Integer -> Bool -> Bool
1325 <para>Be warned: this is an experimental facility, with
1326 fewer checks than usual. Use <literal>-dcore-lint</literal>
1327 to typecheck the desugared program. If Core Lint is happy
1328 you should be all right.</para>
1332 <sect2 id="postfix-operators">
1333 <title>Postfix operators</title>
1336 GHC allows a small extension to the syntax of left operator sections, which
1337 allows you to define postfix operators. The extension is this: the left section
1341 is equivalent (from the point of view of both type checking and execution) to the expression
1345 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1346 The strict Haskell 98 interpretation is that the section is equivalent to
1350 That is, the operator must be a function of two arguments. GHC allows it to
1351 take only one argument, and that in turn allows you to write the function
1354 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1355 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1356 change their behaviour, of course.)
1358 <para>The extension does not extend to the left-hand side of function
1359 definitions; you must define such a function in prefix form.</para>
1363 <sect2 id="disambiguate-fields">
1364 <title>Record field disambiguation</title>
1366 In record construction and record pattern matching
1367 it is entirely unambiguous which field is referred to, even if there are two different
1368 data types in scope with a common field name. For example:
1371 data S = MkS { x :: Int, y :: Bool }
1376 data T = MkT { x :: Int }
1378 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1380 ok2 n = MkT { x = n+1 } -- Unambiguous
1382 bad1 k = k { x = 3 } -- Ambiguous
1383 bad2 k = x k -- Ambiguous
1385 Even though there are two <literal>x</literal>'s in scope,
1386 it is clear that the <literal>x</literal> in the pattern in the
1387 definition of <literal>ok1</literal> can only mean the field
1388 <literal>x</literal> from type <literal>S</literal>. Similarly for
1389 the function <literal>ok2</literal>. However, in the record update
1390 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1391 it is not clear which of the two types is intended.
1394 Haskell 98 regards all four as ambiguous, but with the
1395 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1396 the former two. The rules are precisely the same as those for instance
1397 declarations in Haskell 98, where the method names on the left-hand side
1398 of the method bindings in an instance declaration refer unambiguously
1399 to the method of that class (provided they are in scope at all), even
1400 if there are other variables in scope with the same name.
1401 This reduces the clutter of qualified names when you import two
1402 records from different modules that use the same field name.
1406 <!-- ===================== Record puns =================== -->
1408 <sect2 id="record-puns">
1413 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1417 When using records, it is common to write a pattern that binds a
1418 variable with the same name as a record field, such as:
1421 data C = C {a :: Int}
1427 Record punning permits the variable name to be elided, so one can simply
1434 to mean the same pattern as above. That is, in a record pattern, the
1435 pattern <literal>a</literal> expands into the pattern <literal>a =
1436 a</literal> for the same name <literal>a</literal>.
1440 Note that puns and other patterns can be mixed in the same record:
1442 data C = C {a :: Int, b :: Int}
1443 f (C {a, b = 4}) = a
1445 and that puns can be used wherever record patterns occur (e.g. in
1446 <literal>let</literal> bindings or at the top-level).
1450 Record punning can also be used in an expression, writing, for example,
1456 let a = 1 in C {a = a}
1459 Note that this expansion is purely syntactic, so the record pun
1460 expression refers to the nearest enclosing variable that is spelled the
1461 same as the field name.
1466 <!-- ===================== Record wildcards =================== -->
1468 <sect2 id="record-wildcards">
1469 <title>Record wildcards
1473 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1477 For records with many fields, it can be tiresome to write out each field
1478 individually in a record pattern, as in
1480 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1481 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1486 Record wildcard syntax permits a (<literal>..</literal>) in a record
1487 pattern, where each elided field <literal>f</literal> is replaced by the
1488 pattern <literal>f = f</literal>. For example, the above pattern can be
1491 f (C {a = 1, ..}) = b + c + d
1496 Note that wildcards can be mixed with other patterns, including puns
1497 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1498 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1499 wherever record patterns occur, including in <literal>let</literal>
1500 bindings and at the top-level. For example, the top-level binding
1504 defines <literal>b</literal>, <literal>c</literal>, and
1505 <literal>d</literal>.
1509 Record wildcards can also be used in expressions, writing, for example,
1512 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1518 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1521 Note that this expansion is purely syntactic, so the record wildcard
1522 expression refers to the nearest enclosing variables that are spelled
1523 the same as the omitted field names.
1528 <!-- ===================== Local fixity declarations =================== -->
1530 <sect2 id="local-fixity-declarations">
1531 <title>Local Fixity Declarations
1534 <para>A careful reading of the Haskell 98 Report reveals that fixity
1535 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1536 <literal>infixr</literal>) are permitted to appear inside local bindings
1537 such those introduced by <literal>let</literal> and
1538 <literal>where</literal>. However, the Haskell Report does not specify
1539 the semantics of such bindings very precisely.
1542 <para>In GHC, a fixity declaration may accompany a local binding:
1549 and the fixity declaration applies wherever the binding is in scope.
1550 For example, in a <literal>let</literal>, it applies in the right-hand
1551 sides of other <literal>let</literal>-bindings and the body of the
1552 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1553 expressions (<xref linkend="mdo-notation"/>), the local fixity
1554 declarations of a <literal>let</literal> statement scope over other
1555 statements in the group, just as the bound name does.
1559 Moreover, a local fixity declaration *must* accompany a local binding of
1560 that name: it is not possible to revise the fixity of name bound
1563 let infixr 9 $ in ...
1566 Because local fixity declarations are technically Haskell 98, no flag is
1567 necessary to enable them.
1571 <sect2 id="package-imports">
1572 <title>Package-qualified imports</title>
1574 <para>With the <option>-XPackageImports</option> flag, GHC allows
1575 import declarations to be qualified by the package name that the
1576 module is intended to be imported from. For example:</para>
1579 import "network" Network.Socket
1582 <para>would import the module <literal>Network.Socket</literal> from
1583 the package <literal>network</literal> (any version). This may
1584 be used to disambiguate an import when the same module is
1585 available from multiple packages, or is present in both the
1586 current package being built and an external package.</para>
1588 <para>Note: you probably don't need to use this feature, it was
1589 added mainly so that we can build backwards-compatible versions of
1590 packages when APIs change. It can lead to fragile dependencies in
1591 the common case: modules occasionally move from one package to
1592 another, rendering any package-qualified imports broken.</para>
1597 <!-- TYPE SYSTEM EXTENSIONS -->
1598 <sect1 id="data-type-extensions">
1599 <title>Extensions to data types and type synonyms</title>
1601 <sect2 id="nullary-types">
1602 <title>Data types with no constructors</title>
1604 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1605 a data type with no constructors. For example:</para>
1609 data T a -- T :: * -> *
1612 <para>Syntactically, the declaration lacks the "= constrs" part. The
1613 type can be parameterised over types of any kind, but if the kind is
1614 not <literal>*</literal> then an explicit kind annotation must be used
1615 (see <xref linkend="kinding"/>).</para>
1617 <para>Such data types have only one value, namely bottom.
1618 Nevertheless, they can be useful when defining "phantom types".</para>
1621 <sect2 id="infix-tycons">
1622 <title>Infix type constructors, classes, and type variables</title>
1625 GHC allows type constructors, classes, and type variables to be operators, and
1626 to be written infix, very much like expressions. More specifically:
1629 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1630 The lexical syntax is the same as that for data constructors.
1633 Data type and type-synonym declarations can be written infix, parenthesised
1634 if you want further arguments. E.g.
1636 data a :*: b = Foo a b
1637 type a :+: b = Either a b
1638 class a :=: b where ...
1640 data (a :**: b) x = Baz a b x
1641 type (a :++: b) y = Either (a,b) y
1645 Types, and class constraints, can be written infix. For example
1648 f :: (a :=: b) => a -> b
1652 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1653 The lexical syntax is the same as that for variable operators, excluding "(.)",
1654 "(!)", and "(*)". In a binding position, the operator must be
1655 parenthesised. For example:
1657 type T (+) = Int + Int
1661 liftA2 :: Arrow (~>)
1662 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1668 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1669 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1672 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1673 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1674 sets the fixity for a data constructor and the corresponding type constructor. For example:
1678 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1679 and similarly for <literal>:*:</literal>.
1680 <literal>Int `a` Bool</literal>.
1683 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1690 <sect2 id="type-synonyms">
1691 <title>Liberalised type synonyms</title>
1694 Type synonyms are like macros at the type level, and
1695 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1696 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1698 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1699 in a type synonym, thus:
1701 type Discard a = forall b. Show b => a -> b -> (a, String)
1706 g :: Discard Int -> (Int,String) -- A rank-2 type
1713 You can write an unboxed tuple in a type synonym:
1715 type Pr = (# Int, Int #)
1723 You can apply a type synonym to a forall type:
1725 type Foo a = a -> a -> Bool
1727 f :: Foo (forall b. b->b)
1729 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1731 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1736 You can apply a type synonym to a partially applied type synonym:
1738 type Generic i o = forall x. i x -> o x
1741 foo :: Generic Id []
1743 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1745 foo :: forall x. x -> [x]
1753 GHC currently does kind checking before expanding synonyms (though even that
1757 After expanding type synonyms, GHC does validity checking on types, looking for
1758 the following mal-formedness which isn't detected simply by kind checking:
1761 Type constructor applied to a type involving for-alls.
1764 Unboxed tuple on left of an arrow.
1767 Partially-applied type synonym.
1771 this will be rejected:
1773 type Pr = (# Int, Int #)
1778 because GHC does not allow unboxed tuples on the left of a function arrow.
1783 <sect2 id="existential-quantification">
1784 <title>Existentially quantified data constructors
1788 The idea of using existential quantification in data type declarations
1789 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1790 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1791 London, 1991). It was later formalised by Laufer and Odersky
1792 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1793 TOPLAS, 16(5), pp1411-1430, 1994).
1794 It's been in Lennart
1795 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1796 proved very useful. Here's the idea. Consider the declaration:
1802 data Foo = forall a. MkFoo a (a -> Bool)
1809 The data type <literal>Foo</literal> has two constructors with types:
1815 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1822 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1823 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1824 For example, the following expression is fine:
1830 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1836 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1837 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1838 isUpper</function> packages a character with a compatible function. These
1839 two things are each of type <literal>Foo</literal> and can be put in a list.
1843 What can we do with a value of type <literal>Foo</literal>?. In particular,
1844 what happens when we pattern-match on <function>MkFoo</function>?
1850 f (MkFoo val fn) = ???
1856 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1857 are compatible, the only (useful) thing we can do with them is to
1858 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1865 f (MkFoo val fn) = fn val
1871 What this allows us to do is to package heterogeneous values
1872 together with a bunch of functions that manipulate them, and then treat
1873 that collection of packages in a uniform manner. You can express
1874 quite a bit of object-oriented-like programming this way.
1877 <sect3 id="existential">
1878 <title>Why existential?
1882 What has this to do with <emphasis>existential</emphasis> quantification?
1883 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1889 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1895 But Haskell programmers can safely think of the ordinary
1896 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1897 adding a new existential quantification construct.
1902 <sect3 id="existential-with-context">
1903 <title>Existentials and type classes</title>
1906 An easy extension is to allow
1907 arbitrary contexts before the constructor. For example:
1913 data Baz = forall a. Eq a => Baz1 a a
1914 | forall b. Show b => Baz2 b (b -> b)
1920 The two constructors have the types you'd expect:
1926 Baz1 :: forall a. Eq a => a -> a -> Baz
1927 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1933 But when pattern matching on <function>Baz1</function> the matched values can be compared
1934 for equality, and when pattern matching on <function>Baz2</function> the first matched
1935 value can be converted to a string (as well as applying the function to it).
1936 So this program is legal:
1943 f (Baz1 p q) | p == q = "Yes"
1945 f (Baz2 v fn) = show (fn v)
1951 Operationally, in a dictionary-passing implementation, the
1952 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1953 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1954 extract it on pattern matching.
1959 <sect3 id="existential-records">
1960 <title>Record Constructors</title>
1963 GHC allows existentials to be used with records syntax as well. For example:
1966 data Counter a = forall self. NewCounter
1968 , _inc :: self -> self
1969 , _display :: self -> IO ()
1973 Here <literal>tag</literal> is a public field, with a well-typed selector
1974 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1975 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1976 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1977 compile-time error. In other words, <emphasis>GHC defines a record selector function
1978 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1979 (This example used an underscore in the fields for which record selectors
1980 will not be defined, but that is only programming style; GHC ignores them.)
1984 To make use of these hidden fields, we need to create some helper functions:
1987 inc :: Counter a -> Counter a
1988 inc (NewCounter x i d t) = NewCounter
1989 { _this = i x, _inc = i, _display = d, tag = t }
1991 display :: Counter a -> IO ()
1992 display NewCounter{ _this = x, _display = d } = d x
1995 Now we can define counters with different underlying implementations:
1998 counterA :: Counter String
1999 counterA = NewCounter
2000 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2002 counterB :: Counter String
2003 counterB = NewCounter
2004 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2007 display (inc counterA) -- prints "1"
2008 display (inc (inc counterB)) -- prints "##"
2011 At the moment, record update syntax is only supported for Haskell 98 data types,
2012 so the following function does <emphasis>not</emphasis> work:
2015 -- This is invalid; use explicit NewCounter instead for now
2016 setTag :: Counter a -> a -> Counter a
2017 setTag obj t = obj{ tag = t }
2026 <title>Restrictions</title>
2029 There are several restrictions on the ways in which existentially-quantified
2030 constructors can be use.
2039 When pattern matching, each pattern match introduces a new,
2040 distinct, type for each existential type variable. These types cannot
2041 be unified with any other type, nor can they escape from the scope of
2042 the pattern match. For example, these fragments are incorrect:
2050 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2051 is the result of <function>f1</function>. One way to see why this is wrong is to
2052 ask what type <function>f1</function> has:
2056 f1 :: Foo -> a -- Weird!
2060 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2065 f1 :: forall a. Foo -> a -- Wrong!
2069 The original program is just plain wrong. Here's another sort of error
2073 f2 (Baz1 a b) (Baz1 p q) = a==q
2077 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2078 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2079 from the two <function>Baz1</function> constructors.
2087 You can't pattern-match on an existentially quantified
2088 constructor in a <literal>let</literal> or <literal>where</literal> group of
2089 bindings. So this is illegal:
2093 f3 x = a==b where { Baz1 a b = x }
2096 Instead, use a <literal>case</literal> expression:
2099 f3 x = case x of Baz1 a b -> a==b
2102 In general, you can only pattern-match
2103 on an existentially-quantified constructor in a <literal>case</literal> expression or
2104 in the patterns of a function definition.
2106 The reason for this restriction is really an implementation one.
2107 Type-checking binding groups is already a nightmare without
2108 existentials complicating the picture. Also an existential pattern
2109 binding at the top level of a module doesn't make sense, because it's
2110 not clear how to prevent the existentially-quantified type "escaping".
2111 So for now, there's a simple-to-state restriction. We'll see how
2119 You can't use existential quantification for <literal>newtype</literal>
2120 declarations. So this is illegal:
2124 newtype T = forall a. Ord a => MkT a
2128 Reason: a value of type <literal>T</literal> must be represented as a
2129 pair of a dictionary for <literal>Ord t</literal> and a value of type
2130 <literal>t</literal>. That contradicts the idea that
2131 <literal>newtype</literal> should have no concrete representation.
2132 You can get just the same efficiency and effect by using
2133 <literal>data</literal> instead of <literal>newtype</literal>. If
2134 there is no overloading involved, then there is more of a case for
2135 allowing an existentially-quantified <literal>newtype</literal>,
2136 because the <literal>data</literal> version does carry an
2137 implementation cost, but single-field existentially quantified
2138 constructors aren't much use. So the simple restriction (no
2139 existential stuff on <literal>newtype</literal>) stands, unless there
2140 are convincing reasons to change it.
2148 You can't use <literal>deriving</literal> to define instances of a
2149 data type with existentially quantified data constructors.
2151 Reason: in most cases it would not make sense. For example:;
2154 data T = forall a. MkT [a] deriving( Eq )
2157 To derive <literal>Eq</literal> in the standard way we would need to have equality
2158 between the single component of two <function>MkT</function> constructors:
2162 (MkT a) == (MkT b) = ???
2165 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2166 It's just about possible to imagine examples in which the derived instance
2167 would make sense, but it seems altogether simpler simply to prohibit such
2168 declarations. Define your own instances!
2179 <!-- ====================== Generalised algebraic data types ======================= -->
2181 <sect2 id="gadt-style">
2182 <title>Declaring data types with explicit constructor signatures</title>
2184 <para>GHC allows you to declare an algebraic data type by
2185 giving the type signatures of constructors explicitly. For example:
2189 Just :: a -> Maybe a
2191 The form is called a "GADT-style declaration"
2192 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2193 can only be declared using this form.</para>
2194 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2195 For example, these two declarations are equivalent:
2197 data Foo = forall a. MkFoo a (a -> Bool)
2198 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2201 <para>Any data type that can be declared in standard Haskell-98 syntax
2202 can also be declared using GADT-style syntax.
2203 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2204 they treat class constraints on the data constructors differently.
2205 Specifically, if the constructor is given a type-class context, that
2206 context is made available by pattern matching. For example:
2209 MkSet :: Eq a => [a] -> Set a
2211 makeSet :: Eq a => [a] -> Set a
2212 makeSet xs = MkSet (nub xs)
2214 insert :: a -> Set a -> Set a
2215 insert a (MkSet as) | a `elem` as = MkSet as
2216 | otherwise = MkSet (a:as)
2218 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2219 gives rise to a <literal>(Eq a)</literal>
2220 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2221 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2222 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2223 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2224 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2225 In the example, the equality dictionary is used to satisfy the equality constraint
2226 generated by the call to <literal>elem</literal>, so that the type of
2227 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2230 For example, one possible application is to reify dictionaries:
2232 data NumInst a where
2233 MkNumInst :: Num a => NumInst a
2235 intInst :: NumInst Int
2238 plus :: NumInst a -> a -> a -> a
2239 plus MkNumInst p q = p + q
2241 Here, a value of type <literal>NumInst a</literal> is equivalent
2242 to an explicit <literal>(Num a)</literal> dictionary.
2245 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2246 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2250 = Num a => MkNumInst (NumInst a)
2252 Notice that, unlike the situation when declaring an existential, there is
2253 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2254 data type's universally quantified type variable <literal>a</literal>.
2255 A constructor may have both universal and existential type variables: for example,
2256 the following two declarations are equivalent:
2259 = forall b. (Num a, Eq b) => MkT1 a b
2261 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2264 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2265 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2266 In Haskell 98 the definition
2268 data Eq a => Set' a = MkSet' [a]
2270 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2271 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2272 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2273 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2274 GHC's behaviour is much more useful, as well as much more intuitive.
2278 The rest of this section gives further details about GADT-style data
2283 The result type of each data constructor must begin with the type constructor being defined.
2284 If the result type of all constructors
2285 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2286 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2287 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2291 The type signature of
2292 each constructor is independent, and is implicitly universally quantified as usual.
2293 Different constructors may have different universally-quantified type variables
2294 and different type-class constraints.
2295 For example, this is fine:
2298 T1 :: Eq b => b -> T b
2299 T2 :: (Show c, Ix c) => c -> [c] -> T c
2304 Unlike a Haskell-98-style
2305 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2306 have no scope. Indeed, one can write a kind signature instead:
2308 data Set :: * -> * where ...
2310 or even a mixture of the two:
2312 data Foo a :: (* -> *) -> * where ...
2314 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2317 data Foo a (b :: * -> *) where ...
2323 You can use strictness annotations, in the obvious places
2324 in the constructor type:
2327 Lit :: !Int -> Term Int
2328 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2329 Pair :: Term a -> Term b -> Term (a,b)
2334 You can use a <literal>deriving</literal> clause on a GADT-style data type
2335 declaration. For example, these two declarations are equivalent
2337 data Maybe1 a where {
2338 Nothing1 :: Maybe1 a ;
2339 Just1 :: a -> Maybe1 a
2340 } deriving( Eq, Ord )
2342 data Maybe2 a = Nothing2 | Just2 a
2348 You can use record syntax on a GADT-style data type declaration:
2352 Adult { name :: String, children :: [Person] } :: Person
2353 Child { name :: String } :: Person
2355 As usual, for every constructor that has a field <literal>f</literal>, the type of
2356 field <literal>f</literal> must be the same (modulo alpha conversion).
2359 At the moment, record updates are not yet possible with GADT-style declarations,
2360 so support is limited to record construction, selection and pattern matching.
2363 aPerson = Adult { name = "Fred", children = [] }
2365 shortName :: Person -> Bool
2366 hasChildren (Adult { children = kids }) = not (null kids)
2367 hasChildren (Child {}) = False
2372 As in the case of existentials declared using the Haskell-98-like record syntax
2373 (<xref linkend="existential-records"/>),
2374 record-selector functions are generated only for those fields that have well-typed
2376 Here is the example of that section, in GADT-style syntax:
2378 data Counter a where
2379 NewCounter { _this :: self
2380 , _inc :: self -> self
2381 , _display :: self -> IO ()
2386 As before, only one selector function is generated here, that for <literal>tag</literal>.
2387 Nevertheless, you can still use all the field names in pattern matching and record construction.
2389 </itemizedlist></para>
2393 <title>Generalised Algebraic Data Types (GADTs)</title>
2395 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2396 by allowing constructors to have richer return types. Here is an example:
2399 Lit :: Int -> Term Int
2400 Succ :: Term Int -> Term Int
2401 IsZero :: Term Int -> Term Bool
2402 If :: Term Bool -> Term a -> Term a -> Term a
2403 Pair :: Term a -> Term b -> Term (a,b)
2405 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2406 case with ordinary data types. This generality allows us to
2407 write a well-typed <literal>eval</literal> function
2408 for these <literal>Terms</literal>:
2412 eval (Succ t) = 1 + eval t
2413 eval (IsZero t) = eval t == 0
2414 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2415 eval (Pair e1 e2) = (eval e1, eval e2)
2417 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2418 For example, in the right hand side of the equation
2423 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2424 A precise specification of the type rules is beyond what this user manual aspires to,
2425 but the design closely follows that described in
2427 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2428 unification-based type inference for GADTs</ulink>,
2430 The general principle is this: <emphasis>type refinement is only carried out
2431 based on user-supplied type annotations</emphasis>.
2432 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2433 and lots of obscure error messages will
2434 occur. However, the refinement is quite general. For example, if we had:
2436 eval :: Term a -> a -> a
2437 eval (Lit i) j = i+j
2439 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2440 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2441 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2444 These and many other examples are given in papers by Hongwei Xi, and
2445 Tim Sheard. There is a longer introduction
2446 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2448 <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
2449 may use different notation to that implemented in GHC.
2452 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2453 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2456 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2457 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2458 The result type of each constructor must begin with the type constructor being defined,
2459 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2460 For example, in the <literal>Term</literal> data
2461 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2462 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2467 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2468 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2469 whose result type is not just <literal>T a b</literal>.
2473 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2474 an ordinary data type.
2478 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2482 Lit { val :: Int } :: Term Int
2483 Succ { num :: Term Int } :: Term Int
2484 Pred { num :: Term Int } :: Term Int
2485 IsZero { arg :: Term Int } :: Term Bool
2486 Pair { arg1 :: Term a
2489 If { cnd :: Term Bool
2494 However, for GADTs there is the following additional constraint:
2495 every constructor that has a field <literal>f</literal> must have
2496 the same result type (modulo alpha conversion)
2497 Hence, in the above example, we cannot merge the <literal>num</literal>
2498 and <literal>arg</literal> fields above into a
2499 single name. Although their field types are both <literal>Term Int</literal>,
2500 their selector functions actually have different types:
2503 num :: Term Int -> Term Int
2504 arg :: Term Bool -> Term Int
2509 When pattern-matching against data constructors drawn from a GADT,
2510 for example in a <literal>case</literal> expression, the following rules apply:
2512 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2513 <listitem><para>The type of the result of the <literal>case</literal> expression must be rigid.</para></listitem>
2514 <listitem><para>The type of any free variable mentioned in any of
2515 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2517 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2518 way to ensure that a variable a rigid type is to give it a type signature.
2527 <!-- ====================== End of Generalised algebraic data types ======================= -->
2529 <sect1 id="deriving">
2530 <title>Extensions to the "deriving" mechanism</title>
2532 <sect2 id="deriving-inferred">
2533 <title>Inferred context for deriving clauses</title>
2536 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2539 data T0 f a = MkT0 a deriving( Eq )
2540 data T1 f a = MkT1 (f a) deriving( Eq )
2541 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2543 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2545 instance Eq a => Eq (T0 f a) where ...
2546 instance Eq (f a) => Eq (T1 f a) where ...
2547 instance Eq (f (f a)) => Eq (T2 f a) where ...
2549 The first of these is obviously fine. The second is still fine, although less obviously.
2550 The third is not Haskell 98, and risks losing termination of instances.
2553 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2554 each constraint in the inferred instance context must consist only of type variables,
2555 with no repetitions.
2558 This rule is applied regardless of flags. If you want a more exotic context, you can write
2559 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2563 <sect2 id="stand-alone-deriving">
2564 <title>Stand-alone deriving declarations</title>
2567 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2569 data Foo a = Bar a | Baz String
2571 deriving instance Eq a => Eq (Foo a)
2573 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2574 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2575 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2576 exactly as you would in an ordinary instance declaration.
2577 (In contrast the context is inferred in a <literal>deriving</literal> clause
2578 attached to a data type declaration.)
2580 A <literal>deriving instance</literal> declaration
2581 must obey the same rules concerning form and termination as ordinary instance declarations,
2582 controlled by the same flags; see <xref linkend="instance-decls"/>.
2585 Unlike a <literal>deriving</literal>
2586 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2587 than the data type (assuming you also use
2588 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2591 data Foo a = Bar a | Baz String
2593 deriving instance Eq a => Eq (Foo [a])
2594 deriving instance Eq a => Eq (Foo (Maybe a))
2596 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2597 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2600 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2601 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2604 newtype Foo a = MkFoo (State Int a)
2606 deriving instance MonadState Int Foo
2608 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2609 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2615 <sect2 id="deriving-typeable">
2616 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2619 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2620 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2621 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2622 classes <literal>Eq</literal>, <literal>Ord</literal>,
2623 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2626 GHC extends this list with two more classes that may be automatically derived
2627 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2628 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2629 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2630 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2632 <para>An instance of <literal>Typeable</literal> can only be derived if the
2633 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2634 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2636 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2637 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2639 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2640 are used, and only <literal>Typeable1</literal> up to
2641 <literal>Typeable7</literal> are provided in the library.)
2642 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2643 class, whose kind suits that of the data type constructor, and
2644 then writing the data type instance by hand.
2648 <sect2 id="newtype-deriving">
2649 <title>Generalised derived instances for newtypes</title>
2652 When you define an abstract type using <literal>newtype</literal>, you may want
2653 the new type to inherit some instances from its representation. In
2654 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2655 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2656 other classes you have to write an explicit instance declaration. For
2657 example, if you define
2660 newtype Dollars = Dollars Int
2663 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2664 explicitly define an instance of <literal>Num</literal>:
2667 instance Num Dollars where
2668 Dollars a + Dollars b = Dollars (a+b)
2671 All the instance does is apply and remove the <literal>newtype</literal>
2672 constructor. It is particularly galling that, since the constructor
2673 doesn't appear at run-time, this instance declaration defines a
2674 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2675 dictionary, only slower!
2679 <sect3> <title> Generalising the deriving clause </title>
2681 GHC now permits such instances to be derived instead,
2682 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2685 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2688 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2689 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2690 derives an instance declaration of the form
2693 instance Num Int => Num Dollars
2696 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2700 We can also derive instances of constructor classes in a similar
2701 way. For example, suppose we have implemented state and failure monad
2702 transformers, such that
2705 instance Monad m => Monad (State s m)
2706 instance Monad m => Monad (Failure m)
2708 In Haskell 98, we can define a parsing monad by
2710 type Parser tok m a = State [tok] (Failure m) a
2713 which is automatically a monad thanks to the instance declarations
2714 above. With the extension, we can make the parser type abstract,
2715 without needing to write an instance of class <literal>Monad</literal>, via
2718 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2721 In this case the derived instance declaration is of the form
2723 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2726 Notice that, since <literal>Monad</literal> is a constructor class, the
2727 instance is a <emphasis>partial application</emphasis> of the new type, not the
2728 entire left hand side. We can imagine that the type declaration is
2729 "eta-converted" to generate the context of the instance
2734 We can even derive instances of multi-parameter classes, provided the
2735 newtype is the last class parameter. In this case, a ``partial
2736 application'' of the class appears in the <literal>deriving</literal>
2737 clause. For example, given the class
2740 class StateMonad s m | m -> s where ...
2741 instance Monad m => StateMonad s (State s m) where ...
2743 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2745 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2746 deriving (Monad, StateMonad [tok])
2749 The derived instance is obtained by completing the application of the
2750 class to the new type:
2753 instance StateMonad [tok] (State [tok] (Failure m)) =>
2754 StateMonad [tok] (Parser tok m)
2759 As a result of this extension, all derived instances in newtype
2760 declarations are treated uniformly (and implemented just by reusing
2761 the dictionary for the representation type), <emphasis>except</emphasis>
2762 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2763 the newtype and its representation.
2767 <sect3> <title> A more precise specification </title>
2769 Derived instance declarations are constructed as follows. Consider the
2770 declaration (after expansion of any type synonyms)
2773 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2779 The <literal>ci</literal> are partial applications of
2780 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2781 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2784 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2787 The type <literal>t</literal> is an arbitrary type.
2790 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2791 nor in the <literal>ci</literal>, and
2794 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2795 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2796 should not "look through" the type or its constructor. You can still
2797 derive these classes for a newtype, but it happens in the usual way, not
2798 via this new mechanism.
2801 Then, for each <literal>ci</literal>, the derived instance
2804 instance ci t => ci (T v1...vk)
2806 As an example which does <emphasis>not</emphasis> work, consider
2808 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2810 Here we cannot derive the instance
2812 instance Monad (State s m) => Monad (NonMonad m)
2815 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2816 and so cannot be "eta-converted" away. It is a good thing that this
2817 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2818 not, in fact, a monad --- for the same reason. Try defining
2819 <literal>>>=</literal> with the correct type: you won't be able to.
2823 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2824 important, since we can only derive instances for the last one. If the
2825 <literal>StateMonad</literal> class above were instead defined as
2828 class StateMonad m s | m -> s where ...
2831 then we would not have been able to derive an instance for the
2832 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2833 classes usually have one "main" parameter for which deriving new
2834 instances is most interesting.
2836 <para>Lastly, all of this applies only for classes other than
2837 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2838 and <literal>Data</literal>, for which the built-in derivation applies (section
2839 4.3.3. of the Haskell Report).
2840 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2841 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2842 the standard method is used or the one described here.)
2849 <!-- TYPE SYSTEM EXTENSIONS -->
2850 <sect1 id="type-class-extensions">
2851 <title>Class and instances declarations</title>
2853 <sect2 id="multi-param-type-classes">
2854 <title>Class declarations</title>
2857 This section, and the next one, documents GHC's type-class extensions.
2858 There's lots of background in the paper <ulink
2859 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2860 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2861 Jones, Erik Meijer).
2864 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2868 <title>Multi-parameter type classes</title>
2870 Multi-parameter type classes are permitted. For example:
2874 class Collection c a where
2875 union :: c a -> c a -> c a
2883 <title>The superclasses of a class declaration</title>
2886 There are no restrictions on the context in a class declaration
2887 (which introduces superclasses), except that the class hierarchy must
2888 be acyclic. So these class declarations are OK:
2892 class Functor (m k) => FiniteMap m k where
2895 class (Monad m, Monad (t m)) => Transform t m where
2896 lift :: m a -> (t m) a
2902 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2903 of "acyclic" involves only the superclass relationships. For example,
2909 op :: D b => a -> b -> b
2912 class C a => D a where { ... }
2916 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2917 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2918 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2925 <sect3 id="class-method-types">
2926 <title>Class method types</title>
2929 Haskell 98 prohibits class method types to mention constraints on the
2930 class type variable, thus:
2933 fromList :: [a] -> s a
2934 elem :: Eq a => a -> s a -> Bool
2936 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2937 contains the constraint <literal>Eq a</literal>, constrains only the
2938 class type variable (in this case <literal>a</literal>).
2939 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2946 <sect2 id="functional-dependencies">
2947 <title>Functional dependencies
2950 <para> Functional dependencies are implemented as described by Mark Jones
2951 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2952 In Proceedings of the 9th European Symposium on Programming,
2953 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2957 Functional dependencies are introduced by a vertical bar in the syntax of a
2958 class declaration; e.g.
2960 class (Monad m) => MonadState s m | m -> s where ...
2962 class Foo a b c | a b -> c where ...
2964 There should be more documentation, but there isn't (yet). Yell if you need it.
2967 <sect3><title>Rules for functional dependencies </title>
2969 In a class declaration, all of the class type variables must be reachable (in the sense
2970 mentioned in <xref linkend="type-restrictions"/>)
2971 from the free variables of each method type.
2975 class Coll s a where
2977 insert :: s -> a -> s
2980 is not OK, because the type of <literal>empty</literal> doesn't mention
2981 <literal>a</literal>. Functional dependencies can make the type variable
2984 class Coll s a | s -> a where
2986 insert :: s -> a -> s
2989 Alternatively <literal>Coll</literal> might be rewritten
2992 class Coll s a where
2994 insert :: s a -> a -> s a
2998 which makes the connection between the type of a collection of
2999 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3000 Occasionally this really doesn't work, in which case you can split the
3008 class CollE s => Coll s a where
3009 insert :: s -> a -> s
3016 <title>Background on functional dependencies</title>
3018 <para>The following description of the motivation and use of functional dependencies is taken
3019 from the Hugs user manual, reproduced here (with minor changes) by kind
3020 permission of Mark Jones.
3023 Consider the following class, intended as part of a
3024 library for collection types:
3026 class Collects e ce where
3028 insert :: e -> ce -> ce
3029 member :: e -> ce -> Bool
3031 The type variable e used here represents the element type, while ce is the type
3032 of the container itself. Within this framework, we might want to define
3033 instances of this class for lists or characteristic functions (both of which
3034 can be used to represent collections of any equality type), bit sets (which can
3035 be used to represent collections of characters), or hash tables (which can be
3036 used to represent any collection whose elements have a hash function). Omitting
3037 standard implementation details, this would lead to the following declarations:
3039 instance Eq e => Collects e [e] where ...
3040 instance Eq e => Collects e (e -> Bool) where ...
3041 instance Collects Char BitSet where ...
3042 instance (Hashable e, Collects a ce)
3043 => Collects e (Array Int ce) where ...
3045 All this looks quite promising; we have a class and a range of interesting
3046 implementations. Unfortunately, there are some serious problems with the class
3047 declaration. First, the empty function has an ambiguous type:
3049 empty :: Collects e ce => ce
3051 By "ambiguous" we mean that there is a type variable e that appears on the left
3052 of the <literal>=></literal> symbol, but not on the right. The problem with
3053 this is that, according to the theoretical foundations of Haskell overloading,
3054 we cannot guarantee a well-defined semantics for any term with an ambiguous
3058 We can sidestep this specific problem by removing the empty member from the
3059 class declaration. However, although the remaining members, insert and member,
3060 do not have ambiguous types, we still run into problems when we try to use
3061 them. For example, consider the following two functions:
3063 f x y = insert x . insert y
3066 for which GHC infers the following types:
3068 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3069 g :: (Collects Bool c, Collects Char c) => c -> c
3071 Notice that the type for f allows the two parameters x and y to be assigned
3072 different types, even though it attempts to insert each of the two values, one
3073 after the other, into the same collection. If we're trying to model collections
3074 that contain only one type of value, then this is clearly an inaccurate
3075 type. Worse still, the definition for g is accepted, without causing a type
3076 error. As a result, the error in this code will not be flagged at the point
3077 where it appears. Instead, it will show up only when we try to use g, which
3078 might even be in a different module.
3081 <sect4><title>An attempt to use constructor classes</title>
3084 Faced with the problems described above, some Haskell programmers might be
3085 tempted to use something like the following version of the class declaration:
3087 class Collects e c where
3089 insert :: e -> c e -> c e
3090 member :: e -> c e -> Bool
3092 The key difference here is that we abstract over the type constructor c that is
3093 used to form the collection type c e, and not over that collection type itself,
3094 represented by ce in the original class declaration. This avoids the immediate
3095 problems that we mentioned above: empty has type <literal>Collects e c => c
3096 e</literal>, which is not ambiguous.
3099 The function f from the previous section has a more accurate type:
3101 f :: (Collects e c) => e -> e -> c e -> c e
3103 The function g from the previous section is now rejected with a type error as
3104 we would hope because the type of f does not allow the two arguments to have
3106 This, then, is an example of a multiple parameter class that does actually work
3107 quite well in practice, without ambiguity problems.
3108 There is, however, a catch. This version of the Collects class is nowhere near
3109 as general as the original class seemed to be: only one of the four instances
3110 for <literal>Collects</literal>
3111 given above can be used with this version of Collects because only one of
3112 them---the instance for lists---has a collection type that can be written in
3113 the form c e, for some type constructor c, and element type e.
3117 <sect4><title>Adding functional dependencies</title>
3120 To get a more useful version of the Collects class, Hugs provides a mechanism
3121 that allows programmers to specify dependencies between the parameters of a
3122 multiple parameter class (For readers with an interest in theoretical
3123 foundations and previous work: The use of dependency information can be seen
3124 both as a generalization of the proposal for `parametric type classes' that was
3125 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3126 later framework for "improvement" of qualified types. The
3127 underlying ideas are also discussed in a more theoretical and abstract setting
3128 in a manuscript [implparam], where they are identified as one point in a
3129 general design space for systems of implicit parameterization.).
3131 To start with an abstract example, consider a declaration such as:
3133 class C a b where ...
3135 which tells us simply that C can be thought of as a binary relation on types
3136 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3137 included in the definition of classes to add information about dependencies
3138 between parameters, as in the following examples:
3140 class D a b | a -> b where ...
3141 class E a b | a -> b, b -> a where ...
3143 The notation <literal>a -> b</literal> used here between the | and where
3144 symbols --- not to be
3145 confused with a function type --- indicates that the a parameter uniquely
3146 determines the b parameter, and might be read as "a determines b." Thus D is
3147 not just a relation, but actually a (partial) function. Similarly, from the two
3148 dependencies that are included in the definition of E, we can see that E
3149 represents a (partial) one-one mapping between types.
3152 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3153 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3154 m>=0, meaning that the y parameters are uniquely determined by the x
3155 parameters. Spaces can be used as separators if more than one variable appears
3156 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3157 annotated with multiple dependencies using commas as separators, as in the
3158 definition of E above. Some dependencies that we can write in this notation are
3159 redundant, and will be rejected because they don't serve any useful
3160 purpose, and may instead indicate an error in the program. Examples of
3161 dependencies like this include <literal>a -> a </literal>,
3162 <literal>a -> a a </literal>,
3163 <literal>a -> </literal>, etc. There can also be
3164 some redundancy if multiple dependencies are given, as in
3165 <literal>a->b</literal>,
3166 <literal>b->c </literal>, <literal>a->c </literal>, and
3167 in which some subset implies the remaining dependencies. Examples like this are
3168 not treated as errors. Note that dependencies appear only in class
3169 declarations, and not in any other part of the language. In particular, the
3170 syntax for instance declarations, class constraints, and types is completely
3174 By including dependencies in a class declaration, we provide a mechanism for
3175 the programmer to specify each multiple parameter class more precisely. The
3176 compiler, on the other hand, is responsible for ensuring that the set of
3177 instances that are in scope at any given point in the program is consistent
3178 with any declared dependencies. For example, the following pair of instance
3179 declarations cannot appear together in the same scope because they violate the
3180 dependency for D, even though either one on its own would be acceptable:
3182 instance D Bool Int where ...
3183 instance D Bool Char where ...
3185 Note also that the following declaration is not allowed, even by itself:
3187 instance D [a] b where ...
3189 The problem here is that this instance would allow one particular choice of [a]
3190 to be associated with more than one choice for b, which contradicts the
3191 dependency specified in the definition of D. More generally, this means that,
3192 in any instance of the form:
3194 instance D t s where ...
3196 for some particular types t and s, the only variables that can appear in s are
3197 the ones that appear in t, and hence, if the type t is known, then s will be
3198 uniquely determined.
3201 The benefit of including dependency information is that it allows us to define
3202 more general multiple parameter classes, without ambiguity problems, and with
3203 the benefit of more accurate types. To illustrate this, we return to the
3204 collection class example, and annotate the original definition of <literal>Collects</literal>
3205 with a simple dependency:
3207 class Collects e ce | ce -> e where
3209 insert :: e -> ce -> ce
3210 member :: e -> ce -> Bool
3212 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3213 determined by the type of the collection ce. Note that both parameters of
3214 Collects are of kind *; there are no constructor classes here. Note too that
3215 all of the instances of Collects that we gave earlier can be used
3216 together with this new definition.
3219 What about the ambiguity problems that we encountered with the original
3220 definition? The empty function still has type Collects e ce => ce, but it is no
3221 longer necessary to regard that as an ambiguous type: Although the variable e
3222 does not appear on the right of the => symbol, the dependency for class
3223 Collects tells us that it is uniquely determined by ce, which does appear on
3224 the right of the => symbol. Hence the context in which empty is used can still
3225 give enough information to determine types for both ce and e, without
3226 ambiguity. More generally, we need only regard a type as ambiguous if it
3227 contains a variable on the left of the => that is not uniquely determined
3228 (either directly or indirectly) by the variables on the right.
3231 Dependencies also help to produce more accurate types for user defined
3232 functions, and hence to provide earlier detection of errors, and less cluttered
3233 types for programmers to work with. Recall the previous definition for a
3236 f x y = insert x y = insert x . insert y
3238 for which we originally obtained a type:
3240 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3242 Given the dependency information that we have for Collects, however, we can
3243 deduce that a and b must be equal because they both appear as the second
3244 parameter in a Collects constraint with the same first parameter c. Hence we
3245 can infer a shorter and more accurate type for f:
3247 f :: (Collects a c) => a -> a -> c -> c
3249 In a similar way, the earlier definition of g will now be flagged as a type error.
3252 Although we have given only a few examples here, it should be clear that the
3253 addition of dependency information can help to make multiple parameter classes
3254 more useful in practice, avoiding ambiguity problems, and allowing more general
3255 sets of instance declarations.
3261 <sect2 id="instance-decls">
3262 <title>Instance declarations</title>
3264 <sect3 id="instance-rules">
3265 <title>Relaxed rules for instance declarations</title>
3267 <para>An instance declaration has the form
3269 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 ...
3271 The part before the "<literal>=></literal>" is the
3272 <emphasis>context</emphasis>, while the part after the
3273 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3277 In Haskell 98 the head of an instance declaration
3278 must be of the form <literal>C (T a1 ... an)</literal>, where
3279 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3280 and the <literal>a1 ... an</literal> are distinct type variables.
3281 Furthermore, the assertions in the context of the instance declaration
3282 must be of the form <literal>C a</literal> where <literal>a</literal>
3283 is a type variable that occurs in the head.
3286 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3287 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3288 the context and head of the instance declaration can each consist of arbitrary
3289 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3293 The Paterson Conditions: for each assertion in the context
3295 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3296 <listitem><para>The assertion has fewer constructors and variables (taken together
3297 and counting repetitions) than the head</para></listitem>
3301 <listitem><para>The Coverage Condition. For each functional dependency,
3302 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3303 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3304 every type variable in
3305 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3306 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3307 substitution mapping each type variable in the class declaration to the
3308 corresponding type in the instance declaration.
3311 These restrictions ensure that context reduction terminates: each reduction
3312 step makes the problem smaller by at least one
3313 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3314 if you give the <option>-XUndecidableInstances</option>
3315 flag (<xref linkend="undecidable-instances"/>).
3316 You can find lots of background material about the reason for these
3317 restrictions in the paper <ulink
3318 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3319 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3322 For example, these are OK:
3324 instance C Int [a] -- Multiple parameters
3325 instance Eq (S [a]) -- Structured type in head
3327 -- Repeated type variable in head
3328 instance C4 a a => C4 [a] [a]
3329 instance Stateful (ST s) (MutVar s)
3331 -- Head can consist of type variables only
3333 instance (Eq a, Show b) => C2 a b
3335 -- Non-type variables in context
3336 instance Show (s a) => Show (Sized s a)
3337 instance C2 Int a => C3 Bool [a]
3338 instance C2 Int a => C3 [a] b
3342 -- Context assertion no smaller than head
3343 instance C a => C a where ...
3344 -- (C b b) has more more occurrences of b than the head
3345 instance C b b => Foo [b] where ...
3350 The same restrictions apply to instances generated by
3351 <literal>deriving</literal> clauses. Thus the following is accepted:
3353 data MinHeap h a = H a (h a)
3356 because the derived instance
3358 instance (Show a, Show (h a)) => Show (MinHeap h a)
3360 conforms to the above rules.
3364 A useful idiom permitted by the above rules is as follows.
3365 If one allows overlapping instance declarations then it's quite
3366 convenient to have a "default instance" declaration that applies if
3367 something more specific does not:
3375 <sect3 id="undecidable-instances">
3376 <title>Undecidable instances</title>
3379 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3380 For example, sometimes you might want to use the following to get the
3381 effect of a "class synonym":
3383 class (C1 a, C2 a, C3 a) => C a where { }
3385 instance (C1 a, C2 a, C3 a) => C a where { }
3387 This allows you to write shorter signatures:
3393 f :: (C1 a, C2 a, C3 a) => ...
3395 The restrictions on functional dependencies (<xref
3396 linkend="functional-dependencies"/>) are particularly troublesome.
3397 It is tempting to introduce type variables in the context that do not appear in
3398 the head, something that is excluded by the normal rules. For example:
3400 class HasConverter a b | a -> b where
3403 data Foo a = MkFoo a
3405 instance (HasConverter a b,Show b) => Show (Foo a) where
3406 show (MkFoo value) = show (convert value)
3408 This is dangerous territory, however. Here, for example, is a program that would make the
3413 instance F [a] [[a]]
3414 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3416 Similarly, it can be tempting to lift the coverage condition:
3418 class Mul a b c | a b -> c where
3419 (.*.) :: a -> b -> c
3421 instance Mul Int Int Int where (.*.) = (*)
3422 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3423 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3425 The third instance declaration does not obey the coverage condition;
3426 and indeed the (somewhat strange) definition:
3428 f = \ b x y -> if b then x .*. [y] else y
3430 makes instance inference go into a loop, because it requires the constraint
3431 <literal>(Mul a [b] b)</literal>.
3434 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3435 the experimental flag <option>-XUndecidableInstances</option>
3436 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3437 both the Paterson Conditions and the Coverage Condition
3438 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3439 fixed-depth recursion stack. If you exceed the stack depth you get a
3440 sort of backtrace, and the opportunity to increase the stack depth
3441 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3447 <sect3 id="instance-overlap">
3448 <title>Overlapping instances</title>
3450 In general, <emphasis>GHC requires that that it be unambiguous which instance
3452 should be used to resolve a type-class constraint</emphasis>. This behaviour
3453 can be modified by two flags: <option>-XOverlappingInstances</option>
3454 <indexterm><primary>-XOverlappingInstances
3455 </primary></indexterm>
3456 and <option>-XIncoherentInstances</option>
3457 <indexterm><primary>-XIncoherentInstances
3458 </primary></indexterm>, as this section discusses. Both these
3459 flags are dynamic flags, and can be set on a per-module basis, using
3460 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3462 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3463 it tries to match every instance declaration against the
3465 by instantiating the head of the instance declaration. For example, consider
3468 instance context1 => C Int a where ... -- (A)
3469 instance context2 => C a Bool where ... -- (B)
3470 instance context3 => C Int [a] where ... -- (C)
3471 instance context4 => C Int [Int] where ... -- (D)
3473 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3474 but (C) and (D) do not. When matching, GHC takes
3475 no account of the context of the instance declaration
3476 (<literal>context1</literal> etc).
3477 GHC's default behaviour is that <emphasis>exactly one instance must match the
3478 constraint it is trying to resolve</emphasis>.
3479 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3480 including both declarations (A) and (B), say); an error is only reported if a
3481 particular constraint matches more than one.
3485 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3486 more than one instance to match, provided there is a most specific one. For
3487 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3488 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3489 most-specific match, the program is rejected.
3492 However, GHC is conservative about committing to an overlapping instance. For example:
3497 Suppose that from the RHS of <literal>f</literal> we get the constraint
3498 <literal>C Int [b]</literal>. But
3499 GHC does not commit to instance (C), because in a particular
3500 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3501 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3502 So GHC rejects the program.
3503 (If you add the flag <option>-XIncoherentInstances</option>,
3504 GHC will instead pick (C), without complaining about
3505 the problem of subsequent instantiations.)
3508 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3509 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3510 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3511 it instead. In this case, GHC will refrain from
3512 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3513 as before) but, rather than rejecting the program, it will infer the type
3515 f :: C Int b => [b] -> [b]
3517 That postpones the question of which instance to pick to the
3518 call site for <literal>f</literal>
3519 by which time more is known about the type <literal>b</literal>.
3522 The willingness to be overlapped or incoherent is a property of
3523 the <emphasis>instance declaration</emphasis> itself, controlled by the
3524 presence or otherwise of the <option>-XOverlappingInstances</option>
3525 and <option>-XIncoherentInstances</option> flags when that module is
3526 being defined. Neither flag is required in a module that imports and uses the
3527 instance declaration. Specifically, during the lookup process:
3530 An instance declaration is ignored during the lookup process if (a) a more specific
3531 match is found, and (b) the instance declaration was compiled with
3532 <option>-XOverlappingInstances</option>. The flag setting for the
3533 more-specific instance does not matter.
3536 Suppose an instance declaration does not match the constraint being looked up, but
3537 does unify with it, so that it might match when the constraint is further
3538 instantiated. Usually GHC will regard this as a reason for not committing to
3539 some other constraint. But if the instance declaration was compiled with
3540 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3541 check for that declaration.
3544 These rules make it possible for a library author to design a library that relies on
3545 overlapping instances without the library client having to know.
3548 If an instance declaration is compiled without
3549 <option>-XOverlappingInstances</option>,
3550 then that instance can never be overlapped. This could perhaps be
3551 inconvenient. Perhaps the rule should instead say that the
3552 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3553 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3554 at a usage site should be permitted regardless of how the instance declarations
3555 are compiled, if the <option>-XOverlappingInstances</option> flag is
3556 used at the usage site. (Mind you, the exact usage site can occasionally be
3557 hard to pin down.) We are interested to receive feedback on these points.
3559 <para>The <option>-XIncoherentInstances</option> flag implies the
3560 <option>-XOverlappingInstances</option> flag, but not vice versa.
3565 <title>Type synonyms in the instance head</title>
3568 <emphasis>Unlike Haskell 98, instance heads may use type
3569 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3570 As always, using a type synonym is just shorthand for
3571 writing the RHS of the type synonym definition. For example:
3575 type Point = (Int,Int)
3576 instance C Point where ...
3577 instance C [Point] where ...
3581 is legal. However, if you added
3585 instance C (Int,Int) where ...
3589 as well, then the compiler will complain about the overlapping
3590 (actually, identical) instance declarations. As always, type synonyms
3591 must be fully applied. You cannot, for example, write:
3596 instance Monad P where ...
3600 This design decision is independent of all the others, and easily
3601 reversed, but it makes sense to me.
3609 <sect2 id="overloaded-strings">
3610 <title>Overloaded string literals
3614 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3615 string literal has type <literal>String</literal>, but with overloaded string
3616 literals enabled (with <literal>-XOverloadedStrings</literal>)
3617 a string literal has type <literal>(IsString a) => a</literal>.
3620 This means that the usual string syntax can be used, e.g., for packed strings
3621 and other variations of string like types. String literals behave very much
3622 like integer literals, i.e., they can be used in both expressions and patterns.
3623 If used in a pattern the literal with be replaced by an equality test, in the same
3624 way as an integer literal is.
3627 The class <literal>IsString</literal> is defined as:
3629 class IsString a where
3630 fromString :: String -> a
3632 The only predefined instance is the obvious one to make strings work as usual:
3634 instance IsString [Char] where
3637 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3638 it explicitly (for example, to give an instance declaration for it), you can import it
3639 from module <literal>GHC.Exts</literal>.
3642 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3646 Each type in a default declaration must be an
3647 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3651 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3652 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3653 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3654 <emphasis>or</emphasis> <literal>IsString</literal>.
3663 import GHC.Exts( IsString(..) )
3665 newtype MyString = MyString String deriving (Eq, Show)
3666 instance IsString MyString where
3667 fromString = MyString
3669 greet :: MyString -> MyString
3670 greet "hello" = "world"
3674 print $ greet "hello"
3675 print $ greet "fool"
3679 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3680 to work since it gets translated into an equality comparison.
3686 <sect1 id="other-type-extensions">
3687 <title>Other type system extensions</title>
3689 <sect2 id="type-restrictions">
3690 <title>Type signatures</title>
3692 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3694 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3695 the form <emphasis>(class type-variable)</emphasis> or
3696 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3697 these type signatures are perfectly OK
3700 g :: Ord (T a ()) => ...
3704 GHC imposes the following restrictions on the constraints in a type signature.
3708 forall tv1..tvn (c1, ...,cn) => type
3711 (Here, we write the "foralls" explicitly, although the Haskell source
3712 language omits them; in Haskell 98, all the free type variables of an
3713 explicit source-language type signature are universally quantified,
3714 except for the class type variables in a class declaration. However,
3715 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3724 <emphasis>Each universally quantified type variable
3725 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3727 A type variable <literal>a</literal> is "reachable" if it appears
3728 in the same constraint as either a type variable free in
3729 <literal>type</literal>, or another reachable type variable.
3730 A value with a type that does not obey
3731 this reachability restriction cannot be used without introducing
3732 ambiguity; that is why the type is rejected.
3733 Here, for example, is an illegal type:
3737 forall a. Eq a => Int
3741 When a value with this type was used, the constraint <literal>Eq tv</literal>
3742 would be introduced where <literal>tv</literal> is a fresh type variable, and
3743 (in the dictionary-translation implementation) the value would be
3744 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3745 can never know which instance of <literal>Eq</literal> to use because we never
3746 get any more information about <literal>tv</literal>.
3750 that the reachability condition is weaker than saying that <literal>a</literal> is
3751 functionally dependent on a type variable free in
3752 <literal>type</literal> (see <xref
3753 linkend="functional-dependencies"/>). The reason for this is there
3754 might be a "hidden" dependency, in a superclass perhaps. So
3755 "reachable" is a conservative approximation to "functionally dependent".
3756 For example, consider:
3758 class C a b | a -> b where ...
3759 class C a b => D a b where ...
3760 f :: forall a b. D a b => a -> a
3762 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3763 but that is not immediately apparent from <literal>f</literal>'s type.
3769 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3770 universally quantified type variables <literal>tvi</literal></emphasis>.
3772 For example, this type is OK because <literal>C a b</literal> mentions the
3773 universally quantified type variable <literal>b</literal>:
3777 forall a. C a b => burble
3781 The next type is illegal because the constraint <literal>Eq b</literal> does not
3782 mention <literal>a</literal>:
3786 forall a. Eq b => burble
3790 The reason for this restriction is milder than the other one. The
3791 excluded types are never useful or necessary (because the offending
3792 context doesn't need to be witnessed at this point; it can be floated
3793 out). Furthermore, floating them out increases sharing. Lastly,
3794 excluding them is a conservative choice; it leaves a patch of
3795 territory free in case we need it later.
3809 <sect2 id="implicit-parameters">
3810 <title>Implicit parameters</title>
3812 <para> Implicit parameters are implemented as described in
3813 "Implicit parameters: dynamic scoping with static types",
3814 J Lewis, MB Shields, E Meijer, J Launchbury,
3815 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3819 <para>(Most of the following, still rather incomplete, documentation is
3820 due to Jeff Lewis.)</para>
3822 <para>Implicit parameter support is enabled with the option
3823 <option>-XImplicitParams</option>.</para>
3826 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3827 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3828 context. In Haskell, all variables are statically bound. Dynamic
3829 binding of variables is a notion that goes back to Lisp, but was later
3830 discarded in more modern incarnations, such as Scheme. Dynamic binding
3831 can be very confusing in an untyped language, and unfortunately, typed
3832 languages, in particular Hindley-Milner typed languages like Haskell,
3833 only support static scoping of variables.
3836 However, by a simple extension to the type class system of Haskell, we
3837 can support dynamic binding. Basically, we express the use of a
3838 dynamically bound variable as a constraint on the type. These
3839 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3840 function uses a dynamically-bound variable <literal>?x</literal>
3841 of type <literal>t'</literal>". For
3842 example, the following expresses the type of a sort function,
3843 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3845 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3847 The dynamic binding constraints are just a new form of predicate in the type class system.
3850 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3851 where <literal>x</literal> is
3852 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3853 Use of this construct also introduces a new
3854 dynamic-binding constraint in the type of the expression.
3855 For example, the following definition
3856 shows how we can define an implicitly parameterized sort function in
3857 terms of an explicitly parameterized <literal>sortBy</literal> function:
3859 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3861 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3867 <title>Implicit-parameter type constraints</title>
3869 Dynamic binding constraints behave just like other type class
3870 constraints in that they are automatically propagated. Thus, when a
3871 function is used, its implicit parameters are inherited by the
3872 function that called it. For example, our <literal>sort</literal> function might be used
3873 to pick out the least value in a list:
3875 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3876 least xs = head (sort xs)
3878 Without lifting a finger, the <literal>?cmp</literal> parameter is
3879 propagated to become a parameter of <literal>least</literal> as well. With explicit
3880 parameters, the default is that parameters must always be explicit
3881 propagated. With implicit parameters, the default is to always
3885 An implicit-parameter type constraint differs from other type class constraints in the
3886 following way: All uses of a particular implicit parameter must have
3887 the same type. This means that the type of <literal>(?x, ?x)</literal>
3888 is <literal>(?x::a) => (a,a)</literal>, and not
3889 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3893 <para> You can't have an implicit parameter in the context of a class or instance
3894 declaration. For example, both these declarations are illegal:
3896 class (?x::Int) => C a where ...
3897 instance (?x::a) => Foo [a] where ...
3899 Reason: exactly which implicit parameter you pick up depends on exactly where
3900 you invoke a function. But the ``invocation'' of instance declarations is done
3901 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3902 Easiest thing is to outlaw the offending types.</para>
3904 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3906 f :: (?x :: [a]) => Int -> Int
3909 g :: (Read a, Show a) => String -> String
3912 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3913 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3914 quite unambiguous, and fixes the type <literal>a</literal>.
3919 <title>Implicit-parameter bindings</title>
3922 An implicit parameter is <emphasis>bound</emphasis> using the standard
3923 <literal>let</literal> or <literal>where</literal> binding forms.
3924 For example, we define the <literal>min</literal> function by binding
3925 <literal>cmp</literal>.
3928 min = let ?cmp = (<=) in least
3932 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3933 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3934 (including in a list comprehension, or do-notation, or pattern guards),
3935 or a <literal>where</literal> clause.
3936 Note the following points:
3939 An implicit-parameter binding group must be a
3940 collection of simple bindings to implicit-style variables (no
3941 function-style bindings, and no type signatures); these bindings are
3942 neither polymorphic or recursive.
3945 You may not mix implicit-parameter bindings with ordinary bindings in a
3946 single <literal>let</literal>
3947 expression; use two nested <literal>let</literal>s instead.
3948 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3952 You may put multiple implicit-parameter bindings in a
3953 single binding group; but they are <emphasis>not</emphasis> treated
3954 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3955 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3956 parameter. The bindings are not nested, and may be re-ordered without changing
3957 the meaning of the program.
3958 For example, consider:
3960 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3962 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3963 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3965 f :: (?x::Int) => Int -> Int
3973 <sect3><title>Implicit parameters and polymorphic recursion</title>
3976 Consider these two definitions:
3979 len1 xs = let ?acc = 0 in len_acc1 xs
3982 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3987 len2 xs = let ?acc = 0 in len_acc2 xs
3989 len_acc2 :: (?acc :: Int) => [a] -> Int
3991 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3993 The only difference between the two groups is that in the second group
3994 <literal>len_acc</literal> is given a type signature.
3995 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3996 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3997 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3998 has a type signature, the recursive call is made to the
3999 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4000 as an implicit parameter. So we get the following results in GHCi:
4007 Adding a type signature dramatically changes the result! This is a rather
4008 counter-intuitive phenomenon, worth watching out for.
4012 <sect3><title>Implicit parameters and monomorphism</title>
4014 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4015 Haskell Report) to implicit parameters. For example, consider:
4023 Since the binding for <literal>y</literal> falls under the Monomorphism
4024 Restriction it is not generalised, so the type of <literal>y</literal> is
4025 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4026 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4027 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4028 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4029 <literal>y</literal> in the body of the <literal>let</literal> will see the
4030 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4031 <literal>14</literal>.
4036 <!-- ======================= COMMENTED OUT ========================
4038 We intend to remove linear implicit parameters, so I'm at least removing
4039 them from the 6.6 user manual
4041 <sect2 id="linear-implicit-parameters">
4042 <title>Linear implicit parameters</title>
4044 Linear implicit parameters are an idea developed by Koen Claessen,
4045 Mark Shields, and Simon PJ. They address the long-standing
4046 problem that monads seem over-kill for certain sorts of problem, notably:
4049 <listitem> <para> distributing a supply of unique names </para> </listitem>
4050 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4051 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4055 Linear implicit parameters are just like ordinary implicit parameters,
4056 except that they are "linear"; that is, they cannot be copied, and
4057 must be explicitly "split" instead. Linear implicit parameters are
4058 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4059 (The '/' in the '%' suggests the split!)
4064 import GHC.Exts( Splittable )
4066 data NameSupply = ...
4068 splitNS :: NameSupply -> (NameSupply, NameSupply)
4069 newName :: NameSupply -> Name
4071 instance Splittable NameSupply where
4075 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4076 f env (Lam x e) = Lam x' (f env e)
4079 env' = extend env x x'
4080 ...more equations for f...
4082 Notice that the implicit parameter %ns is consumed
4084 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4085 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4089 So the translation done by the type checker makes
4090 the parameter explicit:
4092 f :: NameSupply -> Env -> Expr -> Expr
4093 f ns env (Lam x e) = Lam x' (f ns1 env e)
4095 (ns1,ns2) = splitNS ns
4097 env = extend env x x'
4099 Notice the call to 'split' introduced by the type checker.
4100 How did it know to use 'splitNS'? Because what it really did
4101 was to introduce a call to the overloaded function 'split',
4102 defined by the class <literal>Splittable</literal>:
4104 class Splittable a where
4107 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4108 split for name supplies. But we can simply write
4114 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4116 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4117 <literal>GHC.Exts</literal>.
4122 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4123 are entirely distinct implicit parameters: you
4124 can use them together and they won't interfere with each other. </para>
4127 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4129 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4130 in the context of a class or instance declaration. </para></listitem>
4134 <sect3><title>Warnings</title>
4137 The monomorphism restriction is even more important than usual.
4138 Consider the example above:
4140 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4141 f env (Lam x e) = Lam x' (f env e)
4144 env' = extend env x x'
4146 If we replaced the two occurrences of x' by (newName %ns), which is
4147 usually a harmless thing to do, we get:
4149 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4150 f env (Lam x e) = Lam (newName %ns) (f env e)
4152 env' = extend env x (newName %ns)
4154 But now the name supply is consumed in <emphasis>three</emphasis> places
4155 (the two calls to newName,and the recursive call to f), so
4156 the result is utterly different. Urk! We don't even have
4160 Well, this is an experimental change. With implicit
4161 parameters we have already lost beta reduction anyway, and
4162 (as John Launchbury puts it) we can't sensibly reason about
4163 Haskell programs without knowing their typing.
4168 <sect3><title>Recursive functions</title>
4169 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4172 foo :: %x::T => Int -> [Int]
4174 foo n = %x : foo (n-1)
4176 where T is some type in class Splittable.</para>
4178 Do you get a list of all the same T's or all different T's
4179 (assuming that split gives two distinct T's back)?
4181 If you supply the type signature, taking advantage of polymorphic
4182 recursion, you get what you'd probably expect. Here's the
4183 translated term, where the implicit param is made explicit:
4186 foo x n = let (x1,x2) = split x
4187 in x1 : foo x2 (n-1)
4189 But if you don't supply a type signature, GHC uses the Hindley
4190 Milner trick of using a single monomorphic instance of the function
4191 for the recursive calls. That is what makes Hindley Milner type inference
4192 work. So the translation becomes
4196 foom n = x : foom (n-1)
4200 Result: 'x' is not split, and you get a list of identical T's. So the
4201 semantics of the program depends on whether or not foo has a type signature.
4204 You may say that this is a good reason to dislike linear implicit parameters
4205 and you'd be right. That is why they are an experimental feature.
4211 ================ END OF Linear Implicit Parameters commented out -->
4213 <sect2 id="kinding">
4214 <title>Explicitly-kinded quantification</title>
4217 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4218 to give the kind explicitly as (machine-checked) documentation,
4219 just as it is nice to give a type signature for a function. On some occasions,
4220 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4221 John Hughes had to define the data type:
4223 data Set cxt a = Set [a]
4224 | Unused (cxt a -> ())
4226 The only use for the <literal>Unused</literal> constructor was to force the correct
4227 kind for the type variable <literal>cxt</literal>.
4230 GHC now instead allows you to specify the kind of a type variable directly, wherever
4231 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4234 This flag enables kind signatures in the following places:
4236 <listitem><para><literal>data</literal> declarations:
4238 data Set (cxt :: * -> *) a = Set [a]
4239 </screen></para></listitem>
4240 <listitem><para><literal>type</literal> declarations:
4242 type T (f :: * -> *) = f Int
4243 </screen></para></listitem>
4244 <listitem><para><literal>class</literal> declarations:
4246 class (Eq a) => C (f :: * -> *) a where ...
4247 </screen></para></listitem>
4248 <listitem><para><literal>forall</literal>'s in type signatures:
4250 f :: forall (cxt :: * -> *). Set cxt Int
4251 </screen></para></listitem>
4256 The parentheses are required. Some of the spaces are required too, to
4257 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4258 will get a parse error, because "<literal>::*->*</literal>" is a
4259 single lexeme in Haskell.
4263 As part of the same extension, you can put kind annotations in types
4266 f :: (Int :: *) -> Int
4267 g :: forall a. a -> (a :: *)
4271 atype ::= '(' ctype '::' kind ')
4273 The parentheses are required.
4278 <sect2 id="universal-quantification">
4279 <title>Arbitrary-rank polymorphism
4283 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4284 allows us to say exactly what this means. For example:
4292 g :: forall b. (b -> b)
4294 The two are treated identically.
4298 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4299 explicit universal quantification in
4301 For example, all the following types are legal:
4303 f1 :: forall a b. a -> b -> a
4304 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4306 f2 :: (forall a. a->a) -> Int -> Int
4307 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4309 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4311 f4 :: Int -> (forall a. a -> a)
4313 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4314 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4315 The <literal>forall</literal> makes explicit the universal quantification that
4316 is implicitly added by Haskell.
4319 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4320 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4321 shows, the polymorphic type on the left of the function arrow can be overloaded.
4324 The function <literal>f3</literal> has a rank-3 type;
4325 it has rank-2 types on the left of a function arrow.
4328 GHC has three flags to control higher-rank types:
4331 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4334 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4337 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4338 That is, you can nest <literal>forall</literal>s
4339 arbitrarily deep in function arrows.
4340 In particular, a forall-type (also called a "type scheme"),
4341 including an operational type class context, is legal:
4343 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4344 of a function arrow </para> </listitem>
4345 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4346 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4347 field type signatures.</para> </listitem>
4348 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4349 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4353 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4354 a type variable any more!
4363 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4364 the types of the constructor arguments. Here are several examples:
4370 data T a = T1 (forall b. b -> b -> b) a
4372 data MonadT m = MkMonad { return :: forall a. a -> m a,
4373 bind :: forall a b. m a -> (a -> m b) -> m b
4376 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4382 The constructors have rank-2 types:
4388 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4389 MkMonad :: forall m. (forall a. a -> m a)
4390 -> (forall a b. m a -> (a -> m b) -> m b)
4392 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4398 Notice that you don't need to use a <literal>forall</literal> if there's an
4399 explicit context. For example in the first argument of the
4400 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4401 prefixed to the argument type. The implicit <literal>forall</literal>
4402 quantifies all type variables that are not already in scope, and are
4403 mentioned in the type quantified over.
4407 As for type signatures, implicit quantification happens for non-overloaded
4408 types too. So if you write this:
4411 data T a = MkT (Either a b) (b -> b)
4414 it's just as if you had written this:
4417 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4420 That is, since the type variable <literal>b</literal> isn't in scope, it's
4421 implicitly universally quantified. (Arguably, it would be better
4422 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4423 where that is what is wanted. Feedback welcomed.)
4427 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4428 the constructor to suitable values, just as usual. For example,
4439 a3 = MkSwizzle reverse
4442 a4 = let r x = Just x
4449 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4450 mkTs f x y = [T1 f x, T1 f y]
4456 The type of the argument can, as usual, be more general than the type
4457 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4458 does not need the <literal>Ord</literal> constraint.)
4462 When you use pattern matching, the bound variables may now have
4463 polymorphic types. For example:
4469 f :: T a -> a -> (a, Char)
4470 f (T1 w k) x = (w k x, w 'c' 'd')
4472 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4473 g (MkSwizzle s) xs f = s (map f (s xs))
4475 h :: MonadT m -> [m a] -> m [a]
4476 h m [] = return m []
4477 h m (x:xs) = bind m x $ \y ->
4478 bind m (h m xs) $ \ys ->
4485 In the function <function>h</function> we use the record selectors <literal>return</literal>
4486 and <literal>bind</literal> to extract the polymorphic bind and return functions
4487 from the <literal>MonadT</literal> data structure, rather than using pattern
4493 <title>Type inference</title>
4496 In general, type inference for arbitrary-rank types is undecidable.
4497 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4498 to get a decidable algorithm by requiring some help from the programmer.
4499 We do not yet have a formal specification of "some help" but the rule is this:
4502 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4503 provides an explicit polymorphic type for x, or GHC's type inference will assume
4504 that x's type has no foralls in it</emphasis>.
4507 What does it mean to "provide" an explicit type for x? You can do that by
4508 giving a type signature for x directly, using a pattern type signature
4509 (<xref linkend="scoped-type-variables"/>), thus:
4511 \ f :: (forall a. a->a) -> (f True, f 'c')
4513 Alternatively, you can give a type signature to the enclosing
4514 context, which GHC can "push down" to find the type for the variable:
4516 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4518 Here the type signature on the expression can be pushed inwards
4519 to give a type signature for f. Similarly, and more commonly,
4520 one can give a type signature for the function itself:
4522 h :: (forall a. a->a) -> (Bool,Char)
4523 h f = (f True, f 'c')
4525 You don't need to give a type signature if the lambda bound variable
4526 is a constructor argument. Here is an example we saw earlier:
4528 f :: T a -> a -> (a, Char)
4529 f (T1 w k) x = (w k x, w 'c' 'd')
4531 Here we do not need to give a type signature to <literal>w</literal>, because
4532 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4539 <sect3 id="implicit-quant">
4540 <title>Implicit quantification</title>
4543 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4544 user-written types, if and only if there is no explicit <literal>forall</literal>,
4545 GHC finds all the type variables mentioned in the type that are not already
4546 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4550 f :: forall a. a -> a
4557 h :: forall b. a -> b -> b
4563 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4566 f :: (a -> a) -> Int
4568 f :: forall a. (a -> a) -> Int
4570 f :: (forall a. a -> a) -> Int
4573 g :: (Ord a => a -> a) -> Int
4574 -- MEANS the illegal type
4575 g :: forall a. (Ord a => a -> a) -> Int
4577 g :: (forall a. Ord a => a -> a) -> Int
4579 The latter produces an illegal type, which you might think is silly,
4580 but at least the rule is simple. If you want the latter type, you
4581 can write your for-alls explicitly. Indeed, doing so is strongly advised
4588 <sect2 id="impredicative-polymorphism">
4589 <title>Impredicative polymorphism
4591 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4592 enabled with <option>-XImpredicativeTypes</option>.
4594 that you can call a polymorphic function at a polymorphic type, and
4595 parameterise data structures over polymorphic types. For example:
4597 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4598 f (Just g) = Just (g [3], g "hello")
4601 Notice here that the <literal>Maybe</literal> type is parameterised by the
4602 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4605 <para>The technical details of this extension are described in the paper
4606 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4607 type inference for higher-rank types and impredicativity</ulink>,
4608 which appeared at ICFP 2006.
4612 <sect2 id="scoped-type-variables">
4613 <title>Lexically scoped type variables
4617 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4618 which some type signatures are simply impossible to write. For example:
4620 f :: forall a. [a] -> [a]
4626 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4627 the entire definition of <literal>f</literal>.
4628 In particular, it is in scope at the type signature for <varname>ys</varname>.
4629 In Haskell 98 it is not possible to declare
4630 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4631 it becomes possible to do so.
4633 <para>Lexically-scoped type variables are enabled by
4634 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4636 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4637 variables work, compared to earlier releases. Read this section
4641 <title>Overview</title>
4643 <para>The design follows the following principles
4645 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4646 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4647 design.)</para></listitem>
4648 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4649 type variables. This means that every programmer-written type signature
4650 (including one that contains free scoped type variables) denotes a
4651 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4652 checker, and no inference is involved.</para></listitem>
4653 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4654 changing the program.</para></listitem>
4658 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4660 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4661 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4662 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4663 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4667 In Haskell, a programmer-written type signature is implicitly quantified over
4668 its free type variables (<ulink
4669 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4671 of the Haskell Report).
4672 Lexically scoped type variables affect this implicit quantification rules
4673 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4674 quantified. For example, if type variable <literal>a</literal> is in scope,
4677 (e :: a -> a) means (e :: a -> a)
4678 (e :: b -> b) means (e :: forall b. b->b)
4679 (e :: a -> b) means (e :: forall b. a->b)
4687 <sect3 id="decl-type-sigs">
4688 <title>Declaration type signatures</title>
4689 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4690 quantification (using <literal>forall</literal>) brings into scope the
4691 explicitly-quantified
4692 type variables, in the definition of the named function. For example:
4694 f :: forall a. [a] -> [a]
4695 f (x:xs) = xs ++ [ x :: a ]
4697 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4698 the definition of "<literal>f</literal>".
4700 <para>This only happens if:
4702 <listitem><para> The quantification in <literal>f</literal>'s type
4703 signature is explicit. For example:
4706 g (x:xs) = xs ++ [ x :: a ]
4708 This program will be rejected, because "<literal>a</literal>" does not scope
4709 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4710 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4711 quantification rules.
4713 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4714 not a pattern binding.
4717 f1 :: forall a. [a] -> [a]
4718 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4720 f2 :: forall a. [a] -> [a]
4721 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4723 f3 :: forall a. [a] -> [a]
4724 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4726 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4727 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4728 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4729 the type signature brings <literal>a</literal> into scope.
4735 <sect3 id="exp-type-sigs">
4736 <title>Expression type signatures</title>
4738 <para>An expression type signature that has <emphasis>explicit</emphasis>
4739 quantification (using <literal>forall</literal>) brings into scope the
4740 explicitly-quantified
4741 type variables, in the annotated expression. For example:
4743 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4745 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4746 type variable <literal>s</literal> into scope, in the annotated expression
4747 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4752 <sect3 id="pattern-type-sigs">
4753 <title>Pattern type signatures</title>
4755 A type signature may occur in any pattern; this is a <emphasis>pattern type
4756 signature</emphasis>.
4759 -- f and g assume that 'a' is already in scope
4760 f = \(x::Int, y::a) -> x
4762 h ((x,y) :: (Int,Bool)) = (y,x)
4764 In the case where all the type variables in the pattern type signature are
4765 already in scope (i.e. bound by the enclosing context), matters are simple: the
4766 signature simply constrains the type of the pattern in the obvious way.
4769 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4770 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4771 that are already in scope. For example:
4773 f :: forall a. [a] -> (Int, [a])
4776 (ys::[a], n) = (reverse xs, length xs) -- OK
4777 zs::[a] = xs ++ ys -- OK
4779 Just (v::b) = ... -- Not OK; b is not in scope
4781 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4782 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4786 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4787 type signature may mention a type variable that is not in scope; in this case,
4788 <emphasis>the signature brings that type variable into scope</emphasis>.
4789 This is particularly important for existential data constructors. For example:
4791 data T = forall a. MkT [a]
4794 k (MkT [t::a]) = MkT t3
4798 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4799 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4800 because it is bound by the pattern match. GHC's rule is that in this situation
4801 (and only then), a pattern type signature can mention a type variable that is
4802 not already in scope; the effect is to bring it into scope, standing for the
4803 existentially-bound type variable.
4806 When a pattern type signature binds a type variable in this way, GHC insists that the
4807 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4808 This means that any user-written type signature always stands for a completely known type.
4811 If all this seems a little odd, we think so too. But we must have
4812 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4813 could not name existentially-bound type variables in subsequent type signatures.
4816 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4817 signature is allowed to mention a lexical variable that is not already in
4819 For example, both <literal>f</literal> and <literal>g</literal> would be
4820 illegal if <literal>a</literal> was not already in scope.
4826 <!-- ==================== Commented out part about result type signatures
4828 <sect3 id="result-type-sigs">
4829 <title>Result type signatures</title>
4832 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4835 {- f assumes that 'a' is already in scope -}
4836 f x y :: [a] = [x,y,x]
4838 g = \ x :: [Int] -> [3,4]
4840 h :: forall a. [a] -> a
4844 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4845 the result of the function. Similarly, the body of the lambda in the RHS of
4846 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4847 alternative in <literal>h</literal> is <literal>a</literal>.
4849 <para> A result type signature never brings new type variables into scope.</para>
4851 There are a couple of syntactic wrinkles. First, notice that all three
4852 examples would parse quite differently with parentheses:
4854 {- f assumes that 'a' is already in scope -}
4855 f x (y :: [a]) = [x,y,x]
4857 g = \ (x :: [Int]) -> [3,4]
4859 h :: forall a. [a] -> a
4863 Now the signature is on the <emphasis>pattern</emphasis>; and
4864 <literal>h</literal> would certainly be ill-typed (since the pattern
4865 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4867 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4868 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4869 token or a parenthesised type of some sort). To see why,
4870 consider how one would parse this:
4879 <sect3 id="cls-inst-scoped-tyvars">
4880 <title>Class and instance declarations</title>
4883 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4884 scope over the methods defined in the <literal>where</literal> part. For example:
4902 <sect2 id="typing-binds">
4903 <title>Generalised typing of mutually recursive bindings</title>
4906 The Haskell Report specifies that a group of bindings (at top level, or in a
4907 <literal>let</literal> or <literal>where</literal>) should be sorted into
4908 strongly-connected components, and then type-checked in dependency order
4909 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4910 Report, Section 4.5.1</ulink>).
4911 As each group is type-checked, any binders of the group that
4913 an explicit type signature are put in the type environment with the specified
4915 and all others are monomorphic until the group is generalised
4916 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4919 <para>Following a suggestion of Mark Jones, in his paper
4920 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4922 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4924 <emphasis>the dependency analysis ignores references to variables that have an explicit
4925 type signature</emphasis>.
4926 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4927 typecheck. For example, consider:
4929 f :: Eq a => a -> Bool
4930 f x = (x == x) || g True || g "Yes"
4932 g y = (y <= y) || f True
4934 This is rejected by Haskell 98, but under Jones's scheme the definition for
4935 <literal>g</literal> is typechecked first, separately from that for
4936 <literal>f</literal>,
4937 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4938 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4939 type is generalised, to get
4941 g :: Ord a => a -> Bool
4943 Now, the definition for <literal>f</literal> is typechecked, with this type for
4944 <literal>g</literal> in the type environment.
4948 The same refined dependency analysis also allows the type signatures of
4949 mutually-recursive functions to have different contexts, something that is illegal in
4950 Haskell 98 (Section 4.5.2, last sentence). With
4951 <option>-XRelaxedPolyRec</option>
4952 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4953 type signatures; in practice this means that only variables bound by the same
4954 pattern binding must have the same context. For example, this is fine:
4956 f :: Eq a => a -> Bool
4957 f x = (x == x) || g True
4959 g :: Ord a => a -> Bool
4960 g y = (y <= y) || f True
4965 <sect2 id="type-families">
4966 <title>Type families
4970 GHC supports the definition of type families indexed by types. They may be
4971 seen as an extension of Haskell 98's class-based overloading of values to
4972 types. When type families are declared in classes, they are also known as
4976 There are two forms of type families: data families and type synonym families.
4977 Currently, only the former are fully implemented, while we are still working
4978 on the latter. As a result, the specification of the language extension is
4979 also still to some degree in flux. Hence, a more detailed description of
4980 the language extension and its use is currently available
4981 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4982 wiki page on type families</ulink>. The material will be moved to this user's
4983 guide when it has stabilised.
4986 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4993 <!-- ==================== End of type system extensions ================= -->
4995 <!-- ====================== TEMPLATE HASKELL ======================= -->
4997 <sect1 id="template-haskell">
4998 <title>Template Haskell</title>
5000 <para>Template Haskell allows you to do compile-time meta-programming in
5003 the main technical innovations is discussed in "<ulink
5004 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5005 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5008 There is a Wiki page about
5009 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5010 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5014 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5015 Haskell library reference material</ulink>
5016 (look for module <literal>Language.Haskell.TH</literal>).
5017 Many changes to the original design are described in
5018 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5019 Notes on Template Haskell version 2</ulink>.
5020 Not all of these changes are in GHC, however.
5023 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5024 as a worked example to help get you started.
5028 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5029 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5034 <title>Syntax</title>
5036 <para> Template Haskell has the following new syntactic
5037 constructions. You need to use the flag
5038 <option>-XTemplateHaskell</option>
5039 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5040 </indexterm>to switch these syntactic extensions on
5041 (<option>-XTemplateHaskell</option> is no longer implied by
5042 <option>-fglasgow-exts</option>).</para>
5046 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5047 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5048 There must be no space between the "$" and the identifier or parenthesis. This use
5049 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5050 of "." as an infix operator. If you want the infix operator, put spaces around it.
5052 <para> A splice can occur in place of
5054 <listitem><para> an expression; the spliced expression must
5055 have type <literal>Q Exp</literal></para></listitem>
5056 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5059 Inside a splice you can can only call functions defined in imported modules,
5060 not functions defined elsewhere in the same module.</listitem>
5064 A expression quotation is written in Oxford brackets, thus:
5066 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5067 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5068 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5069 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5070 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5071 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5072 </itemizedlist></para></listitem>
5075 A quasi-quotation can appear in either a pattern context or an
5076 expression context and is also written in Oxford brackets:
5078 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5079 where the "..." is an arbitrary string; a full description of the
5080 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5081 </itemizedlist></para></listitem>
5084 A name can be quoted with either one or two prefix single quotes:
5086 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5087 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5088 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5090 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5091 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5094 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5095 may also be given as an argument to the <literal>reify</literal> function.
5101 (Compared to the original paper, there are many differences of detail.
5102 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5103 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5104 Type splices are not implemented, and neither are pattern splices or quotations.
5108 <sect2> <title> Using Template Haskell </title>
5112 The data types and monadic constructor functions for Template Haskell are in the library
5113 <literal>Language.Haskell.THSyntax</literal>.
5117 You can only run a function at compile time if it is imported from another module. That is,
5118 you can't define a function in a module, and call it from within a splice in the same module.
5119 (It would make sense to do so, but it's hard to implement.)
5123 You can only run a function at compile time if it is imported
5124 from another module <emphasis>that is not part of a mutually-recursive group of modules
5125 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5126 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5127 splice is to be run.</para>
5129 For example, when compiling module A,
5130 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5131 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5135 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5138 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5139 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5140 compiles and runs a program, and then looks at the result. So it's important that
5141 the program it compiles produces results whose representations are identical to
5142 those of the compiler itself.
5146 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5147 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5152 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5153 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5154 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5161 -- Import our template "pr"
5162 import Printf ( pr )
5164 -- The splice operator $ takes the Haskell source code
5165 -- generated at compile time by "pr" and splices it into
5166 -- the argument of "putStrLn".
5167 main = putStrLn ( $(pr "Hello") )
5173 -- Skeletal printf from the paper.
5174 -- It needs to be in a separate module to the one where
5175 -- you intend to use it.
5177 -- Import some Template Haskell syntax
5178 import Language.Haskell.TH
5180 -- Describe a format string
5181 data Format = D | S | L String
5183 -- Parse a format string. This is left largely to you
5184 -- as we are here interested in building our first ever
5185 -- Template Haskell program and not in building printf.
5186 parse :: String -> [Format]
5189 -- Generate Haskell source code from a parsed representation
5190 -- of the format string. This code will be spliced into
5191 -- the module which calls "pr", at compile time.
5192 gen :: [Format] -> Q Exp
5193 gen [D] = [| \n -> show n |]
5194 gen [S] = [| \s -> s |]
5195 gen [L s] = stringE s
5197 -- Here we generate the Haskell code for the splice
5198 -- from an input format string.
5199 pr :: String -> Q Exp
5200 pr s = gen (parse s)
5203 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5206 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5209 <para>Run "main.exe" and here is your output:</para>
5219 <title>Using Template Haskell with Profiling</title>
5220 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5222 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5223 interpreter to run the splice expressions. The bytecode interpreter
5224 runs the compiled expression on top of the same runtime on which GHC
5225 itself is running; this means that the compiled code referred to by
5226 the interpreted expression must be compatible with this runtime, and
5227 in particular this means that object code that is compiled for
5228 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5229 expression, because profiled object code is only compatible with the
5230 profiling version of the runtime.</para>
5232 <para>This causes difficulties if you have a multi-module program
5233 containing Template Haskell code and you need to compile it for
5234 profiling, because GHC cannot load the profiled object code and use it
5235 when executing the splices. Fortunately GHC provides a workaround.
5236 The basic idea is to compile the program twice:</para>
5240 <para>Compile the program or library first the normal way, without
5241 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5244 <para>Then compile it again with <option>-prof</option>, and
5245 additionally use <option>-osuf
5246 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5247 to name the object files differently (you can choose any suffix
5248 that isn't the normal object suffix here). GHC will automatically
5249 load the object files built in the first step when executing splice
5250 expressions. If you omit the <option>-osuf</option> flag when
5251 building with <option>-prof</option> and Template Haskell is used,
5252 GHC will emit an error message. </para>
5257 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5258 <para>Quasi-quotation allows patterns and expressions to be written using
5259 programmer-defined concrete syntax; the motivation behind the extension and
5260 several examples are documented in
5261 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5262 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5263 2007). The example below shows how to write a quasiquoter for a simple
5264 expression language.</para>
5267 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5268 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5269 functions for quoting expressions and patterns, respectively. The first argument
5270 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5271 context of the quasi-quotation statement determines which of the two parsers is
5272 called: if the quasi-quotation occurs in an expression context, the expression
5273 parser is called, and if it occurs in a pattern context, the pattern parser is
5277 Note that in the example we make use of an antiquoted
5278 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5279 (this syntax for anti-quotation was defined by the parser's
5280 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5281 integer value argument of the constructor <literal>IntExpr</literal> when
5282 pattern matching. Please see the referenced paper for further details regarding
5283 anti-quotation as well as the description of a technique that uses SYB to
5284 leverage a single parser of type <literal>String -> a</literal> to generate both
5285 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5286 pattern parser that returns a value of type <literal>Q Pat</literal>.
5289 <para>In general, a quasi-quote has the form
5290 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5291 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5292 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5293 can be arbitrary, and may contain newlines.
5296 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5297 the example, <literal>expr</literal> cannot be defined
5298 in <literal>Main.hs</literal> where it is used, but must be imported.
5309 main = do { print $ eval [$expr|1 + 2|]
5311 { [$expr|'int:n|] -> print n
5320 import qualified Language.Haskell.TH as TH
5321 import Language.Haskell.TH.Quasi
5323 data Expr = IntExpr Integer
5324 | AntiIntExpr String
5325 | BinopExpr BinOp Expr Expr
5327 deriving(Show, Typeable, Data)
5333 deriving(Show, Typeable, Data)
5335 eval :: Expr -> Integer
5336 eval (IntExpr n) = n
5337 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5344 expr = QuasiQuoter parseExprExp parseExprPat
5346 -- Parse an Expr, returning its representation as
5347 -- either a Q Exp or a Q Pat. See the referenced paper
5348 -- for how to use SYB to do this by writing a single
5349 -- parser of type String -> Expr instead of two
5350 -- separate parsers.
5352 parseExprExp :: String -> Q Exp
5355 parseExprPat :: String -> Q Pat
5359 <para>Now run the compiler:
5362 $ ghc --make -XQuasiQuotes Main.hs -o main
5365 <para>Run "main" and here is your output:</para>
5377 <!-- ===================== Arrow notation =================== -->
5379 <sect1 id="arrow-notation">
5380 <title>Arrow notation
5383 <para>Arrows are a generalization of monads introduced by John Hughes.
5384 For more details, see
5389 “Generalising Monads to Arrows”,
5390 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5391 pp67–111, May 2000.
5397 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5398 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5404 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5405 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5411 and the arrows web page at
5412 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5413 With the <option>-XArrows</option> flag, GHC supports the arrow
5414 notation described in the second of these papers.
5415 What follows is a brief introduction to the notation;
5416 it won't make much sense unless you've read Hughes's paper.
5417 This notation is translated to ordinary Haskell,
5418 using combinators from the
5419 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5423 <para>The extension adds a new kind of expression for defining arrows:
5425 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5426 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5428 where <literal>proc</literal> is a new keyword.
5429 The variables of the pattern are bound in the body of the
5430 <literal>proc</literal>-expression,
5431 which is a new sort of thing called a <firstterm>command</firstterm>.
5432 The syntax of commands is as follows:
5434 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5435 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5436 | <replaceable>cmd</replaceable><superscript>0</superscript>
5438 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5439 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5440 infix operators as for expressions, and
5442 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5443 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5444 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5445 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5446 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5447 | <replaceable>fcmd</replaceable>
5449 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5450 | ( <replaceable>cmd</replaceable> )
5451 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5453 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5454 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5455 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5456 | <replaceable>cmd</replaceable>
5458 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5459 except that the bodies are commands instead of expressions.
5463 Commands produce values, but (like monadic computations)
5464 may yield more than one value,
5465 or none, and may do other things as well.
5466 For the most part, familiarity with monadic notation is a good guide to
5468 However the values of expressions, even monadic ones,
5469 are determined by the values of the variables they contain;
5470 this is not necessarily the case for commands.
5474 A simple example of the new notation is the expression
5476 proc x -> f -< x+1
5478 We call this a <firstterm>procedure</firstterm> or
5479 <firstterm>arrow abstraction</firstterm>.
5480 As with a lambda expression, the variable <literal>x</literal>
5481 is a new variable bound within the <literal>proc</literal>-expression.
5482 It refers to the input to the arrow.
5483 In the above example, <literal>-<</literal> is not an identifier but an
5484 new reserved symbol used for building commands from an expression of arrow
5485 type and an expression to be fed as input to that arrow.
5486 (The weird look will make more sense later.)
5487 It may be read as analogue of application for arrows.
5488 The above example is equivalent to the Haskell expression
5490 arr (\ x -> x+1) >>> f
5492 That would make no sense if the expression to the left of
5493 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5494 More generally, the expression to the left of <literal>-<</literal>
5495 may not involve any <firstterm>local variable</firstterm>,
5496 i.e. a variable bound in the current arrow abstraction.
5497 For such a situation there is a variant <literal>-<<</literal>, as in
5499 proc x -> f x -<< x+1
5501 which is equivalent to
5503 arr (\ x -> (f x, x+1)) >>> app
5505 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5507 Such an arrow is equivalent to a monad, so if you're using this form
5508 you may find a monadic formulation more convenient.
5512 <title>do-notation for commands</title>
5515 Another form of command is a form of <literal>do</literal>-notation.
5516 For example, you can write
5525 You can read this much like ordinary <literal>do</literal>-notation,
5526 but with commands in place of monadic expressions.
5527 The first line sends the value of <literal>x+1</literal> as an input to
5528 the arrow <literal>f</literal>, and matches its output against
5529 <literal>y</literal>.
5530 In the next line, the output is discarded.
5531 The arrow <function>returnA</function> is defined in the
5532 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5533 module as <literal>arr id</literal>.
5534 The above example is treated as an abbreviation for
5536 arr (\ x -> (x, x)) >>>
5537 first (arr (\ x -> x+1) >>> f) >>>
5538 arr (\ (y, x) -> (y, (x, y))) >>>
5539 first (arr (\ y -> 2*y) >>> g) >>>
5541 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5542 first (arr (\ (x, z) -> x*z) >>> h) >>>
5543 arr (\ (t, z) -> t+z) >>>
5546 Note that variables not used later in the composition are projected out.
5547 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5549 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5550 module, this reduces to
5552 arr (\ x -> (x+1, x)) >>>
5554 arr (\ (y, x) -> (2*y, (x, y))) >>>
5556 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5558 arr (\ (t, z) -> t+z)
5560 which is what you might have written by hand.
5561 With arrow notation, GHC keeps track of all those tuples of variables for you.
5565 Note that although the above translation suggests that
5566 <literal>let</literal>-bound variables like <literal>z</literal> must be
5567 monomorphic, the actual translation produces Core,
5568 so polymorphic variables are allowed.
5572 It's also possible to have mutually recursive bindings,
5573 using the new <literal>rec</literal> keyword, as in the following example:
5575 counter :: ArrowCircuit a => a Bool Int
5576 counter = proc reset -> do
5577 rec output <- returnA -< if reset then 0 else next
5578 next <- delay 0 -< output+1
5579 returnA -< output
5581 The translation of such forms uses the <function>loop</function> combinator,
5582 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5588 <title>Conditional commands</title>
5591 In the previous example, we used a conditional expression to construct the
5593 Sometimes we want to conditionally execute different commands, as in
5600 which is translated to
5602 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5603 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5605 Since the translation uses <function>|||</function>,
5606 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5610 There are also <literal>case</literal> commands, like
5616 y <- h -< (x1, x2)
5620 The syntax is the same as for <literal>case</literal> expressions,
5621 except that the bodies of the alternatives are commands rather than expressions.
5622 The translation is similar to that of <literal>if</literal> commands.
5628 <title>Defining your own control structures</title>
5631 As we're seen, arrow notation provides constructs,
5632 modelled on those for expressions,
5633 for sequencing, value recursion and conditionals.
5634 But suitable combinators,
5635 which you can define in ordinary Haskell,
5636 may also be used to build new commands out of existing ones.
5637 The basic idea is that a command defines an arrow from environments to values.
5638 These environments assign values to the free local variables of the command.
5639 Thus combinators that produce arrows from arrows
5640 may also be used to build commands from commands.
5641 For example, the <literal>ArrowChoice</literal> class includes a combinator
5643 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5645 so we can use it to build commands:
5647 expr' = proc x -> do
5650 symbol Plus -< ()
5651 y <- term -< ()
5654 symbol Minus -< ()
5655 y <- term -< ()
5658 (The <literal>do</literal> on the first line is needed to prevent the first
5659 <literal><+> ...</literal> from being interpreted as part of the
5660 expression on the previous line.)
5661 This is equivalent to
5663 expr' = (proc x -> returnA -< x)
5664 <+> (proc x -> do
5665 symbol Plus -< ()
5666 y <- term -< ()
5668 <+> (proc x -> do
5669 symbol Minus -< ()
5670 y <- term -< ()
5673 It is essential that this operator be polymorphic in <literal>e</literal>
5674 (representing the environment input to the command
5675 and thence to its subcommands)
5676 and satisfy the corresponding naturality property
5678 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5680 at least for strict <literal>k</literal>.
5681 (This should be automatic if you're not using <function>seq</function>.)
5682 This ensures that environments seen by the subcommands are environments
5683 of the whole command,
5684 and also allows the translation to safely trim these environments.
5685 The operator must also not use any variable defined within the current
5690 We could define our own operator
5692 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5693 untilA body cond = proc x ->
5694 if cond x then returnA -< ()
5697 untilA body cond -< x
5699 and use it in the same way.
5700 Of course this infix syntax only makes sense for binary operators;
5701 there is also a more general syntax involving special brackets:
5705 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5712 <title>Primitive constructs</title>
5715 Some operators will need to pass additional inputs to their subcommands.
5716 For example, in an arrow type supporting exceptions,
5717 the operator that attaches an exception handler will wish to pass the
5718 exception that occurred to the handler.
5719 Such an operator might have a type
5721 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5723 where <literal>Ex</literal> is the type of exceptions handled.
5724 You could then use this with arrow notation by writing a command
5726 body `handleA` \ ex -> handler
5728 so that if an exception is raised in the command <literal>body</literal>,
5729 the variable <literal>ex</literal> is bound to the value of the exception
5730 and the command <literal>handler</literal>,
5731 which typically refers to <literal>ex</literal>, is entered.
5732 Though the syntax here looks like a functional lambda,
5733 we are talking about commands, and something different is going on.
5734 The input to the arrow represented by a command consists of values for
5735 the free local variables in the command, plus a stack of anonymous values.
5736 In all the prior examples, this stack was empty.
5737 In the second argument to <function>handleA</function>,
5738 this stack consists of one value, the value of the exception.
5739 The command form of lambda merely gives this value a name.
5744 the values on the stack are paired to the right of the environment.
5745 So operators like <function>handleA</function> that pass
5746 extra inputs to their subcommands can be designed for use with the notation
5747 by pairing the values with the environment in this way.
5748 More precisely, the type of each argument of the operator (and its result)
5749 should have the form
5751 a (...(e,t1), ... tn) t
5753 where <replaceable>e</replaceable> is a polymorphic variable
5754 (representing the environment)
5755 and <replaceable>ti</replaceable> are the types of the values on the stack,
5756 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5757 The polymorphic variable <replaceable>e</replaceable> must not occur in
5758 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5759 <replaceable>t</replaceable>.
5760 However the arrows involved need not be the same.
5761 Here are some more examples of suitable operators:
5763 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5764 runReader :: ... => a e c -> a' (e,State) c
5765 runState :: ... => a e c -> a' (e,State) (c,State)
5767 We can supply the extra input required by commands built with the last two
5768 by applying them to ordinary expressions, as in
5772 (|runReader (do { ... })|) s
5774 which adds <literal>s</literal> to the stack of inputs to the command
5775 built using <function>runReader</function>.
5779 The command versions of lambda abstraction and application are analogous to
5780 the expression versions.
5781 In particular, the beta and eta rules describe equivalences of commands.
5782 These three features (operators, lambda abstraction and application)
5783 are the core of the notation; everything else can be built using them,
5784 though the results would be somewhat clumsy.
5785 For example, we could simulate <literal>do</literal>-notation by defining
5787 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5788 u `bind` f = returnA &&& u >>> f
5790 bind_ :: Arrow a => a e b -> a e c -> a e c
5791 u `bind_` f = u `bind` (arr fst >>> f)
5793 We could simulate <literal>if</literal> by defining
5795 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5796 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5803 <title>Differences with the paper</title>
5808 <para>Instead of a single form of arrow application (arrow tail) with two
5809 translations, the implementation provides two forms
5810 <quote><literal>-<</literal></quote> (first-order)
5811 and <quote><literal>-<<</literal></quote> (higher-order).
5816 <para>User-defined operators are flagged with banana brackets instead of
5817 a new <literal>form</literal> keyword.
5826 <title>Portability</title>
5829 Although only GHC implements arrow notation directly,
5830 there is also a preprocessor
5832 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5833 that translates arrow notation into Haskell 98
5834 for use with other Haskell systems.
5835 You would still want to check arrow programs with GHC;
5836 tracing type errors in the preprocessor output is not easy.
5837 Modules intended for both GHC and the preprocessor must observe some
5838 additional restrictions:
5843 The module must import
5844 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5850 The preprocessor cannot cope with other Haskell extensions.
5851 These would have to go in separate modules.
5857 Because the preprocessor targets Haskell (rather than Core),
5858 <literal>let</literal>-bound variables are monomorphic.
5869 <!-- ==================== BANG PATTERNS ================= -->
5871 <sect1 id="bang-patterns">
5872 <title>Bang patterns
5873 <indexterm><primary>Bang patterns</primary></indexterm>
5875 <para>GHC supports an extension of pattern matching called <emphasis>bang
5876 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5878 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5879 prime feature description</ulink> contains more discussion and examples
5880 than the material below.
5883 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5886 <sect2 id="bang-patterns-informal">
5887 <title>Informal description of bang patterns
5890 The main idea is to add a single new production to the syntax of patterns:
5894 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5895 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5900 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5901 whereas without the bang it would be lazy.
5902 Bang patterns can be nested of course:
5906 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5907 <literal>y</literal>.
5908 A bang only really has an effect if it precedes a variable or wild-card pattern:
5913 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5914 forces evaluation anyway does nothing.
5916 Bang patterns work in <literal>case</literal> expressions too, of course:
5918 g5 x = let y = f x in body
5919 g6 x = case f x of { y -> body }
5920 g7 x = case f x of { !y -> body }
5922 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5923 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5924 result, and then evaluates <literal>body</literal>.
5926 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5927 definitions too. For example:
5931 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5932 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5933 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5934 in a function argument <literal>![x,y]</literal> means the
5935 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5936 is part of the syntax of <literal>let</literal> bindings.
5941 <sect2 id="bang-patterns-sem">
5942 <title>Syntax and semantics
5946 We add a single new production to the syntax of patterns:
5950 There is one problem with syntactic ambiguity. Consider:
5954 Is this a definition of the infix function "<literal>(!)</literal>",
5955 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5956 ambiguity in favour of the latter. If you want to define
5957 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5962 The semantics of Haskell pattern matching is described in <ulink
5963 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5964 Section 3.17.2</ulink> of the Haskell Report. To this description add
5965 one extra item 10, saying:
5966 <itemizedlist><listitem><para>Matching
5967 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5968 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5969 <listitem><para>otherwise, <literal>pat</literal> is matched against
5970 <literal>v</literal></para></listitem>
5972 </para></listitem></itemizedlist>
5973 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5974 Section 3.17.3</ulink>, add a new case (t):
5976 case v of { !pat -> e; _ -> e' }
5977 = v `seq` case v of { pat -> e; _ -> e' }
5980 That leaves let expressions, whose translation is given in
5981 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5983 of the Haskell Report.
5984 In the translation box, first apply
5985 the following transformation: for each pattern <literal>pi</literal> that is of
5986 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5987 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5988 have a bang at the top, apply the rules in the existing box.
5990 <para>The effect of the let rule is to force complete matching of the pattern
5991 <literal>qi</literal> before evaluation of the body is begun. The bang is
5992 retained in the translated form in case <literal>qi</literal> is a variable,
6000 The let-binding can be recursive. However, it is much more common for
6001 the let-binding to be non-recursive, in which case the following law holds:
6002 <literal>(let !p = rhs in body)</literal>
6004 <literal>(case rhs of !p -> body)</literal>
6007 A pattern with a bang at the outermost level is not allowed at the top level of
6013 <!-- ==================== ASSERTIONS ================= -->
6015 <sect1 id="assertions">
6017 <indexterm><primary>Assertions</primary></indexterm>
6021 If you want to make use of assertions in your standard Haskell code, you
6022 could define a function like the following:
6028 assert :: Bool -> a -> a
6029 assert False x = error "assertion failed!"
6036 which works, but gives you back a less than useful error message --
6037 an assertion failed, but which and where?
6041 One way out is to define an extended <function>assert</function> function which also
6042 takes a descriptive string to include in the error message and
6043 perhaps combine this with the use of a pre-processor which inserts
6044 the source location where <function>assert</function> was used.
6048 Ghc offers a helping hand here, doing all of this for you. For every
6049 use of <function>assert</function> in the user's source:
6055 kelvinToC :: Double -> Double
6056 kelvinToC k = assert (k >= 0.0) (k+273.15)
6062 Ghc will rewrite this to also include the source location where the
6069 assert pred val ==> assertError "Main.hs|15" pred val
6075 The rewrite is only performed by the compiler when it spots
6076 applications of <function>Control.Exception.assert</function>, so you
6077 can still define and use your own versions of
6078 <function>assert</function>, should you so wish. If not, import
6079 <literal>Control.Exception</literal> to make use
6080 <function>assert</function> in your code.
6084 GHC ignores assertions when optimisation is turned on with the
6085 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6086 <literal>assert pred e</literal> will be rewritten to
6087 <literal>e</literal>. You can also disable assertions using the
6088 <option>-fignore-asserts</option>
6089 option<indexterm><primary><option>-fignore-asserts</option></primary>
6090 </indexterm>.</para>
6093 Assertion failures can be caught, see the documentation for the
6094 <literal>Control.Exception</literal> library for the details.
6100 <!-- =============================== PRAGMAS =========================== -->
6102 <sect1 id="pragmas">
6103 <title>Pragmas</title>
6105 <indexterm><primary>pragma</primary></indexterm>
6107 <para>GHC supports several pragmas, or instructions to the
6108 compiler placed in the source code. Pragmas don't normally affect
6109 the meaning of the program, but they might affect the efficiency
6110 of the generated code.</para>
6112 <para>Pragmas all take the form
6114 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6116 where <replaceable>word</replaceable> indicates the type of
6117 pragma, and is followed optionally by information specific to that
6118 type of pragma. Case is ignored in
6119 <replaceable>word</replaceable>. The various values for
6120 <replaceable>word</replaceable> that GHC understands are described
6121 in the following sections; any pragma encountered with an
6122 unrecognised <replaceable>word</replaceable> is (silently)
6123 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6124 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6126 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6127 pragma must precede the <literal>module</literal> keyword in the file.
6128 There can be as many file-header pragmas as you please, and they can be
6129 preceded or followed by comments.</para>
6131 <sect2 id="language-pragma">
6132 <title>LANGUAGE pragma</title>
6134 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6135 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6137 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6139 It is the intention that all Haskell compilers support the
6140 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6141 all extensions are supported by all compilers, of
6142 course. The <literal>LANGUAGE</literal> pragma should be used instead
6143 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6145 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6147 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6149 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6151 <para>Every language extension can also be turned into a command-line flag
6152 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6153 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6156 <para>A list of all supported language extensions can be obtained by invoking
6157 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6159 <para>Any extension from the <literal>Extension</literal> type defined in
6161 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6162 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6166 <sect2 id="options-pragma">
6167 <title>OPTIONS_GHC pragma</title>
6168 <indexterm><primary>OPTIONS_GHC</primary>
6170 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6173 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6174 additional options that are given to the compiler when compiling
6175 this source file. See <xref linkend="source-file-options"/> for
6178 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6179 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6182 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6184 <sect2 id="include-pragma">
6185 <title>INCLUDE pragma</title>
6187 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6188 of C header files that should be <literal>#include</literal>'d into
6189 the C source code generated by the compiler for the current module (if
6190 compiling via C). For example:</para>
6193 {-# INCLUDE "foo.h" #-}
6194 {-# INCLUDE <stdio.h> #-}</programlisting>
6196 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6198 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6199 to the <option>-#include</option> option (<xref
6200 linkend="options-C-compiler" />), because the
6201 <literal>INCLUDE</literal> pragma is understood by other
6202 compilers. Yet another alternative is to add the include file to each
6203 <literal>foreign import</literal> declaration in your code, but we
6204 don't recommend using this approach with GHC.</para>
6207 <sect2 id="warning-deprecated-pragma">
6208 <title>WARNING and DEPRECATED pragmas</title>
6209 <indexterm><primary>WARNING</primary></indexterm>
6210 <indexterm><primary>DEPRECATED</primary></indexterm>
6212 <para>The WARNING pragma allows you to attach an arbitrary warning
6213 to a particular function, class, or type.
6214 A DEPRECATED pragma lets you specify that
6215 a particular function, class, or type is deprecated.
6216 There are two ways of using these pragmas.
6220 <para>You can work on an entire module thus:</para>
6222 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6227 module Wibble {-# WARNING "This is an unstable interface." #-} where
6230 <para>When you compile any module that import
6231 <literal>Wibble</literal>, GHC will print the specified
6236 <para>You can attach a warning to a function, class, type, or data constructor, with the
6237 following top-level declarations:</para>
6239 {-# DEPRECATED f, C, T "Don't use these" #-}
6240 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6242 <para>When you compile any module that imports and uses any
6243 of the specified entities, GHC will print the specified
6245 <para> You can only attach to entities declared at top level in the module
6246 being compiled, and you can only use unqualified names in the list of
6247 entities. A capitalised name, such as <literal>T</literal>
6248 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6249 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6250 both are in scope. If both are in scope, there is currently no way to
6251 specify one without the other (c.f. fixities
6252 <xref linkend="infix-tycons"/>).</para>
6255 Warnings and deprecations are not reported for
6256 (a) uses within the defining module, and
6257 (b) uses in an export list.
6258 The latter reduces spurious complaints within a library
6259 in which one module gathers together and re-exports
6260 the exports of several others.
6262 <para>You can suppress the warnings with the flag
6263 <option>-fno-warn-warnings-deprecations</option>.</para>
6266 <sect2 id="inline-noinline-pragma">
6267 <title>INLINE and NOINLINE pragmas</title>
6269 <para>These pragmas control the inlining of function
6272 <sect3 id="inline-pragma">
6273 <title>INLINE pragma</title>
6274 <indexterm><primary>INLINE</primary></indexterm>
6276 <para>GHC (with <option>-O</option>, as always) tries to
6277 inline (or “unfold”) functions/values that are
6278 “small enough,” thus avoiding the call overhead
6279 and possibly exposing other more-wonderful optimisations.
6280 Normally, if GHC decides a function is “too
6281 expensive” to inline, it will not do so, nor will it
6282 export that unfolding for other modules to use.</para>
6284 <para>The sledgehammer you can bring to bear is the
6285 <literal>INLINE</literal><indexterm><primary>INLINE
6286 pragma</primary></indexterm> pragma, used thusly:</para>
6289 key_function :: Int -> String -> (Bool, Double)
6290 {-# INLINE key_function #-}
6293 <para>The major effect of an <literal>INLINE</literal> pragma
6294 is to declare a function's “cost” to be very low.
6295 The normal unfolding machinery will then be very keen to
6296 inline it. However, an <literal>INLINE</literal> pragma for a
6297 function "<literal>f</literal>" has a number of other effects:
6300 No functions are inlined into <literal>f</literal>. Otherwise
6301 GHC might inline a big function into <literal>f</literal>'s right hand side,
6302 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6305 The float-in, float-out, and common-sub-expression transformations are not
6306 applied to the body of <literal>f</literal>.
6309 An INLINE function is not worker/wrappered by strictness analysis.
6310 It's going to be inlined wholesale instead.
6313 All of these effects are aimed at ensuring that what gets inlined is
6314 exactly what you asked for, no more and no less.
6316 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6317 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6318 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6319 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6320 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6321 when there is no choice even an INLINE function can be selected, in which case
6322 the INLINE pragma is ignored.
6323 For example, for a self-recursive function, the loop breaker can only be the function
6324 itself, so an INLINE pragma is always ignored.</para>
6326 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6327 function can be put anywhere its type signature could be
6330 <para><literal>INLINE</literal> pragmas are a particularly
6332 <literal>then</literal>/<literal>return</literal> (or
6333 <literal>bind</literal>/<literal>unit</literal>) functions in
6334 a monad. For example, in GHC's own
6335 <literal>UniqueSupply</literal> monad code, we have:</para>
6338 {-# INLINE thenUs #-}
6339 {-# INLINE returnUs #-}
6342 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6343 linkend="noinline-pragma"/>).</para>
6345 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6346 so if you want your code to be HBC-compatible you'll have to surround
6347 the pragma with C pre-processor directives
6348 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6352 <sect3 id="noinline-pragma">
6353 <title>NOINLINE pragma</title>
6355 <indexterm><primary>NOINLINE</primary></indexterm>
6356 <indexterm><primary>NOTINLINE</primary></indexterm>
6358 <para>The <literal>NOINLINE</literal> pragma does exactly what
6359 you'd expect: it stops the named function from being inlined
6360 by the compiler. You shouldn't ever need to do this, unless
6361 you're very cautious about code size.</para>
6363 <para><literal>NOTINLINE</literal> is a synonym for
6364 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6365 specified by Haskell 98 as the standard way to disable
6366 inlining, so it should be used if you want your code to be
6370 <sect3 id="phase-control">
6371 <title>Phase control</title>
6373 <para> Sometimes you want to control exactly when in GHC's
6374 pipeline the INLINE pragma is switched on. Inlining happens
6375 only during runs of the <emphasis>simplifier</emphasis>. Each
6376 run of the simplifier has a different <emphasis>phase
6377 number</emphasis>; the phase number decreases towards zero.
6378 If you use <option>-dverbose-core2core</option> you'll see the
6379 sequence of phase numbers for successive runs of the
6380 simplifier. In an INLINE pragma you can optionally specify a
6384 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6385 <literal>f</literal>
6386 until phase <literal>k</literal>, but from phase
6387 <literal>k</literal> onwards be very keen to inline it.
6390 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6391 <literal>f</literal>
6392 until phase <literal>k</literal>, but from phase
6393 <literal>k</literal> onwards do not inline it.
6396 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6397 <literal>f</literal>
6398 until phase <literal>k</literal>, but from phase
6399 <literal>k</literal> onwards be willing to inline it (as if
6400 there was no pragma).
6403 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6404 <literal>f</literal>
6405 until phase <literal>k</literal>, but from phase
6406 <literal>k</literal> onwards do not inline it.
6409 The same information is summarised here:
6411 -- Before phase 2 Phase 2 and later
6412 {-# INLINE [2] f #-} -- No Yes
6413 {-# INLINE [~2] f #-} -- Yes No
6414 {-# NOINLINE [2] f #-} -- No Maybe
6415 {-# NOINLINE [~2] f #-} -- Maybe No
6417 {-# INLINE f #-} -- Yes Yes
6418 {-# NOINLINE f #-} -- No No
6420 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6421 function body is small, or it is applied to interesting-looking arguments etc).
6422 Another way to understand the semantics is this:
6424 <listitem><para>For both INLINE and NOINLINE, the phase number says
6425 when inlining is allowed at all.</para></listitem>
6426 <listitem><para>The INLINE pragma has the additional effect of making the
6427 function body look small, so that when inlining is allowed it is very likely to
6432 <para>The same phase-numbering control is available for RULES
6433 (<xref linkend="rewrite-rules"/>).</para>
6437 <sect2 id="line-pragma">
6438 <title>LINE pragma</title>
6440 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6441 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6442 <para>This pragma is similar to C's <literal>#line</literal>
6443 pragma, and is mainly for use in automatically generated Haskell
6444 code. It lets you specify the line number and filename of the
6445 original code; for example</para>
6447 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6449 <para>if you'd generated the current file from something called
6450 <filename>Foo.vhs</filename> and this line corresponds to line
6451 42 in the original. GHC will adjust its error messages to refer
6452 to the line/file named in the <literal>LINE</literal>
6457 <title>RULES pragma</title>
6459 <para>The RULES pragma lets you specify rewrite rules. It is
6460 described in <xref linkend="rewrite-rules"/>.</para>
6463 <sect2 id="specialize-pragma">
6464 <title>SPECIALIZE pragma</title>
6466 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6467 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6468 <indexterm><primary>overloading, death to</primary></indexterm>
6470 <para>(UK spelling also accepted.) For key overloaded
6471 functions, you can create extra versions (NB: more code space)
6472 specialised to particular types. Thus, if you have an
6473 overloaded function:</para>
6476 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6479 <para>If it is heavily used on lists with
6480 <literal>Widget</literal> keys, you could specialise it as
6484 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6487 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6488 be put anywhere its type signature could be put.</para>
6490 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6491 (a) a specialised version of the function and (b) a rewrite rule
6492 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6493 un-specialised function into a call to the specialised one.</para>
6495 <para>The type in a SPECIALIZE pragma can be any type that is less
6496 polymorphic than the type of the original function. In concrete terms,
6497 if the original function is <literal>f</literal> then the pragma
6499 {-# SPECIALIZE f :: <type> #-}
6501 is valid if and only if the definition
6503 f_spec :: <type>
6506 is valid. Here are some examples (where we only give the type signature
6507 for the original function, not its code):
6509 f :: Eq a => a -> b -> b
6510 {-# SPECIALISE f :: Int -> b -> b #-}
6512 g :: (Eq a, Ix b) => a -> b -> b
6513 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6515 h :: Eq a => a -> a -> a
6516 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6518 The last of these examples will generate a
6519 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6520 well. If you use this kind of specialisation, let us know how well it works.
6523 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6524 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6525 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6526 The <literal>INLINE</literal> pragma affects the specialised version of the
6527 function (only), and applies even if the function is recursive. The motivating
6530 -- A GADT for arrays with type-indexed representation
6532 ArrInt :: !Int -> ByteArray# -> Arr Int
6533 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6535 (!:) :: Arr e -> Int -> e
6536 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6537 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6538 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6539 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6541 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6542 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6543 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6544 the specialised function will be inlined. It has two calls to
6545 <literal>(!:)</literal>,
6546 both at type <literal>Int</literal>. Both these calls fire the first
6547 specialisation, whose body is also inlined. The result is a type-based
6548 unrolling of the indexing function.</para>
6549 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6550 on an ordinarily-recursive function.</para>
6552 <para>Note: In earlier versions of GHC, it was possible to provide your own
6553 specialised function for a given type:
6556 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6559 This feature has been removed, as it is now subsumed by the
6560 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6564 <sect2 id="specialize-instance-pragma">
6565 <title>SPECIALIZE instance pragma
6569 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6570 <indexterm><primary>overloading, death to</primary></indexterm>
6571 Same idea, except for instance declarations. For example:
6574 instance (Eq a) => Eq (Foo a) where {
6575 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6579 The pragma must occur inside the <literal>where</literal> part
6580 of the instance declaration.
6583 Compatible with HBC, by the way, except perhaps in the placement
6589 <sect2 id="unpack-pragma">
6590 <title>UNPACK pragma</title>
6592 <indexterm><primary>UNPACK</primary></indexterm>
6594 <para>The <literal>UNPACK</literal> indicates to the compiler
6595 that it should unpack the contents of a constructor field into
6596 the constructor itself, removing a level of indirection. For
6600 data T = T {-# UNPACK #-} !Float
6601 {-# UNPACK #-} !Float
6604 <para>will create a constructor <literal>T</literal> containing
6605 two unboxed floats. This may not always be an optimisation: if
6606 the <function>T</function> constructor is scrutinised and the
6607 floats passed to a non-strict function for example, they will
6608 have to be reboxed (this is done automatically by the
6611 <para>Unpacking constructor fields should only be used in
6612 conjunction with <option>-O</option>, in order to expose
6613 unfoldings to the compiler so the reboxing can be removed as
6614 often as possible. For example:</para>
6618 f (T f1 f2) = f1 + f2
6621 <para>The compiler will avoid reboxing <function>f1</function>
6622 and <function>f2</function> by inlining <function>+</function>
6623 on floats, but only when <option>-O</option> is on.</para>
6625 <para>Any single-constructor data is eligible for unpacking; for
6629 data T = T {-# UNPACK #-} !(Int,Int)
6632 <para>will store the two <literal>Int</literal>s directly in the
6633 <function>T</function> constructor, by flattening the pair.
6634 Multi-level unpacking is also supported:
6637 data T = T {-# UNPACK #-} !S
6638 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6641 will store two unboxed <literal>Int#</literal>s
6642 directly in the <function>T</function> constructor. The
6643 unpacker can see through newtypes, too.</para>
6645 <para>If a field cannot be unpacked, you will not get a warning,
6646 so it might be an idea to check the generated code with
6647 <option>-ddump-simpl</option>.</para>
6649 <para>See also the <option>-funbox-strict-fields</option> flag,
6650 which essentially has the effect of adding
6651 <literal>{-# UNPACK #-}</literal> to every strict
6652 constructor field.</para>
6655 <sect2 id="source-pragma">
6656 <title>SOURCE pragma</title>
6658 <indexterm><primary>SOURCE</primary></indexterm>
6659 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6660 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6666 <!-- ======================= REWRITE RULES ======================== -->
6668 <sect1 id="rewrite-rules">
6669 <title>Rewrite rules
6671 <indexterm><primary>RULES pragma</primary></indexterm>
6672 <indexterm><primary>pragma, RULES</primary></indexterm>
6673 <indexterm><primary>rewrite rules</primary></indexterm></title>
6676 The programmer can specify rewrite rules as part of the source program
6677 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6678 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6679 and (b) the <option>-fno-rewrite-rules</option> flag
6680 (<xref linkend="options-f"/>) is not specified, and (c) the
6681 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6690 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6695 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6696 If you need more information, then <option>-ddump-rule-firings</option> shows you
6697 each individual rule firing in detail.
6701 <title>Syntax</title>
6704 From a syntactic point of view:
6710 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6711 may be generated by the layout rule).
6717 The layout rule applies in a pragma.
6718 Currently no new indentation level
6719 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6720 you must lay out the starting in the same column as the enclosing definitions.
6723 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6724 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6727 Furthermore, the closing <literal>#-}</literal>
6728 should start in a column to the right of the opening <literal>{-#</literal>.
6734 Each rule has a name, enclosed in double quotes. The name itself has
6735 no significance at all. It is only used when reporting how many times the rule fired.
6741 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6742 immediately after the name of the rule. Thus:
6745 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6748 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6749 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6758 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6759 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6760 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6761 by spaces, just like in a type <literal>forall</literal>.
6767 A pattern variable may optionally have a type signature.
6768 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6769 For example, here is the <literal>foldr/build</literal> rule:
6772 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6773 foldr k z (build g) = g k z
6776 Since <function>g</function> has a polymorphic type, it must have a type signature.
6783 The left hand side of a rule must consist of a top-level variable applied
6784 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6787 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6788 "wrong2" forall f. f True = True
6791 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6798 A rule does not need to be in the same module as (any of) the
6799 variables it mentions, though of course they need to be in scope.
6805 Rules are automatically exported from a module, just as instance declarations are.
6816 <title>Semantics</title>
6819 From a semantic point of view:
6825 Rules are only applied if you use the <option>-O</option> flag.
6831 Rules are regarded as left-to-right rewrite rules.
6832 When GHC finds an expression that is a substitution instance of the LHS
6833 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6834 By "a substitution instance" we mean that the LHS can be made equal to the
6835 expression by substituting for the pattern variables.
6842 The LHS and RHS of a rule are typechecked, and must have the
6850 GHC makes absolutely no attempt to verify that the LHS and RHS
6851 of a rule have the same meaning. That is undecidable in general, and
6852 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6859 GHC makes no attempt to make sure that the rules are confluent or
6860 terminating. For example:
6863 "loop" forall x y. f x y = f y x
6866 This rule will cause the compiler to go into an infinite loop.
6873 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6879 GHC currently uses a very simple, syntactic, matching algorithm
6880 for matching a rule LHS with an expression. It seeks a substitution
6881 which makes the LHS and expression syntactically equal modulo alpha
6882 conversion. The pattern (rule), but not the expression, is eta-expanded if
6883 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6884 But not beta conversion (that's called higher-order matching).
6888 Matching is carried out on GHC's intermediate language, which includes
6889 type abstractions and applications. So a rule only matches if the
6890 types match too. See <xref linkend="rule-spec"/> below.
6896 GHC keeps trying to apply the rules as it optimises the program.
6897 For example, consider:
6906 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6907 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6908 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6909 not be substituted, and the rule would not fire.
6916 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6917 results. Consider this (artificial) example
6920 {-# RULES "f" f True = False #-}
6926 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
6931 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
6933 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
6934 would have been a better chance that <literal>f</literal>'s RULE might fire.
6937 The way to get predictable behaviour is to use a NOINLINE
6938 pragma on <literal>f</literal>, to ensure
6939 that it is not inlined until its RULEs have had a chance to fire.
6945 All rules are implicitly exported from the module, and are therefore
6946 in force in any module that imports the module that defined the rule, directly
6947 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6948 in force when compiling A.) The situation is very similar to that for instance
6960 <title>List fusion</title>
6963 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6964 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6965 intermediate list should be eliminated entirely.
6969 The following are good producers:
6981 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6987 Explicit lists (e.g. <literal>[True, False]</literal>)
6993 The cons constructor (e.g <literal>3:4:[]</literal>)
6999 <function>++</function>
7005 <function>map</function>
7011 <function>take</function>, <function>filter</function>
7017 <function>iterate</function>, <function>repeat</function>
7023 <function>zip</function>, <function>zipWith</function>
7032 The following are good consumers:
7044 <function>array</function> (on its second argument)
7050 <function>++</function> (on its first argument)
7056 <function>foldr</function>
7062 <function>map</function>
7068 <function>take</function>, <function>filter</function>
7074 <function>concat</function>
7080 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7086 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7087 will fuse with one but not the other)
7093 <function>partition</function>
7099 <function>head</function>
7105 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7111 <function>sequence_</function>
7117 <function>msum</function>
7123 <function>sortBy</function>
7132 So, for example, the following should generate no intermediate lists:
7135 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7141 This list could readily be extended; if there are Prelude functions that you use
7142 a lot which are not included, please tell us.
7146 If you want to write your own good consumers or producers, look at the
7147 Prelude definitions of the above functions to see how to do so.
7152 <sect2 id="rule-spec">
7153 <title>Specialisation
7157 Rewrite rules can be used to get the same effect as a feature
7158 present in earlier versions of GHC.
7159 For example, suppose that:
7162 genericLookup :: Ord a => Table a b -> a -> b
7163 intLookup :: Table Int b -> Int -> b
7166 where <function>intLookup</function> is an implementation of
7167 <function>genericLookup</function> that works very fast for
7168 keys of type <literal>Int</literal>. You might wish
7169 to tell GHC to use <function>intLookup</function> instead of
7170 <function>genericLookup</function> whenever the latter was called with
7171 type <literal>Table Int b -> Int -> b</literal>.
7172 It used to be possible to write
7175 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7178 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7181 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7184 This slightly odd-looking rule instructs GHC to replace
7185 <function>genericLookup</function> by <function>intLookup</function>
7186 <emphasis>whenever the types match</emphasis>.
7187 What is more, this rule does not need to be in the same
7188 file as <function>genericLookup</function>, unlike the
7189 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7190 have an original definition available to specialise).
7193 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7194 <function>intLookup</function> really behaves as a specialised version
7195 of <function>genericLookup</function>!!!</para>
7197 <para>An example in which using <literal>RULES</literal> for
7198 specialisation will Win Big:
7201 toDouble :: Real a => a -> Double
7202 toDouble = fromRational . toRational
7204 {-# RULES "toDouble/Int" toDouble = i2d #-}
7205 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7208 The <function>i2d</function> function is virtually one machine
7209 instruction; the default conversion—via an intermediate
7210 <literal>Rational</literal>—is obscenely expensive by
7217 <title>Controlling what's going on</title>
7225 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7231 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7232 If you add <option>-dppr-debug</option> you get a more detailed listing.
7238 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7241 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7242 {-# INLINE build #-}
7246 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7247 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7248 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7249 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7256 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7257 see how to write rules that will do fusion and yet give an efficient
7258 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7268 <sect2 id="core-pragma">
7269 <title>CORE pragma</title>
7271 <indexterm><primary>CORE pragma</primary></indexterm>
7272 <indexterm><primary>pragma, CORE</primary></indexterm>
7273 <indexterm><primary>core, annotation</primary></indexterm>
7276 The external core format supports <quote>Note</quote> annotations;
7277 the <literal>CORE</literal> pragma gives a way to specify what these
7278 should be in your Haskell source code. Syntactically, core
7279 annotations are attached to expressions and take a Haskell string
7280 literal as an argument. The following function definition shows an
7284 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7287 Semantically, this is equivalent to:
7295 However, when external core is generated (via
7296 <option>-fext-core</option>), there will be Notes attached to the
7297 expressions <function>show</function> and <varname>x</varname>.
7298 The core function declaration for <function>f</function> is:
7302 f :: %forall a . GHCziShow.ZCTShow a ->
7303 a -> GHCziBase.ZMZN GHCziBase.Char =
7304 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7306 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7308 (tpl1::GHCziBase.Int ->
7310 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7312 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7313 (tpl3::GHCziBase.ZMZN a ->
7314 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7322 Here, we can see that the function <function>show</function> (which
7323 has been expanded out to a case expression over the Show dictionary)
7324 has a <literal>%note</literal> attached to it, as does the
7325 expression <varname>eta</varname> (which used to be called
7326 <varname>x</varname>).
7333 <sect1 id="special-ids">
7334 <title>Special built-in functions</title>
7335 <para>GHC has a few built-in functions with special behaviour. These
7336 are now described in the module <ulink
7337 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7338 in the library documentation.</para>
7342 <sect1 id="generic-classes">
7343 <title>Generic classes</title>
7346 The ideas behind this extension are described in detail in "Derivable type classes",
7347 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7348 An example will give the idea:
7356 fromBin :: [Int] -> (a, [Int])
7358 toBin {| Unit |} Unit = []
7359 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7360 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7361 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7363 fromBin {| Unit |} bs = (Unit, bs)
7364 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7365 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7366 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7367 (y,bs'') = fromBin bs'
7370 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7371 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7372 which are defined thus in the library module <literal>Generics</literal>:
7376 data a :+: b = Inl a | Inr b
7377 data a :*: b = a :*: b
7380 Now you can make a data type into an instance of Bin like this:
7382 instance (Bin a, Bin b) => Bin (a,b)
7383 instance Bin a => Bin [a]
7385 That is, just leave off the "where" clause. Of course, you can put in the
7386 where clause and over-ride whichever methods you please.
7390 <title> Using generics </title>
7391 <para>To use generics you need to</para>
7394 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7395 <option>-XGenerics</option> (to generate extra per-data-type code),
7396 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7400 <para>Import the module <literal>Generics</literal> from the
7401 <literal>lang</literal> package. This import brings into
7402 scope the data types <literal>Unit</literal>,
7403 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7404 don't need this import if you don't mention these types
7405 explicitly; for example, if you are simply giving instance
7406 declarations.)</para>
7411 <sect2> <title> Changes wrt the paper </title>
7413 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7414 can be written infix (indeed, you can now use
7415 any operator starting in a colon as an infix type constructor). Also note that
7416 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7417 Finally, note that the syntax of the type patterns in the class declaration
7418 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7419 alone would ambiguous when they appear on right hand sides (an extension we
7420 anticipate wanting).
7424 <sect2> <title>Terminology and restrictions</title>
7426 Terminology. A "generic default method" in a class declaration
7427 is one that is defined using type patterns as above.
7428 A "polymorphic default method" is a default method defined as in Haskell 98.
7429 A "generic class declaration" is a class declaration with at least one
7430 generic default method.
7438 Alas, we do not yet implement the stuff about constructor names and
7445 A generic class can have only one parameter; you can't have a generic
7446 multi-parameter class.
7452 A default method must be defined entirely using type patterns, or entirely
7453 without. So this is illegal:
7456 op :: a -> (a, Bool)
7457 op {| Unit |} Unit = (Unit, True)
7460 However it is perfectly OK for some methods of a generic class to have
7461 generic default methods and others to have polymorphic default methods.
7467 The type variable(s) in the type pattern for a generic method declaration
7468 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:
7472 op {| p :*: q |} (x :*: y) = op (x :: p)
7480 The type patterns in a generic default method must take one of the forms:
7486 where "a" and "b" are type variables. Furthermore, all the type patterns for
7487 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7488 must use the same type variables. So this is illegal:
7492 op {| a :+: b |} (Inl x) = True
7493 op {| p :+: q |} (Inr y) = False
7495 The type patterns must be identical, even in equations for different methods of the class.
7496 So this too is illegal:
7500 op1 {| a :*: b |} (x :*: y) = True
7503 op2 {| p :*: q |} (x :*: y) = False
7505 (The reason for this restriction is that we gather all the equations for a particular type constructor
7506 into a single generic instance declaration.)
7512 A generic method declaration must give a case for each of the three type constructors.
7518 The type for a generic method can be built only from:
7520 <listitem> <para> Function arrows </para> </listitem>
7521 <listitem> <para> Type variables </para> </listitem>
7522 <listitem> <para> Tuples </para> </listitem>
7523 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7525 Here are some example type signatures for generic methods:
7528 op2 :: Bool -> (a,Bool)
7529 op3 :: [Int] -> a -> a
7532 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7536 This restriction is an implementation restriction: we just haven't got around to
7537 implementing the necessary bidirectional maps over arbitrary type constructors.
7538 It would be relatively easy to add specific type constructors, such as Maybe and list,
7539 to the ones that are allowed.</para>
7544 In an instance declaration for a generic class, the idea is that the compiler
7545 will fill in the methods for you, based on the generic templates. However it can only
7550 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7555 No constructor of the instance type has unboxed fields.
7559 (Of course, these things can only arise if you are already using GHC extensions.)
7560 However, you can still give an instance declarations for types which break these rules,
7561 provided you give explicit code to override any generic default methods.
7569 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7570 what the compiler does with generic declarations.
7575 <sect2> <title> Another example </title>
7577 Just to finish with, here's another example I rather like:
7581 nCons {| Unit |} _ = 1
7582 nCons {| a :*: b |} _ = 1
7583 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7586 tag {| Unit |} _ = 1
7587 tag {| a :*: b |} _ = 1
7588 tag {| a :+: b |} (Inl x) = tag x
7589 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7595 <sect1 id="monomorphism">
7596 <title>Control over monomorphism</title>
7598 <para>GHC supports two flags that control the way in which generalisation is
7599 carried out at let and where bindings.
7603 <title>Switching off the dreaded Monomorphism Restriction</title>
7604 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7606 <para>Haskell's monomorphism restriction (see
7607 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7609 of the Haskell Report)
7610 can be completely switched off by
7611 <option>-XNoMonomorphismRestriction</option>.
7616 <title>Monomorphic pattern bindings</title>
7617 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7618 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7620 <para> As an experimental change, we are exploring the possibility of
7621 making pattern bindings monomorphic; that is, not generalised at all.
7622 A pattern binding is a binding whose LHS has no function arguments,
7623 and is not a simple variable. For example:
7625 f x = x -- Not a pattern binding
7626 f = \x -> x -- Not a pattern binding
7627 f :: Int -> Int = \x -> x -- Not a pattern binding
7629 (g,h) = e -- A pattern binding
7630 (f) = e -- A pattern binding
7631 [x] = e -- A pattern binding
7633 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7634 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7643 ;;; Local Variables: ***
7645 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7646 ;;; ispell-local-dictionary: "british" ***
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