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.
1574 <!-- TYPE SYSTEM EXTENSIONS -->
1575 <sect1 id="data-type-extensions">
1576 <title>Extensions to data types and type synonyms</title>
1578 <sect2 id="nullary-types">
1579 <title>Data types with no constructors</title>
1581 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1582 a data type with no constructors. For example:</para>
1586 data T a -- T :: * -> *
1589 <para>Syntactically, the declaration lacks the "= constrs" part. The
1590 type can be parameterised over types of any kind, but if the kind is
1591 not <literal>*</literal> then an explicit kind annotation must be used
1592 (see <xref linkend="kinding"/>).</para>
1594 <para>Such data types have only one value, namely bottom.
1595 Nevertheless, they can be useful when defining "phantom types".</para>
1598 <sect2 id="infix-tycons">
1599 <title>Infix type constructors, classes, and type variables</title>
1602 GHC allows type constructors, classes, and type variables to be operators, and
1603 to be written infix, very much like expressions. More specifically:
1606 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1607 The lexical syntax is the same as that for data constructors.
1610 Data type and type-synonym declarations can be written infix, parenthesised
1611 if you want further arguments. E.g.
1613 data a :*: b = Foo a b
1614 type a :+: b = Either a b
1615 class a :=: b where ...
1617 data (a :**: b) x = Baz a b x
1618 type (a :++: b) y = Either (a,b) y
1622 Types, and class constraints, can be written infix. For example
1625 f :: (a :=: b) => a -> b
1629 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1630 The lexical syntax is the same as that for variable operators, excluding "(.)",
1631 "(!)", and "(*)". In a binding position, the operator must be
1632 parenthesised. For example:
1634 type T (+) = Int + Int
1638 liftA2 :: Arrow (~>)
1639 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1645 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1646 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1649 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1650 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1651 sets the fixity for a data constructor and the corresponding type constructor. For example:
1655 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1656 and similarly for <literal>:*:</literal>.
1657 <literal>Int `a` Bool</literal>.
1660 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1667 <sect2 id="type-synonyms">
1668 <title>Liberalised type synonyms</title>
1671 Type synonyms are like macros at the type level, and
1672 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1673 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1675 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1676 in a type synonym, thus:
1678 type Discard a = forall b. Show b => a -> b -> (a, String)
1683 g :: Discard Int -> (Int,String) -- A rank-2 type
1690 You can write an unboxed tuple in a type synonym:
1692 type Pr = (# Int, Int #)
1700 You can apply a type synonym to a forall type:
1702 type Foo a = a -> a -> Bool
1704 f :: Foo (forall b. b->b)
1706 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1708 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1713 You can apply a type synonym to a partially applied type synonym:
1715 type Generic i o = forall x. i x -> o x
1718 foo :: Generic Id []
1720 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1722 foo :: forall x. x -> [x]
1730 GHC currently does kind checking before expanding synonyms (though even that
1734 After expanding type synonyms, GHC does validity checking on types, looking for
1735 the following mal-formedness which isn't detected simply by kind checking:
1738 Type constructor applied to a type involving for-alls.
1741 Unboxed tuple on left of an arrow.
1744 Partially-applied type synonym.
1748 this will be rejected:
1750 type Pr = (# Int, Int #)
1755 because GHC does not allow unboxed tuples on the left of a function arrow.
1760 <sect2 id="existential-quantification">
1761 <title>Existentially quantified data constructors
1765 The idea of using existential quantification in data type declarations
1766 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1767 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1768 London, 1991). It was later formalised by Laufer and Odersky
1769 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1770 TOPLAS, 16(5), pp1411-1430, 1994).
1771 It's been in Lennart
1772 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1773 proved very useful. Here's the idea. Consider the declaration:
1779 data Foo = forall a. MkFoo a (a -> Bool)
1786 The data type <literal>Foo</literal> has two constructors with types:
1792 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1799 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1800 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1801 For example, the following expression is fine:
1807 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1813 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1814 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1815 isUpper</function> packages a character with a compatible function. These
1816 two things are each of type <literal>Foo</literal> and can be put in a list.
1820 What can we do with a value of type <literal>Foo</literal>?. In particular,
1821 what happens when we pattern-match on <function>MkFoo</function>?
1827 f (MkFoo val fn) = ???
1833 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1834 are compatible, the only (useful) thing we can do with them is to
1835 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1842 f (MkFoo val fn) = fn val
1848 What this allows us to do is to package heterogeneous values
1849 together with a bunch of functions that manipulate them, and then treat
1850 that collection of packages in a uniform manner. You can express
1851 quite a bit of object-oriented-like programming this way.
1854 <sect3 id="existential">
1855 <title>Why existential?
1859 What has this to do with <emphasis>existential</emphasis> quantification?
1860 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1866 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1872 But Haskell programmers can safely think of the ordinary
1873 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1874 adding a new existential quantification construct.
1879 <sect3 id="existential-with-context">
1880 <title>Existentials and type classes</title>
1883 An easy extension is to allow
1884 arbitrary contexts before the constructor. For example:
1890 data Baz = forall a. Eq a => Baz1 a a
1891 | forall b. Show b => Baz2 b (b -> b)
1897 The two constructors have the types you'd expect:
1903 Baz1 :: forall a. Eq a => a -> a -> Baz
1904 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1910 But when pattern matching on <function>Baz1</function> the matched values can be compared
1911 for equality, and when pattern matching on <function>Baz2</function> the first matched
1912 value can be converted to a string (as well as applying the function to it).
1913 So this program is legal:
1920 f (Baz1 p q) | p == q = "Yes"
1922 f (Baz2 v fn) = show (fn v)
1928 Operationally, in a dictionary-passing implementation, the
1929 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1930 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1931 extract it on pattern matching.
1936 <sect3 id="existential-records">
1937 <title>Record Constructors</title>
1940 GHC allows existentials to be used with records syntax as well. For example:
1943 data Counter a = forall self. NewCounter
1945 , _inc :: self -> self
1946 , _display :: self -> IO ()
1950 Here <literal>tag</literal> is a public field, with a well-typed selector
1951 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1952 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1953 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1954 compile-time error. In other words, <emphasis>GHC defines a record selector function
1955 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1956 (This example used an underscore in the fields for which record selectors
1957 will not be defined, but that is only programming style; GHC ignores them.)
1961 To make use of these hidden fields, we need to create some helper functions:
1964 inc :: Counter a -> Counter a
1965 inc (NewCounter x i d t) = NewCounter
1966 { _this = i x, _inc = i, _display = d, tag = t }
1968 display :: Counter a -> IO ()
1969 display NewCounter{ _this = x, _display = d } = d x
1972 Now we can define counters with different underlying implementations:
1975 counterA :: Counter String
1976 counterA = NewCounter
1977 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1979 counterB :: Counter String
1980 counterB = NewCounter
1981 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1984 display (inc counterA) -- prints "1"
1985 display (inc (inc counterB)) -- prints "##"
1988 At the moment, record update syntax is only supported for Haskell 98 data types,
1989 so the following function does <emphasis>not</emphasis> work:
1992 -- This is invalid; use explicit NewCounter instead for now
1993 setTag :: Counter a -> a -> Counter a
1994 setTag obj t = obj{ tag = t }
2003 <title>Restrictions</title>
2006 There are several restrictions on the ways in which existentially-quantified
2007 constructors can be use.
2016 When pattern matching, each pattern match introduces a new,
2017 distinct, type for each existential type variable. These types cannot
2018 be unified with any other type, nor can they escape from the scope of
2019 the pattern match. For example, these fragments are incorrect:
2027 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2028 is the result of <function>f1</function>. One way to see why this is wrong is to
2029 ask what type <function>f1</function> has:
2033 f1 :: Foo -> a -- Weird!
2037 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2042 f1 :: forall a. Foo -> a -- Wrong!
2046 The original program is just plain wrong. Here's another sort of error
2050 f2 (Baz1 a b) (Baz1 p q) = a==q
2054 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2055 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2056 from the two <function>Baz1</function> constructors.
2064 You can't pattern-match on an existentially quantified
2065 constructor in a <literal>let</literal> or <literal>where</literal> group of
2066 bindings. So this is illegal:
2070 f3 x = a==b where { Baz1 a b = x }
2073 Instead, use a <literal>case</literal> expression:
2076 f3 x = case x of Baz1 a b -> a==b
2079 In general, you can only pattern-match
2080 on an existentially-quantified constructor in a <literal>case</literal> expression or
2081 in the patterns of a function definition.
2083 The reason for this restriction is really an implementation one.
2084 Type-checking binding groups is already a nightmare without
2085 existentials complicating the picture. Also an existential pattern
2086 binding at the top level of a module doesn't make sense, because it's
2087 not clear how to prevent the existentially-quantified type "escaping".
2088 So for now, there's a simple-to-state restriction. We'll see how
2096 You can't use existential quantification for <literal>newtype</literal>
2097 declarations. So this is illegal:
2101 newtype T = forall a. Ord a => MkT a
2105 Reason: a value of type <literal>T</literal> must be represented as a
2106 pair of a dictionary for <literal>Ord t</literal> and a value of type
2107 <literal>t</literal>. That contradicts the idea that
2108 <literal>newtype</literal> should have no concrete representation.
2109 You can get just the same efficiency and effect by using
2110 <literal>data</literal> instead of <literal>newtype</literal>. If
2111 there is no overloading involved, then there is more of a case for
2112 allowing an existentially-quantified <literal>newtype</literal>,
2113 because the <literal>data</literal> version does carry an
2114 implementation cost, but single-field existentially quantified
2115 constructors aren't much use. So the simple restriction (no
2116 existential stuff on <literal>newtype</literal>) stands, unless there
2117 are convincing reasons to change it.
2125 You can't use <literal>deriving</literal> to define instances of a
2126 data type with existentially quantified data constructors.
2128 Reason: in most cases it would not make sense. For example:;
2131 data T = forall a. MkT [a] deriving( Eq )
2134 To derive <literal>Eq</literal> in the standard way we would need to have equality
2135 between the single component of two <function>MkT</function> constructors:
2139 (MkT a) == (MkT b) = ???
2142 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2143 It's just about possible to imagine examples in which the derived instance
2144 would make sense, but it seems altogether simpler simply to prohibit such
2145 declarations. Define your own instances!
2156 <!-- ====================== Generalised algebraic data types ======================= -->
2158 <sect2 id="gadt-style">
2159 <title>Declaring data types with explicit constructor signatures</title>
2161 <para>GHC allows you to declare an algebraic data type by
2162 giving the type signatures of constructors explicitly. For example:
2166 Just :: a -> Maybe a
2168 The form is called a "GADT-style declaration"
2169 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2170 can only be declared using this form.</para>
2171 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2172 For example, these two declarations are equivalent:
2174 data Foo = forall a. MkFoo a (a -> Bool)
2175 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2178 <para>Any data type that can be declared in standard Haskell-98 syntax
2179 can also be declared using GADT-style syntax.
2180 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2181 they treat class constraints on the data constructors differently.
2182 Specifically, if the constructor is given a type-class context, that
2183 context is made available by pattern matching. For example:
2186 MkSet :: Eq a => [a] -> Set a
2188 makeSet :: Eq a => [a] -> Set a
2189 makeSet xs = MkSet (nub xs)
2191 insert :: a -> Set a -> Set a
2192 insert a (MkSet as) | a `elem` as = MkSet as
2193 | otherwise = MkSet (a:as)
2195 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2196 gives rise to a <literal>(Eq a)</literal>
2197 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2198 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2199 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2200 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2201 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2202 In the example, the equality dictionary is used to satisfy the equality constraint
2203 generated by the call to <literal>elem</literal>, so that the type of
2204 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2207 For example, one possible application is to reify dictionaries:
2209 data NumInst a where
2210 MkNumInst :: Num a => NumInst a
2212 intInst :: NumInst Int
2215 plus :: NumInst a -> a -> a -> a
2216 plus MkNumInst p q = p + q
2218 Here, a value of type <literal>NumInst a</literal> is equivalent
2219 to an explicit <literal>(Num a)</literal> dictionary.
2222 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2223 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2227 = Num a => MkNumInst (NumInst a)
2229 Notice that, unlike the situation when declaring an existential, there is
2230 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2231 data type's universally quantified type variable <literal>a</literal>.
2232 A constructor may have both universal and existential type variables: for example,
2233 the following two declarations are equivalent:
2236 = forall b. (Num a, Eq b) => MkT1 a b
2238 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2241 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2242 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2243 In Haskell 98 the definition
2245 data Eq a => Set' a = MkSet' [a]
2247 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2248 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2249 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2250 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2251 GHC's behaviour is much more useful, as well as much more intuitive.
2255 The rest of this section gives further details about GADT-style data
2260 The result type of each data constructor must begin with the type constructor being defined.
2261 If the result type of all constructors
2262 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2263 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2264 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2268 The type signature of
2269 each constructor is independent, and is implicitly universally quantified as usual.
2270 Different constructors may have different universally-quantified type variables
2271 and different type-class constraints.
2272 For example, this is fine:
2275 T1 :: Eq b => b -> T b
2276 T2 :: (Show c, Ix c) => c -> [c] -> T c
2281 Unlike a Haskell-98-style
2282 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2283 have no scope. Indeed, one can write a kind signature instead:
2285 data Set :: * -> * where ...
2287 or even a mixture of the two:
2289 data Foo a :: (* -> *) -> * where ...
2291 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2294 data Foo a (b :: * -> *) where ...
2300 You can use strictness annotations, in the obvious places
2301 in the constructor type:
2304 Lit :: !Int -> Term Int
2305 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2306 Pair :: Term a -> Term b -> Term (a,b)
2311 You can use a <literal>deriving</literal> clause on a GADT-style data type
2312 declaration. For example, these two declarations are equivalent
2314 data Maybe1 a where {
2315 Nothing1 :: Maybe1 a ;
2316 Just1 :: a -> Maybe1 a
2317 } deriving( Eq, Ord )
2319 data Maybe2 a = Nothing2 | Just2 a
2325 You can use record syntax on a GADT-style data type declaration:
2329 Adult { name :: String, children :: [Person] } :: Person
2330 Child { name :: String } :: Person
2332 As usual, for every constructor that has a field <literal>f</literal>, the type of
2333 field <literal>f</literal> must be the same (modulo alpha conversion).
2336 At the moment, record updates are not yet possible with GADT-style declarations,
2337 so support is limited to record construction, selection and pattern matching.
2340 aPerson = Adult { name = "Fred", children = [] }
2342 shortName :: Person -> Bool
2343 hasChildren (Adult { children = kids }) = not (null kids)
2344 hasChildren (Child {}) = False
2349 As in the case of existentials declared using the Haskell-98-like record syntax
2350 (<xref linkend="existential-records"/>),
2351 record-selector functions are generated only for those fields that have well-typed
2353 Here is the example of that section, in GADT-style syntax:
2355 data Counter a where
2356 NewCounter { _this :: self
2357 , _inc :: self -> self
2358 , _display :: self -> IO ()
2363 As before, only one selector function is generated here, that for <literal>tag</literal>.
2364 Nevertheless, you can still use all the field names in pattern matching and record construction.
2366 </itemizedlist></para>
2370 <title>Generalised Algebraic Data Types (GADTs)</title>
2372 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2373 by allowing constructors to have richer return types. Here is an example:
2376 Lit :: Int -> Term Int
2377 Succ :: Term Int -> Term Int
2378 IsZero :: Term Int -> Term Bool
2379 If :: Term Bool -> Term a -> Term a -> Term a
2380 Pair :: Term a -> Term b -> Term (a,b)
2382 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2383 case with ordinary data types. This generality allows us to
2384 write a well-typed <literal>eval</literal> function
2385 for these <literal>Terms</literal>:
2389 eval (Succ t) = 1 + eval t
2390 eval (IsZero t) = eval t == 0
2391 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2392 eval (Pair e1 e2) = (eval e1, eval e2)
2394 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2395 For example, in the right hand side of the equation
2400 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2401 A precise specification of the type rules is beyond what this user manual aspires to,
2402 but the design closely follows that described in
2404 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2405 unification-based type inference for GADTs</ulink>,
2407 The general principle is this: <emphasis>type refinement is only carried out
2408 based on user-supplied type annotations</emphasis>.
2409 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2410 and lots of obscure error messages will
2411 occur. However, the refinement is quite general. For example, if we had:
2413 eval :: Term a -> a -> a
2414 eval (Lit i) j = i+j
2416 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2417 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2418 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2421 These and many other examples are given in papers by Hongwei Xi, and
2422 Tim Sheard. There is a longer introduction
2423 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2425 <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
2426 may use different notation to that implemented in GHC.
2429 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2430 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2433 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2434 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2435 The result type of each constructor must begin with the type constructor being defined,
2436 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2437 For example, in the <literal>Term</literal> data
2438 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2439 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2444 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2445 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2446 whose result type is not just <literal>T a b</literal>.
2450 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2451 an ordinary data type.
2455 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2459 Lit { val :: Int } :: Term Int
2460 Succ { num :: Term Int } :: Term Int
2461 Pred { num :: Term Int } :: Term Int
2462 IsZero { arg :: Term Int } :: Term Bool
2463 Pair { arg1 :: Term a
2466 If { cnd :: Term Bool
2471 However, for GADTs there is the following additional constraint:
2472 every constructor that has a field <literal>f</literal> must have
2473 the same result type (modulo alpha conversion)
2474 Hence, in the above example, we cannot merge the <literal>num</literal>
2475 and <literal>arg</literal> fields above into a
2476 single name. Although their field types are both <literal>Term Int</literal>,
2477 their selector functions actually have different types:
2480 num :: Term Int -> Term Int
2481 arg :: Term Bool -> Term Int
2486 When pattern-matching against data constructors drawn from a GADT,
2487 for example in a <literal>case</literal> expression, the following rules apply:
2489 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2490 <listitem><para>The type of the result of the <literal>case</literal> expression must be rigid.</para></listitem>
2491 <listitem><para>The type of any free variable mentioned in any of
2492 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2494 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2495 way to ensure that a variable a rigid type is to give it a type signature.
2504 <!-- ====================== End of Generalised algebraic data types ======================= -->
2506 <sect1 id="deriving">
2507 <title>Extensions to the "deriving" mechanism</title>
2509 <sect2 id="deriving-inferred">
2510 <title>Inferred context for deriving clauses</title>
2513 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2516 data T0 f a = MkT0 a deriving( Eq )
2517 data T1 f a = MkT1 (f a) deriving( Eq )
2518 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2520 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2522 instance Eq a => Eq (T0 f a) where ...
2523 instance Eq (f a) => Eq (T1 f a) where ...
2524 instance Eq (f (f a)) => Eq (T2 f a) where ...
2526 The first of these is obviously fine. The second is still fine, although less obviously.
2527 The third is not Haskell 98, and risks losing termination of instances.
2530 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2531 each constraint in the inferred instance context must consist only of type variables,
2532 with no repetitions.
2535 This rule is applied regardless of flags. If you want a more exotic context, you can write
2536 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2540 <sect2 id="stand-alone-deriving">
2541 <title>Stand-alone deriving declarations</title>
2544 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2546 data Foo a = Bar a | Baz String
2548 deriving instance Eq a => Eq (Foo a)
2550 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2551 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2552 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2553 exactly as you would in an ordinary instance declaration.
2554 (In contrast the context is inferred in a <literal>deriving</literal> clause
2555 attached to a data type declaration.)
2557 A <literal>deriving instance</literal> declaration
2558 must obey the same rules concerning form and termination as ordinary instance declarations,
2559 controlled by the same flags; see <xref linkend="instance-decls"/>.
2562 Unlike a <literal>deriving</literal>
2563 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2564 than the data type (assuming you also use
2565 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2568 data Foo a = Bar a | Baz String
2570 deriving instance Eq a => Eq (Foo [a])
2571 deriving instance Eq a => Eq (Foo (Maybe a))
2573 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2574 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2577 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2578 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2581 newtype Foo a = MkFoo (State Int a)
2583 deriving instance MonadState Int Foo
2585 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2586 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2592 <sect2 id="deriving-typeable">
2593 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2596 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2597 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2598 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2599 classes <literal>Eq</literal>, <literal>Ord</literal>,
2600 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2603 GHC extends this list with two more classes that may be automatically derived
2604 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2605 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2606 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2607 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2609 <para>An instance of <literal>Typeable</literal> can only be derived if the
2610 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2611 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2613 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2614 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2616 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2617 are used, and only <literal>Typeable1</literal> up to
2618 <literal>Typeable7</literal> are provided in the library.)
2619 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2620 class, whose kind suits that of the data type constructor, and
2621 then writing the data type instance by hand.
2625 <sect2 id="newtype-deriving">
2626 <title>Generalised derived instances for newtypes</title>
2629 When you define an abstract type using <literal>newtype</literal>, you may want
2630 the new type to inherit some instances from its representation. In
2631 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2632 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2633 other classes you have to write an explicit instance declaration. For
2634 example, if you define
2637 newtype Dollars = Dollars Int
2640 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2641 explicitly define an instance of <literal>Num</literal>:
2644 instance Num Dollars where
2645 Dollars a + Dollars b = Dollars (a+b)
2648 All the instance does is apply and remove the <literal>newtype</literal>
2649 constructor. It is particularly galling that, since the constructor
2650 doesn't appear at run-time, this instance declaration defines a
2651 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2652 dictionary, only slower!
2656 <sect3> <title> Generalising the deriving clause </title>
2658 GHC now permits such instances to be derived instead,
2659 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2662 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2665 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2666 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2667 derives an instance declaration of the form
2670 instance Num Int => Num Dollars
2673 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2677 We can also derive instances of constructor classes in a similar
2678 way. For example, suppose we have implemented state and failure monad
2679 transformers, such that
2682 instance Monad m => Monad (State s m)
2683 instance Monad m => Monad (Failure m)
2685 In Haskell 98, we can define a parsing monad by
2687 type Parser tok m a = State [tok] (Failure m) a
2690 which is automatically a monad thanks to the instance declarations
2691 above. With the extension, we can make the parser type abstract,
2692 without needing to write an instance of class <literal>Monad</literal>, via
2695 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2698 In this case the derived instance declaration is of the form
2700 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2703 Notice that, since <literal>Monad</literal> is a constructor class, the
2704 instance is a <emphasis>partial application</emphasis> of the new type, not the
2705 entire left hand side. We can imagine that the type declaration is
2706 "eta-converted" to generate the context of the instance
2711 We can even derive instances of multi-parameter classes, provided the
2712 newtype is the last class parameter. In this case, a ``partial
2713 application'' of the class appears in the <literal>deriving</literal>
2714 clause. For example, given the class
2717 class StateMonad s m | m -> s where ...
2718 instance Monad m => StateMonad s (State s m) where ...
2720 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2722 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2723 deriving (Monad, StateMonad [tok])
2726 The derived instance is obtained by completing the application of the
2727 class to the new type:
2730 instance StateMonad [tok] (State [tok] (Failure m)) =>
2731 StateMonad [tok] (Parser tok m)
2736 As a result of this extension, all derived instances in newtype
2737 declarations are treated uniformly (and implemented just by reusing
2738 the dictionary for the representation type), <emphasis>except</emphasis>
2739 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2740 the newtype and its representation.
2744 <sect3> <title> A more precise specification </title>
2746 Derived instance declarations are constructed as follows. Consider the
2747 declaration (after expansion of any type synonyms)
2750 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2756 The <literal>ci</literal> are partial applications of
2757 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2758 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2761 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2764 The type <literal>t</literal> is an arbitrary type.
2767 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2768 nor in the <literal>ci</literal>, and
2771 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2772 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2773 should not "look through" the type or its constructor. You can still
2774 derive these classes for a newtype, but it happens in the usual way, not
2775 via this new mechanism.
2778 Then, for each <literal>ci</literal>, the derived instance
2781 instance ci t => ci (T v1...vk)
2783 As an example which does <emphasis>not</emphasis> work, consider
2785 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2787 Here we cannot derive the instance
2789 instance Monad (State s m) => Monad (NonMonad m)
2792 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2793 and so cannot be "eta-converted" away. It is a good thing that this
2794 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2795 not, in fact, a monad --- for the same reason. Try defining
2796 <literal>>>=</literal> with the correct type: you won't be able to.
2800 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2801 important, since we can only derive instances for the last one. If the
2802 <literal>StateMonad</literal> class above were instead defined as
2805 class StateMonad m s | m -> s where ...
2808 then we would not have been able to derive an instance for the
2809 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2810 classes usually have one "main" parameter for which deriving new
2811 instances is most interesting.
2813 <para>Lastly, all of this applies only for classes other than
2814 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2815 and <literal>Data</literal>, for which the built-in derivation applies (section
2816 4.3.3. of the Haskell Report).
2817 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2818 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2819 the standard method is used or the one described here.)
2826 <!-- TYPE SYSTEM EXTENSIONS -->
2827 <sect1 id="type-class-extensions">
2828 <title>Class and instances declarations</title>
2830 <sect2 id="multi-param-type-classes">
2831 <title>Class declarations</title>
2834 This section, and the next one, documents GHC's type-class extensions.
2835 There's lots of background in the paper <ulink
2836 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2837 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2838 Jones, Erik Meijer).
2841 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2845 <title>Multi-parameter type classes</title>
2847 Multi-parameter type classes are permitted. For example:
2851 class Collection c a where
2852 union :: c a -> c a -> c a
2860 <title>The superclasses of a class declaration</title>
2863 There are no restrictions on the context in a class declaration
2864 (which introduces superclasses), except that the class hierarchy must
2865 be acyclic. So these class declarations are OK:
2869 class Functor (m k) => FiniteMap m k where
2872 class (Monad m, Monad (t m)) => Transform t m where
2873 lift :: m a -> (t m) a
2879 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2880 of "acyclic" involves only the superclass relationships. For example,
2886 op :: D b => a -> b -> b
2889 class C a => D a where { ... }
2893 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2894 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2895 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2902 <sect3 id="class-method-types">
2903 <title>Class method types</title>
2906 Haskell 98 prohibits class method types to mention constraints on the
2907 class type variable, thus:
2910 fromList :: [a] -> s a
2911 elem :: Eq a => a -> s a -> Bool
2913 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2914 contains the constraint <literal>Eq a</literal>, constrains only the
2915 class type variable (in this case <literal>a</literal>).
2916 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2923 <sect2 id="functional-dependencies">
2924 <title>Functional dependencies
2927 <para> Functional dependencies are implemented as described by Mark Jones
2928 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2929 In Proceedings of the 9th European Symposium on Programming,
2930 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2934 Functional dependencies are introduced by a vertical bar in the syntax of a
2935 class declaration; e.g.
2937 class (Monad m) => MonadState s m | m -> s where ...
2939 class Foo a b c | a b -> c where ...
2941 There should be more documentation, but there isn't (yet). Yell if you need it.
2944 <sect3><title>Rules for functional dependencies </title>
2946 In a class declaration, all of the class type variables must be reachable (in the sense
2947 mentioned in <xref linkend="type-restrictions"/>)
2948 from the free variables of each method type.
2952 class Coll s a where
2954 insert :: s -> a -> s
2957 is not OK, because the type of <literal>empty</literal> doesn't mention
2958 <literal>a</literal>. Functional dependencies can make the type variable
2961 class Coll s a | s -> a where
2963 insert :: s -> a -> s
2966 Alternatively <literal>Coll</literal> might be rewritten
2969 class Coll s a where
2971 insert :: s a -> a -> s a
2975 which makes the connection between the type of a collection of
2976 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2977 Occasionally this really doesn't work, in which case you can split the
2985 class CollE s => Coll s a where
2986 insert :: s -> a -> s
2993 <title>Background on functional dependencies</title>
2995 <para>The following description of the motivation and use of functional dependencies is taken
2996 from the Hugs user manual, reproduced here (with minor changes) by kind
2997 permission of Mark Jones.
3000 Consider the following class, intended as part of a
3001 library for collection types:
3003 class Collects e ce where
3005 insert :: e -> ce -> ce
3006 member :: e -> ce -> Bool
3008 The type variable e used here represents the element type, while ce is the type
3009 of the container itself. Within this framework, we might want to define
3010 instances of this class for lists or characteristic functions (both of which
3011 can be used to represent collections of any equality type), bit sets (which can
3012 be used to represent collections of characters), or hash tables (which can be
3013 used to represent any collection whose elements have a hash function). Omitting
3014 standard implementation details, this would lead to the following declarations:
3016 instance Eq e => Collects e [e] where ...
3017 instance Eq e => Collects e (e -> Bool) where ...
3018 instance Collects Char BitSet where ...
3019 instance (Hashable e, Collects a ce)
3020 => Collects e (Array Int ce) where ...
3022 All this looks quite promising; we have a class and a range of interesting
3023 implementations. Unfortunately, there are some serious problems with the class
3024 declaration. First, the empty function has an ambiguous type:
3026 empty :: Collects e ce => ce
3028 By "ambiguous" we mean that there is a type variable e that appears on the left
3029 of the <literal>=></literal> symbol, but not on the right. The problem with
3030 this is that, according to the theoretical foundations of Haskell overloading,
3031 we cannot guarantee a well-defined semantics for any term with an ambiguous
3035 We can sidestep this specific problem by removing the empty member from the
3036 class declaration. However, although the remaining members, insert and member,
3037 do not have ambiguous types, we still run into problems when we try to use
3038 them. For example, consider the following two functions:
3040 f x y = insert x . insert y
3043 for which GHC infers the following types:
3045 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3046 g :: (Collects Bool c, Collects Char c) => c -> c
3048 Notice that the type for f allows the two parameters x and y to be assigned
3049 different types, even though it attempts to insert each of the two values, one
3050 after the other, into the same collection. If we're trying to model collections
3051 that contain only one type of value, then this is clearly an inaccurate
3052 type. Worse still, the definition for g is accepted, without causing a type
3053 error. As a result, the error in this code will not be flagged at the point
3054 where it appears. Instead, it will show up only when we try to use g, which
3055 might even be in a different module.
3058 <sect4><title>An attempt to use constructor classes</title>
3061 Faced with the problems described above, some Haskell programmers might be
3062 tempted to use something like the following version of the class declaration:
3064 class Collects e c where
3066 insert :: e -> c e -> c e
3067 member :: e -> c e -> Bool
3069 The key difference here is that we abstract over the type constructor c that is
3070 used to form the collection type c e, and not over that collection type itself,
3071 represented by ce in the original class declaration. This avoids the immediate
3072 problems that we mentioned above: empty has type <literal>Collects e c => c
3073 e</literal>, which is not ambiguous.
3076 The function f from the previous section has a more accurate type:
3078 f :: (Collects e c) => e -> e -> c e -> c e
3080 The function g from the previous section is now rejected with a type error as
3081 we would hope because the type of f does not allow the two arguments to have
3083 This, then, is an example of a multiple parameter class that does actually work
3084 quite well in practice, without ambiguity problems.
3085 There is, however, a catch. This version of the Collects class is nowhere near
3086 as general as the original class seemed to be: only one of the four instances
3087 for <literal>Collects</literal>
3088 given above can be used with this version of Collects because only one of
3089 them---the instance for lists---has a collection type that can be written in
3090 the form c e, for some type constructor c, and element type e.
3094 <sect4><title>Adding functional dependencies</title>
3097 To get a more useful version of the Collects class, Hugs provides a mechanism
3098 that allows programmers to specify dependencies between the parameters of a
3099 multiple parameter class (For readers with an interest in theoretical
3100 foundations and previous work: The use of dependency information can be seen
3101 both as a generalization of the proposal for `parametric type classes' that was
3102 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3103 later framework for "improvement" of qualified types. The
3104 underlying ideas are also discussed in a more theoretical and abstract setting
3105 in a manuscript [implparam], where they are identified as one point in a
3106 general design space for systems of implicit parameterization.).
3108 To start with an abstract example, consider a declaration such as:
3110 class C a b where ...
3112 which tells us simply that C can be thought of as a binary relation on types
3113 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3114 included in the definition of classes to add information about dependencies
3115 between parameters, as in the following examples:
3117 class D a b | a -> b where ...
3118 class E a b | a -> b, b -> a where ...
3120 The notation <literal>a -> b</literal> used here between the | and where
3121 symbols --- not to be
3122 confused with a function type --- indicates that the a parameter uniquely
3123 determines the b parameter, and might be read as "a determines b." Thus D is
3124 not just a relation, but actually a (partial) function. Similarly, from the two
3125 dependencies that are included in the definition of E, we can see that E
3126 represents a (partial) one-one mapping between types.
3129 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3130 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3131 m>=0, meaning that the y parameters are uniquely determined by the x
3132 parameters. Spaces can be used as separators if more than one variable appears
3133 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3134 annotated with multiple dependencies using commas as separators, as in the
3135 definition of E above. Some dependencies that we can write in this notation are
3136 redundant, and will be rejected because they don't serve any useful
3137 purpose, and may instead indicate an error in the program. Examples of
3138 dependencies like this include <literal>a -> a </literal>,
3139 <literal>a -> a a </literal>,
3140 <literal>a -> </literal>, etc. There can also be
3141 some redundancy if multiple dependencies are given, as in
3142 <literal>a->b</literal>,
3143 <literal>b->c </literal>, <literal>a->c </literal>, and
3144 in which some subset implies the remaining dependencies. Examples like this are
3145 not treated as errors. Note that dependencies appear only in class
3146 declarations, and not in any other part of the language. In particular, the
3147 syntax for instance declarations, class constraints, and types is completely
3151 By including dependencies in a class declaration, we provide a mechanism for
3152 the programmer to specify each multiple parameter class more precisely. The
3153 compiler, on the other hand, is responsible for ensuring that the set of
3154 instances that are in scope at any given point in the program is consistent
3155 with any declared dependencies. For example, the following pair of instance
3156 declarations cannot appear together in the same scope because they violate the
3157 dependency for D, even though either one on its own would be acceptable:
3159 instance D Bool Int where ...
3160 instance D Bool Char where ...
3162 Note also that the following declaration is not allowed, even by itself:
3164 instance D [a] b where ...
3166 The problem here is that this instance would allow one particular choice of [a]
3167 to be associated with more than one choice for b, which contradicts the
3168 dependency specified in the definition of D. More generally, this means that,
3169 in any instance of the form:
3171 instance D t s where ...
3173 for some particular types t and s, the only variables that can appear in s are
3174 the ones that appear in t, and hence, if the type t is known, then s will be
3175 uniquely determined.
3178 The benefit of including dependency information is that it allows us to define
3179 more general multiple parameter classes, without ambiguity problems, and with
3180 the benefit of more accurate types. To illustrate this, we return to the
3181 collection class example, and annotate the original definition of <literal>Collects</literal>
3182 with a simple dependency:
3184 class Collects e ce | ce -> e where
3186 insert :: e -> ce -> ce
3187 member :: e -> ce -> Bool
3189 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3190 determined by the type of the collection ce. Note that both parameters of
3191 Collects are of kind *; there are no constructor classes here. Note too that
3192 all of the instances of Collects that we gave earlier can be used
3193 together with this new definition.
3196 What about the ambiguity problems that we encountered with the original
3197 definition? The empty function still has type Collects e ce => ce, but it is no
3198 longer necessary to regard that as an ambiguous type: Although the variable e
3199 does not appear on the right of the => symbol, the dependency for class
3200 Collects tells us that it is uniquely determined by ce, which does appear on
3201 the right of the => symbol. Hence the context in which empty is used can still
3202 give enough information to determine types for both ce and e, without
3203 ambiguity. More generally, we need only regard a type as ambiguous if it
3204 contains a variable on the left of the => that is not uniquely determined
3205 (either directly or indirectly) by the variables on the right.
3208 Dependencies also help to produce more accurate types for user defined
3209 functions, and hence to provide earlier detection of errors, and less cluttered
3210 types for programmers to work with. Recall the previous definition for a
3213 f x y = insert x y = insert x . insert y
3215 for which we originally obtained a type:
3217 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3219 Given the dependency information that we have for Collects, however, we can
3220 deduce that a and b must be equal because they both appear as the second
3221 parameter in a Collects constraint with the same first parameter c. Hence we
3222 can infer a shorter and more accurate type for f:
3224 f :: (Collects a c) => a -> a -> c -> c
3226 In a similar way, the earlier definition of g will now be flagged as a type error.
3229 Although we have given only a few examples here, it should be clear that the
3230 addition of dependency information can help to make multiple parameter classes
3231 more useful in practice, avoiding ambiguity problems, and allowing more general
3232 sets of instance declarations.
3238 <sect2 id="instance-decls">
3239 <title>Instance declarations</title>
3241 <sect3 id="instance-rules">
3242 <title>Relaxed rules for instance declarations</title>
3244 <para>An instance declaration has the form
3246 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 ...
3248 The part before the "<literal>=></literal>" is the
3249 <emphasis>context</emphasis>, while the part after the
3250 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3254 In Haskell 98 the head of an instance declaration
3255 must be of the form <literal>C (T a1 ... an)</literal>, where
3256 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3257 and the <literal>a1 ... an</literal> are distinct type variables.
3258 Furthermore, the assertions in the context of the instance declaration
3259 must be of the form <literal>C a</literal> where <literal>a</literal>
3260 is a type variable that occurs in the head.
3263 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3264 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3265 the context and head of the instance declaration can each consist of arbitrary
3266 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3270 The Paterson Conditions: for each assertion in the context
3272 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3273 <listitem><para>The assertion has fewer constructors and variables (taken together
3274 and counting repetitions) than the head</para></listitem>
3278 <listitem><para>The Coverage Condition. For each functional dependency,
3279 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3280 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3281 every type variable in
3282 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3283 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3284 substitution mapping each type variable in the class declaration to the
3285 corresponding type in the instance declaration.
3288 These restrictions ensure that context reduction terminates: each reduction
3289 step makes the problem smaller by at least one
3290 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3291 if you give the <option>-XUndecidableInstances</option>
3292 flag (<xref linkend="undecidable-instances"/>).
3293 You can find lots of background material about the reason for these
3294 restrictions in the paper <ulink
3295 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3296 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3299 For example, these are OK:
3301 instance C Int [a] -- Multiple parameters
3302 instance Eq (S [a]) -- Structured type in head
3304 -- Repeated type variable in head
3305 instance C4 a a => C4 [a] [a]
3306 instance Stateful (ST s) (MutVar s)
3308 -- Head can consist of type variables only
3310 instance (Eq a, Show b) => C2 a b
3312 -- Non-type variables in context
3313 instance Show (s a) => Show (Sized s a)
3314 instance C2 Int a => C3 Bool [a]
3315 instance C2 Int a => C3 [a] b
3319 -- Context assertion no smaller than head
3320 instance C a => C a where ...
3321 -- (C b b) has more more occurrences of b than the head
3322 instance C b b => Foo [b] where ...
3327 The same restrictions apply to instances generated by
3328 <literal>deriving</literal> clauses. Thus the following is accepted:
3330 data MinHeap h a = H a (h a)
3333 because the derived instance
3335 instance (Show a, Show (h a)) => Show (MinHeap h a)
3337 conforms to the above rules.
3341 A useful idiom permitted by the above rules is as follows.
3342 If one allows overlapping instance declarations then it's quite
3343 convenient to have a "default instance" declaration that applies if
3344 something more specific does not:
3352 <sect3 id="undecidable-instances">
3353 <title>Undecidable instances</title>
3356 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3357 For example, sometimes you might want to use the following to get the
3358 effect of a "class synonym":
3360 class (C1 a, C2 a, C3 a) => C a where { }
3362 instance (C1 a, C2 a, C3 a) => C a where { }
3364 This allows you to write shorter signatures:
3370 f :: (C1 a, C2 a, C3 a) => ...
3372 The restrictions on functional dependencies (<xref
3373 linkend="functional-dependencies"/>) are particularly troublesome.
3374 It is tempting to introduce type variables in the context that do not appear in
3375 the head, something that is excluded by the normal rules. For example:
3377 class HasConverter a b | a -> b where
3380 data Foo a = MkFoo a
3382 instance (HasConverter a b,Show b) => Show (Foo a) where
3383 show (MkFoo value) = show (convert value)
3385 This is dangerous territory, however. Here, for example, is a program that would make the
3390 instance F [a] [[a]]
3391 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3393 Similarly, it can be tempting to lift the coverage condition:
3395 class Mul a b c | a b -> c where
3396 (.*.) :: a -> b -> c
3398 instance Mul Int Int Int where (.*.) = (*)
3399 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3400 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3402 The third instance declaration does not obey the coverage condition;
3403 and indeed the (somewhat strange) definition:
3405 f = \ b x y -> if b then x .*. [y] else y
3407 makes instance inference go into a loop, because it requires the constraint
3408 <literal>(Mul a [b] b)</literal>.
3411 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3412 the experimental flag <option>-XUndecidableInstances</option>
3413 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3414 both the Paterson Conditions and the Coverage Condition
3415 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3416 fixed-depth recursion stack. If you exceed the stack depth you get a
3417 sort of backtrace, and the opportunity to increase the stack depth
3418 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3424 <sect3 id="instance-overlap">
3425 <title>Overlapping instances</title>
3427 In general, <emphasis>GHC requires that that it be unambiguous which instance
3429 should be used to resolve a type-class constraint</emphasis>. This behaviour
3430 can be modified by two flags: <option>-XOverlappingInstances</option>
3431 <indexterm><primary>-XOverlappingInstances
3432 </primary></indexterm>
3433 and <option>-XIncoherentInstances</option>
3434 <indexterm><primary>-XIncoherentInstances
3435 </primary></indexterm>, as this section discusses. Both these
3436 flags are dynamic flags, and can be set on a per-module basis, using
3437 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3439 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3440 it tries to match every instance declaration against the
3442 by instantiating the head of the instance declaration. For example, consider
3445 instance context1 => C Int a where ... -- (A)
3446 instance context2 => C a Bool where ... -- (B)
3447 instance context3 => C Int [a] where ... -- (C)
3448 instance context4 => C Int [Int] where ... -- (D)
3450 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3451 but (C) and (D) do not. When matching, GHC takes
3452 no account of the context of the instance declaration
3453 (<literal>context1</literal> etc).
3454 GHC's default behaviour is that <emphasis>exactly one instance must match the
3455 constraint it is trying to resolve</emphasis>.
3456 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3457 including both declarations (A) and (B), say); an error is only reported if a
3458 particular constraint matches more than one.
3462 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3463 more than one instance to match, provided there is a most specific one. For
3464 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3465 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3466 most-specific match, the program is rejected.
3469 However, GHC is conservative about committing to an overlapping instance. For example:
3474 Suppose that from the RHS of <literal>f</literal> we get the constraint
3475 <literal>C Int [b]</literal>. But
3476 GHC does not commit to instance (C), because in a particular
3477 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3478 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3479 So GHC rejects the program.
3480 (If you add the flag <option>-XIncoherentInstances</option>,
3481 GHC will instead pick (C), without complaining about
3482 the problem of subsequent instantiations.)
3485 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3486 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3487 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3488 it instead. In this case, GHC will refrain from
3489 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3490 as before) but, rather than rejecting the program, it will infer the type
3492 f :: C Int b => [b] -> [b]
3494 That postpones the question of which instance to pick to the
3495 call site for <literal>f</literal>
3496 by which time more is known about the type <literal>b</literal>.
3499 The willingness to be overlapped or incoherent is a property of
3500 the <emphasis>instance declaration</emphasis> itself, controlled by the
3501 presence or otherwise of the <option>-XOverlappingInstances</option>
3502 and <option>-XIncoherentInstances</option> flags when that module is
3503 being defined. Neither flag is required in a module that imports and uses the
3504 instance declaration. Specifically, during the lookup process:
3507 An instance declaration is ignored during the lookup process if (a) a more specific
3508 match is found, and (b) the instance declaration was compiled with
3509 <option>-XOverlappingInstances</option>. The flag setting for the
3510 more-specific instance does not matter.
3513 Suppose an instance declaration does not match the constraint being looked up, but
3514 does unify with it, so that it might match when the constraint is further
3515 instantiated. Usually GHC will regard this as a reason for not committing to
3516 some other constraint. But if the instance declaration was compiled with
3517 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3518 check for that declaration.
3521 These rules make it possible for a library author to design a library that relies on
3522 overlapping instances without the library client having to know.
3525 If an instance declaration is compiled without
3526 <option>-XOverlappingInstances</option>,
3527 then that instance can never be overlapped. This could perhaps be
3528 inconvenient. Perhaps the rule should instead say that the
3529 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3530 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3531 at a usage site should be permitted regardless of how the instance declarations
3532 are compiled, if the <option>-XOverlappingInstances</option> flag is
3533 used at the usage site. (Mind you, the exact usage site can occasionally be
3534 hard to pin down.) We are interested to receive feedback on these points.
3536 <para>The <option>-XIncoherentInstances</option> flag implies the
3537 <option>-XOverlappingInstances</option> flag, but not vice versa.
3542 <title>Type synonyms in the instance head</title>
3545 <emphasis>Unlike Haskell 98, instance heads may use type
3546 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3547 As always, using a type synonym is just shorthand for
3548 writing the RHS of the type synonym definition. For example:
3552 type Point = (Int,Int)
3553 instance C Point where ...
3554 instance C [Point] where ...
3558 is legal. However, if you added
3562 instance C (Int,Int) where ...
3566 as well, then the compiler will complain about the overlapping
3567 (actually, identical) instance declarations. As always, type synonyms
3568 must be fully applied. You cannot, for example, write:
3573 instance Monad P where ...
3577 This design decision is independent of all the others, and easily
3578 reversed, but it makes sense to me.
3586 <sect2 id="overloaded-strings">
3587 <title>Overloaded string literals
3591 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3592 string literal has type <literal>String</literal>, but with overloaded string
3593 literals enabled (with <literal>-XOverloadedStrings</literal>)
3594 a string literal has type <literal>(IsString a) => a</literal>.
3597 This means that the usual string syntax can be used, e.g., for packed strings
3598 and other variations of string like types. String literals behave very much
3599 like integer literals, i.e., they can be used in both expressions and patterns.
3600 If used in a pattern the literal with be replaced by an equality test, in the same
3601 way as an integer literal is.
3604 The class <literal>IsString</literal> is defined as:
3606 class IsString a where
3607 fromString :: String -> a
3609 The only predefined instance is the obvious one to make strings work as usual:
3611 instance IsString [Char] where
3614 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3615 it explicitly (for example, to give an instance declaration for it), you can import it
3616 from module <literal>GHC.Exts</literal>.
3619 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3623 Each type in a default declaration must be an
3624 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3628 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3629 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3630 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3631 <emphasis>or</emphasis> <literal>IsString</literal>.
3640 import GHC.Exts( IsString(..) )
3642 newtype MyString = MyString String deriving (Eq, Show)
3643 instance IsString MyString where
3644 fromString = MyString
3646 greet :: MyString -> MyString
3647 greet "hello" = "world"
3651 print $ greet "hello"
3652 print $ greet "fool"
3656 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3657 to work since it gets translated into an equality comparison.
3663 <sect1 id="other-type-extensions">
3664 <title>Other type system extensions</title>
3666 <sect2 id="type-restrictions">
3667 <title>Type signatures</title>
3669 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3671 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3672 the form <emphasis>(class type-variable)</emphasis> or
3673 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3674 these type signatures are perfectly OK
3677 g :: Ord (T a ()) => ...
3681 GHC imposes the following restrictions on the constraints in a type signature.
3685 forall tv1..tvn (c1, ...,cn) => type
3688 (Here, we write the "foralls" explicitly, although the Haskell source
3689 language omits them; in Haskell 98, all the free type variables of an
3690 explicit source-language type signature are universally quantified,
3691 except for the class type variables in a class declaration. However,
3692 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3701 <emphasis>Each universally quantified type variable
3702 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3704 A type variable <literal>a</literal> is "reachable" if it appears
3705 in the same constraint as either a type variable free in
3706 <literal>type</literal>, or another reachable type variable.
3707 A value with a type that does not obey
3708 this reachability restriction cannot be used without introducing
3709 ambiguity; that is why the type is rejected.
3710 Here, for example, is an illegal type:
3714 forall a. Eq a => Int
3718 When a value with this type was used, the constraint <literal>Eq tv</literal>
3719 would be introduced where <literal>tv</literal> is a fresh type variable, and
3720 (in the dictionary-translation implementation) the value would be
3721 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3722 can never know which instance of <literal>Eq</literal> to use because we never
3723 get any more information about <literal>tv</literal>.
3727 that the reachability condition is weaker than saying that <literal>a</literal> is
3728 functionally dependent on a type variable free in
3729 <literal>type</literal> (see <xref
3730 linkend="functional-dependencies"/>). The reason for this is there
3731 might be a "hidden" dependency, in a superclass perhaps. So
3732 "reachable" is a conservative approximation to "functionally dependent".
3733 For example, consider:
3735 class C a b | a -> b where ...
3736 class C a b => D a b where ...
3737 f :: forall a b. D a b => a -> a
3739 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3740 but that is not immediately apparent from <literal>f</literal>'s type.
3746 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3747 universally quantified type variables <literal>tvi</literal></emphasis>.
3749 For example, this type is OK because <literal>C a b</literal> mentions the
3750 universally quantified type variable <literal>b</literal>:
3754 forall a. C a b => burble
3758 The next type is illegal because the constraint <literal>Eq b</literal> does not
3759 mention <literal>a</literal>:
3763 forall a. Eq b => burble
3767 The reason for this restriction is milder than the other one. The
3768 excluded types are never useful or necessary (because the offending
3769 context doesn't need to be witnessed at this point; it can be floated
3770 out). Furthermore, floating them out increases sharing. Lastly,
3771 excluding them is a conservative choice; it leaves a patch of
3772 territory free in case we need it later.
3786 <sect2 id="implicit-parameters">
3787 <title>Implicit parameters</title>
3789 <para> Implicit parameters are implemented as described in
3790 "Implicit parameters: dynamic scoping with static types",
3791 J Lewis, MB Shields, E Meijer, J Launchbury,
3792 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3796 <para>(Most of the following, still rather incomplete, documentation is
3797 due to Jeff Lewis.)</para>
3799 <para>Implicit parameter support is enabled with the option
3800 <option>-XImplicitParams</option>.</para>
3803 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3804 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3805 context. In Haskell, all variables are statically bound. Dynamic
3806 binding of variables is a notion that goes back to Lisp, but was later
3807 discarded in more modern incarnations, such as Scheme. Dynamic binding
3808 can be very confusing in an untyped language, and unfortunately, typed
3809 languages, in particular Hindley-Milner typed languages like Haskell,
3810 only support static scoping of variables.
3813 However, by a simple extension to the type class system of Haskell, we
3814 can support dynamic binding. Basically, we express the use of a
3815 dynamically bound variable as a constraint on the type. These
3816 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3817 function uses a dynamically-bound variable <literal>?x</literal>
3818 of type <literal>t'</literal>". For
3819 example, the following expresses the type of a sort function,
3820 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3822 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3824 The dynamic binding constraints are just a new form of predicate in the type class system.
3827 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3828 where <literal>x</literal> is
3829 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3830 Use of this construct also introduces a new
3831 dynamic-binding constraint in the type of the expression.
3832 For example, the following definition
3833 shows how we can define an implicitly parameterized sort function in
3834 terms of an explicitly parameterized <literal>sortBy</literal> function:
3836 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3838 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3844 <title>Implicit-parameter type constraints</title>
3846 Dynamic binding constraints behave just like other type class
3847 constraints in that they are automatically propagated. Thus, when a
3848 function is used, its implicit parameters are inherited by the
3849 function that called it. For example, our <literal>sort</literal> function might be used
3850 to pick out the least value in a list:
3852 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3853 least xs = head (sort xs)
3855 Without lifting a finger, the <literal>?cmp</literal> parameter is
3856 propagated to become a parameter of <literal>least</literal> as well. With explicit
3857 parameters, the default is that parameters must always be explicit
3858 propagated. With implicit parameters, the default is to always
3862 An implicit-parameter type constraint differs from other type class constraints in the
3863 following way: All uses of a particular implicit parameter must have
3864 the same type. This means that the type of <literal>(?x, ?x)</literal>
3865 is <literal>(?x::a) => (a,a)</literal>, and not
3866 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3870 <para> You can't have an implicit parameter in the context of a class or instance
3871 declaration. For example, both these declarations are illegal:
3873 class (?x::Int) => C a where ...
3874 instance (?x::a) => Foo [a] where ...
3876 Reason: exactly which implicit parameter you pick up depends on exactly where
3877 you invoke a function. But the ``invocation'' of instance declarations is done
3878 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3879 Easiest thing is to outlaw the offending types.</para>
3881 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3883 f :: (?x :: [a]) => Int -> Int
3886 g :: (Read a, Show a) => String -> String
3889 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3890 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3891 quite unambiguous, and fixes the type <literal>a</literal>.
3896 <title>Implicit-parameter bindings</title>
3899 An implicit parameter is <emphasis>bound</emphasis> using the standard
3900 <literal>let</literal> or <literal>where</literal> binding forms.
3901 For example, we define the <literal>min</literal> function by binding
3902 <literal>cmp</literal>.
3905 min = let ?cmp = (<=) in least
3909 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3910 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3911 (including in a list comprehension, or do-notation, or pattern guards),
3912 or a <literal>where</literal> clause.
3913 Note the following points:
3916 An implicit-parameter binding group must be a
3917 collection of simple bindings to implicit-style variables (no
3918 function-style bindings, and no type signatures); these bindings are
3919 neither polymorphic or recursive.
3922 You may not mix implicit-parameter bindings with ordinary bindings in a
3923 single <literal>let</literal>
3924 expression; use two nested <literal>let</literal>s instead.
3925 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3929 You may put multiple implicit-parameter bindings in a
3930 single binding group; but they are <emphasis>not</emphasis> treated
3931 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3932 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3933 parameter. The bindings are not nested, and may be re-ordered without changing
3934 the meaning of the program.
3935 For example, consider:
3937 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3939 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3940 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3942 f :: (?x::Int) => Int -> Int
3950 <sect3><title>Implicit parameters and polymorphic recursion</title>
3953 Consider these two definitions:
3956 len1 xs = let ?acc = 0 in len_acc1 xs
3959 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3964 len2 xs = let ?acc = 0 in len_acc2 xs
3966 len_acc2 :: (?acc :: Int) => [a] -> Int
3968 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3970 The only difference between the two groups is that in the second group
3971 <literal>len_acc</literal> is given a type signature.
3972 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3973 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3974 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3975 has a type signature, the recursive call is made to the
3976 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3977 as an implicit parameter. So we get the following results in GHCi:
3984 Adding a type signature dramatically changes the result! This is a rather
3985 counter-intuitive phenomenon, worth watching out for.
3989 <sect3><title>Implicit parameters and monomorphism</title>
3991 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3992 Haskell Report) to implicit parameters. For example, consider:
4000 Since the binding for <literal>y</literal> falls under the Monomorphism
4001 Restriction it is not generalised, so the type of <literal>y</literal> is
4002 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4003 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4004 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4005 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4006 <literal>y</literal> in the body of the <literal>let</literal> will see the
4007 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4008 <literal>14</literal>.
4013 <!-- ======================= COMMENTED OUT ========================
4015 We intend to remove linear implicit parameters, so I'm at least removing
4016 them from the 6.6 user manual
4018 <sect2 id="linear-implicit-parameters">
4019 <title>Linear implicit parameters</title>
4021 Linear implicit parameters are an idea developed by Koen Claessen,
4022 Mark Shields, and Simon PJ. They address the long-standing
4023 problem that monads seem over-kill for certain sorts of problem, notably:
4026 <listitem> <para> distributing a supply of unique names </para> </listitem>
4027 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4028 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4032 Linear implicit parameters are just like ordinary implicit parameters,
4033 except that they are "linear"; that is, they cannot be copied, and
4034 must be explicitly "split" instead. Linear implicit parameters are
4035 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4036 (The '/' in the '%' suggests the split!)
4041 import GHC.Exts( Splittable )
4043 data NameSupply = ...
4045 splitNS :: NameSupply -> (NameSupply, NameSupply)
4046 newName :: NameSupply -> Name
4048 instance Splittable NameSupply where
4052 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4053 f env (Lam x e) = Lam x' (f env e)
4056 env' = extend env x x'
4057 ...more equations for f...
4059 Notice that the implicit parameter %ns is consumed
4061 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4062 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4066 So the translation done by the type checker makes
4067 the parameter explicit:
4069 f :: NameSupply -> Env -> Expr -> Expr
4070 f ns env (Lam x e) = Lam x' (f ns1 env e)
4072 (ns1,ns2) = splitNS ns
4074 env = extend env x x'
4076 Notice the call to 'split' introduced by the type checker.
4077 How did it know to use 'splitNS'? Because what it really did
4078 was to introduce a call to the overloaded function 'split',
4079 defined by the class <literal>Splittable</literal>:
4081 class Splittable a where
4084 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4085 split for name supplies. But we can simply write
4091 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4093 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4094 <literal>GHC.Exts</literal>.
4099 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4100 are entirely distinct implicit parameters: you
4101 can use them together and they won't interfere with each other. </para>
4104 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4106 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4107 in the context of a class or instance declaration. </para></listitem>
4111 <sect3><title>Warnings</title>
4114 The monomorphism restriction is even more important than usual.
4115 Consider the example above:
4117 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4118 f env (Lam x e) = Lam x' (f env e)
4121 env' = extend env x x'
4123 If we replaced the two occurrences of x' by (newName %ns), which is
4124 usually a harmless thing to do, we get:
4126 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4127 f env (Lam x e) = Lam (newName %ns) (f env e)
4129 env' = extend env x (newName %ns)
4131 But now the name supply is consumed in <emphasis>three</emphasis> places
4132 (the two calls to newName,and the recursive call to f), so
4133 the result is utterly different. Urk! We don't even have
4137 Well, this is an experimental change. With implicit
4138 parameters we have already lost beta reduction anyway, and
4139 (as John Launchbury puts it) we can't sensibly reason about
4140 Haskell programs without knowing their typing.
4145 <sect3><title>Recursive functions</title>
4146 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4149 foo :: %x::T => Int -> [Int]
4151 foo n = %x : foo (n-1)
4153 where T is some type in class Splittable.</para>
4155 Do you get a list of all the same T's or all different T's
4156 (assuming that split gives two distinct T's back)?
4158 If you supply the type signature, taking advantage of polymorphic
4159 recursion, you get what you'd probably expect. Here's the
4160 translated term, where the implicit param is made explicit:
4163 foo x n = let (x1,x2) = split x
4164 in x1 : foo x2 (n-1)
4166 But if you don't supply a type signature, GHC uses the Hindley
4167 Milner trick of using a single monomorphic instance of the function
4168 for the recursive calls. That is what makes Hindley Milner type inference
4169 work. So the translation becomes
4173 foom n = x : foom (n-1)
4177 Result: 'x' is not split, and you get a list of identical T's. So the
4178 semantics of the program depends on whether or not foo has a type signature.
4181 You may say that this is a good reason to dislike linear implicit parameters
4182 and you'd be right. That is why they are an experimental feature.
4188 ================ END OF Linear Implicit Parameters commented out -->
4190 <sect2 id="kinding">
4191 <title>Explicitly-kinded quantification</title>
4194 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4195 to give the kind explicitly as (machine-checked) documentation,
4196 just as it is nice to give a type signature for a function. On some occasions,
4197 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4198 John Hughes had to define the data type:
4200 data Set cxt a = Set [a]
4201 | Unused (cxt a -> ())
4203 The only use for the <literal>Unused</literal> constructor was to force the correct
4204 kind for the type variable <literal>cxt</literal>.
4207 GHC now instead allows you to specify the kind of a type variable directly, wherever
4208 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4211 This flag enables kind signatures in the following places:
4213 <listitem><para><literal>data</literal> declarations:
4215 data Set (cxt :: * -> *) a = Set [a]
4216 </screen></para></listitem>
4217 <listitem><para><literal>type</literal> declarations:
4219 type T (f :: * -> *) = f Int
4220 </screen></para></listitem>
4221 <listitem><para><literal>class</literal> declarations:
4223 class (Eq a) => C (f :: * -> *) a where ...
4224 </screen></para></listitem>
4225 <listitem><para><literal>forall</literal>'s in type signatures:
4227 f :: forall (cxt :: * -> *). Set cxt Int
4228 </screen></para></listitem>
4233 The parentheses are required. Some of the spaces are required too, to
4234 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4235 will get a parse error, because "<literal>::*->*</literal>" is a
4236 single lexeme in Haskell.
4240 As part of the same extension, you can put kind annotations in types
4243 f :: (Int :: *) -> Int
4244 g :: forall a. a -> (a :: *)
4248 atype ::= '(' ctype '::' kind ')
4250 The parentheses are required.
4255 <sect2 id="universal-quantification">
4256 <title>Arbitrary-rank polymorphism
4260 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4261 allows us to say exactly what this means. For example:
4269 g :: forall b. (b -> b)
4271 The two are treated identically.
4275 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4276 explicit universal quantification in
4278 For example, all the following types are legal:
4280 f1 :: forall a b. a -> b -> a
4281 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4283 f2 :: (forall a. a->a) -> Int -> Int
4284 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4286 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4288 f4 :: Int -> (forall a. a -> a)
4290 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4291 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4292 The <literal>forall</literal> makes explicit the universal quantification that
4293 is implicitly added by Haskell.
4296 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4297 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4298 shows, the polymorphic type on the left of the function arrow can be overloaded.
4301 The function <literal>f3</literal> has a rank-3 type;
4302 it has rank-2 types on the left of a function arrow.
4305 GHC has three flags to control higher-rank types:
4308 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4311 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4314 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4315 That is, you can nest <literal>forall</literal>s
4316 arbitrarily deep in function arrows.
4317 In particular, a forall-type (also called a "type scheme"),
4318 including an operational type class context, is legal:
4320 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4321 of a function arrow </para> </listitem>
4322 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4323 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4324 field type signatures.</para> </listitem>
4325 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4326 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4330 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4331 a type variable any more!
4340 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4341 the types of the constructor arguments. Here are several examples:
4347 data T a = T1 (forall b. b -> b -> b) a
4349 data MonadT m = MkMonad { return :: forall a. a -> m a,
4350 bind :: forall a b. m a -> (a -> m b) -> m b
4353 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4359 The constructors have rank-2 types:
4365 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4366 MkMonad :: forall m. (forall a. a -> m a)
4367 -> (forall a b. m a -> (a -> m b) -> m b)
4369 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4375 Notice that you don't need to use a <literal>forall</literal> if there's an
4376 explicit context. For example in the first argument of the
4377 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4378 prefixed to the argument type. The implicit <literal>forall</literal>
4379 quantifies all type variables that are not already in scope, and are
4380 mentioned in the type quantified over.
4384 As for type signatures, implicit quantification happens for non-overloaded
4385 types too. So if you write this:
4388 data T a = MkT (Either a b) (b -> b)
4391 it's just as if you had written this:
4394 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4397 That is, since the type variable <literal>b</literal> isn't in scope, it's
4398 implicitly universally quantified. (Arguably, it would be better
4399 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4400 where that is what is wanted. Feedback welcomed.)
4404 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4405 the constructor to suitable values, just as usual. For example,
4416 a3 = MkSwizzle reverse
4419 a4 = let r x = Just x
4426 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4427 mkTs f x y = [T1 f x, T1 f y]
4433 The type of the argument can, as usual, be more general than the type
4434 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4435 does not need the <literal>Ord</literal> constraint.)
4439 When you use pattern matching, the bound variables may now have
4440 polymorphic types. For example:
4446 f :: T a -> a -> (a, Char)
4447 f (T1 w k) x = (w k x, w 'c' 'd')
4449 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4450 g (MkSwizzle s) xs f = s (map f (s xs))
4452 h :: MonadT m -> [m a] -> m [a]
4453 h m [] = return m []
4454 h m (x:xs) = bind m x $ \y ->
4455 bind m (h m xs) $ \ys ->
4462 In the function <function>h</function> we use the record selectors <literal>return</literal>
4463 and <literal>bind</literal> to extract the polymorphic bind and return functions
4464 from the <literal>MonadT</literal> data structure, rather than using pattern
4470 <title>Type inference</title>
4473 In general, type inference for arbitrary-rank types is undecidable.
4474 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4475 to get a decidable algorithm by requiring some help from the programmer.
4476 We do not yet have a formal specification of "some help" but the rule is this:
4479 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4480 provides an explicit polymorphic type for x, or GHC's type inference will assume
4481 that x's type has no foralls in it</emphasis>.
4484 What does it mean to "provide" an explicit type for x? You can do that by
4485 giving a type signature for x directly, using a pattern type signature
4486 (<xref linkend="scoped-type-variables"/>), thus:
4488 \ f :: (forall a. a->a) -> (f True, f 'c')
4490 Alternatively, you can give a type signature to the enclosing
4491 context, which GHC can "push down" to find the type for the variable:
4493 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4495 Here the type signature on the expression can be pushed inwards
4496 to give a type signature for f. Similarly, and more commonly,
4497 one can give a type signature for the function itself:
4499 h :: (forall a. a->a) -> (Bool,Char)
4500 h f = (f True, f 'c')
4502 You don't need to give a type signature if the lambda bound variable
4503 is a constructor argument. Here is an example we saw earlier:
4505 f :: T a -> a -> (a, Char)
4506 f (T1 w k) x = (w k x, w 'c' 'd')
4508 Here we do not need to give a type signature to <literal>w</literal>, because
4509 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4516 <sect3 id="implicit-quant">
4517 <title>Implicit quantification</title>
4520 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4521 user-written types, if and only if there is no explicit <literal>forall</literal>,
4522 GHC finds all the type variables mentioned in the type that are not already
4523 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4527 f :: forall a. a -> a
4534 h :: forall b. a -> b -> b
4540 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4543 f :: (a -> a) -> Int
4545 f :: forall a. (a -> a) -> Int
4547 f :: (forall a. a -> a) -> Int
4550 g :: (Ord a => a -> a) -> Int
4551 -- MEANS the illegal type
4552 g :: forall a. (Ord a => a -> a) -> Int
4554 g :: (forall a. Ord a => a -> a) -> Int
4556 The latter produces an illegal type, which you might think is silly,
4557 but at least the rule is simple. If you want the latter type, you
4558 can write your for-alls explicitly. Indeed, doing so is strongly advised
4565 <sect2 id="impredicative-polymorphism">
4566 <title>Impredicative polymorphism
4568 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4569 enabled with <option>-XImpredicativeTypes</option>.
4571 that you can call a polymorphic function at a polymorphic type, and
4572 parameterise data structures over polymorphic types. For example:
4574 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4575 f (Just g) = Just (g [3], g "hello")
4578 Notice here that the <literal>Maybe</literal> type is parameterised by the
4579 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4582 <para>The technical details of this extension are described in the paper
4583 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4584 type inference for higher-rank types and impredicativity</ulink>,
4585 which appeared at ICFP 2006.
4589 <sect2 id="scoped-type-variables">
4590 <title>Lexically scoped type variables
4594 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4595 which some type signatures are simply impossible to write. For example:
4597 f :: forall a. [a] -> [a]
4603 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4604 the entire definition of <literal>f</literal>.
4605 In particular, it is in scope at the type signature for <varname>ys</varname>.
4606 In Haskell 98 it is not possible to declare
4607 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4608 it becomes possible to do so.
4610 <para>Lexically-scoped type variables are enabled by
4611 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4613 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4614 variables work, compared to earlier releases. Read this section
4618 <title>Overview</title>
4620 <para>The design follows the following principles
4622 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4623 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4624 design.)</para></listitem>
4625 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4626 type variables. This means that every programmer-written type signature
4627 (including one that contains free scoped type variables) denotes a
4628 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4629 checker, and no inference is involved.</para></listitem>
4630 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4631 changing the program.</para></listitem>
4635 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4637 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4638 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4639 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4640 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4644 In Haskell, a programmer-written type signature is implicitly quantified over
4645 its free type variables (<ulink
4646 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4648 of the Haskell Report).
4649 Lexically scoped type variables affect this implicit quantification rules
4650 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4651 quantified. For example, if type variable <literal>a</literal> is in scope,
4654 (e :: a -> a) means (e :: a -> a)
4655 (e :: b -> b) means (e :: forall b. b->b)
4656 (e :: a -> b) means (e :: forall b. a->b)
4664 <sect3 id="decl-type-sigs">
4665 <title>Declaration type signatures</title>
4666 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4667 quantification (using <literal>forall</literal>) brings into scope the
4668 explicitly-quantified
4669 type variables, in the definition of the named function. For example:
4671 f :: forall a. [a] -> [a]
4672 f (x:xs) = xs ++ [ x :: a ]
4674 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4675 the definition of "<literal>f</literal>".
4677 <para>This only happens if:
4679 <listitem><para> The quantification in <literal>f</literal>'s type
4680 signature is explicit. For example:
4683 g (x:xs) = xs ++ [ x :: a ]
4685 This program will be rejected, because "<literal>a</literal>" does not scope
4686 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4687 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4688 quantification rules.
4690 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4691 not a pattern binding.
4694 f1 :: forall a. [a] -> [a]
4695 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4697 f2 :: forall a. [a] -> [a]
4698 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4700 f3 :: forall a. [a] -> [a]
4701 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4703 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4704 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4705 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4706 the type signature brings <literal>a</literal> into scope.
4712 <sect3 id="exp-type-sigs">
4713 <title>Expression type signatures</title>
4715 <para>An expression type signature that has <emphasis>explicit</emphasis>
4716 quantification (using <literal>forall</literal>) brings into scope the
4717 explicitly-quantified
4718 type variables, in the annotated expression. For example:
4720 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4722 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4723 type variable <literal>s</literal> into scope, in the annotated expression
4724 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4729 <sect3 id="pattern-type-sigs">
4730 <title>Pattern type signatures</title>
4732 A type signature may occur in any pattern; this is a <emphasis>pattern type
4733 signature</emphasis>.
4736 -- f and g assume that 'a' is already in scope
4737 f = \(x::Int, y::a) -> x
4739 h ((x,y) :: (Int,Bool)) = (y,x)
4741 In the case where all the type variables in the pattern type signature are
4742 already in scope (i.e. bound by the enclosing context), matters are simple: the
4743 signature simply constrains the type of the pattern in the obvious way.
4746 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4747 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4748 that are already in scope. For example:
4750 f :: forall a. [a] -> (Int, [a])
4753 (ys::[a], n) = (reverse xs, length xs) -- OK
4754 zs::[a] = xs ++ ys -- OK
4756 Just (v::b) = ... -- Not OK; b is not in scope
4758 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4759 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4763 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4764 type signature may mention a type variable that is not in scope; in this case,
4765 <emphasis>the signature brings that type variable into scope</emphasis>.
4766 This is particularly important for existential data constructors. For example:
4768 data T = forall a. MkT [a]
4771 k (MkT [t::a]) = MkT t3
4775 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4776 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4777 because it is bound by the pattern match. GHC's rule is that in this situation
4778 (and only then), a pattern type signature can mention a type variable that is
4779 not already in scope; the effect is to bring it into scope, standing for the
4780 existentially-bound type variable.
4783 When a pattern type signature binds a type variable in this way, GHC insists that the
4784 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4785 This means that any user-written type signature always stands for a completely known type.
4788 If all this seems a little odd, we think so too. But we must have
4789 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4790 could not name existentially-bound type variables in subsequent type signatures.
4793 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4794 signature is allowed to mention a lexical variable that is not already in
4796 For example, both <literal>f</literal> and <literal>g</literal> would be
4797 illegal if <literal>a</literal> was not already in scope.
4803 <!-- ==================== Commented out part about result type signatures
4805 <sect3 id="result-type-sigs">
4806 <title>Result type signatures</title>
4809 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4812 {- f assumes that 'a' is already in scope -}
4813 f x y :: [a] = [x,y,x]
4815 g = \ x :: [Int] -> [3,4]
4817 h :: forall a. [a] -> a
4821 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4822 the result of the function. Similarly, the body of the lambda in the RHS of
4823 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4824 alternative in <literal>h</literal> is <literal>a</literal>.
4826 <para> A result type signature never brings new type variables into scope.</para>
4828 There are a couple of syntactic wrinkles. First, notice that all three
4829 examples would parse quite differently with parentheses:
4831 {- f assumes that 'a' is already in scope -}
4832 f x (y :: [a]) = [x,y,x]
4834 g = \ (x :: [Int]) -> [3,4]
4836 h :: forall a. [a] -> a
4840 Now the signature is on the <emphasis>pattern</emphasis>; and
4841 <literal>h</literal> would certainly be ill-typed (since the pattern
4842 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4844 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4845 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4846 token or a parenthesised type of some sort). To see why,
4847 consider how one would parse this:
4856 <sect3 id="cls-inst-scoped-tyvars">
4857 <title>Class and instance declarations</title>
4860 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4861 scope over the methods defined in the <literal>where</literal> part. For example:
4879 <sect2 id="typing-binds">
4880 <title>Generalised typing of mutually recursive bindings</title>
4883 The Haskell Report specifies that a group of bindings (at top level, or in a
4884 <literal>let</literal> or <literal>where</literal>) should be sorted into
4885 strongly-connected components, and then type-checked in dependency order
4886 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4887 Report, Section 4.5.1</ulink>).
4888 As each group is type-checked, any binders of the group that
4890 an explicit type signature are put in the type environment with the specified
4892 and all others are monomorphic until the group is generalised
4893 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4896 <para>Following a suggestion of Mark Jones, in his paper
4897 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4899 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4901 <emphasis>the dependency analysis ignores references to variables that have an explicit
4902 type signature</emphasis>.
4903 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4904 typecheck. For example, consider:
4906 f :: Eq a => a -> Bool
4907 f x = (x == x) || g True || g "Yes"
4909 g y = (y <= y) || f True
4911 This is rejected by Haskell 98, but under Jones's scheme the definition for
4912 <literal>g</literal> is typechecked first, separately from that for
4913 <literal>f</literal>,
4914 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4915 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4916 type is generalised, to get
4918 g :: Ord a => a -> Bool
4920 Now, the definition for <literal>f</literal> is typechecked, with this type for
4921 <literal>g</literal> in the type environment.
4925 The same refined dependency analysis also allows the type signatures of
4926 mutually-recursive functions to have different contexts, something that is illegal in
4927 Haskell 98 (Section 4.5.2, last sentence). With
4928 <option>-XRelaxedPolyRec</option>
4929 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4930 type signatures; in practice this means that only variables bound by the same
4931 pattern binding must have the same context. For example, this is fine:
4933 f :: Eq a => a -> Bool
4934 f x = (x == x) || g True
4936 g :: Ord a => a -> Bool
4937 g y = (y <= y) || f True
4942 <sect2 id="type-families">
4943 <title>Type families
4947 GHC supports the definition of type families indexed by types. They may be
4948 seen as an extension of Haskell 98's class-based overloading of values to
4949 types. When type families are declared in classes, they are also known as
4953 There are two forms of type families: data families and type synonym families.
4954 Currently, only the former are fully implemented, while we are still working
4955 on the latter. As a result, the specification of the language extension is
4956 also still to some degree in flux. Hence, a more detailed description of
4957 the language extension and its use is currently available
4958 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4959 wiki page on type families</ulink>. The material will be moved to this user's
4960 guide when it has stabilised.
4963 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4970 <!-- ==================== End of type system extensions ================= -->
4972 <!-- ====================== TEMPLATE HASKELL ======================= -->
4974 <sect1 id="template-haskell">
4975 <title>Template Haskell</title>
4977 <para>Template Haskell allows you to do compile-time meta-programming in
4980 the main technical innovations is discussed in "<ulink
4981 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
4982 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4985 There is a Wiki page about
4986 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
4987 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4991 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4992 Haskell library reference material</ulink>
4993 (look for module <literal>Language.Haskell.TH</literal>).
4994 Many changes to the original design are described in
4995 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4996 Notes on Template Haskell version 2</ulink>.
4997 Not all of these changes are in GHC, however.
5000 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5001 as a worked example to help get you started.
5005 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5006 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5011 <title>Syntax</title>
5013 <para> Template Haskell has the following new syntactic
5014 constructions. You need to use the flag
5015 <option>-XTemplateHaskell</option>
5016 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5017 </indexterm>to switch these syntactic extensions on
5018 (<option>-XTemplateHaskell</option> is no longer implied by
5019 <option>-fglasgow-exts</option>).</para>
5023 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5024 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5025 There must be no space between the "$" and the identifier or parenthesis. This use
5026 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5027 of "." as an infix operator. If you want the infix operator, put spaces around it.
5029 <para> A splice can occur in place of
5031 <listitem><para> an expression; the spliced expression must
5032 have type <literal>Q Exp</literal></para></listitem>
5033 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5036 Inside a splice you can can only call functions defined in imported modules,
5037 not functions defined elsewhere in the same module.</listitem>
5041 A expression quotation is written in Oxford brackets, thus:
5043 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5044 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5045 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5046 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5047 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5048 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5049 </itemizedlist></para></listitem>
5052 A quasi-quotation can appear in either a pattern context or an
5053 expression context and is also written in Oxford brackets:
5055 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5056 where the "..." is an arbitrary string; a full description of the
5057 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5058 </itemizedlist></para></listitem>
5061 A name can be quoted with either one or two prefix single quotes:
5063 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5064 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5065 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5067 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5068 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5071 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5072 may also be given as an argument to the <literal>reify</literal> function.
5078 (Compared to the original paper, there are many differences of detail.
5079 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5080 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5081 Type splices are not implemented, and neither are pattern splices or quotations.
5085 <sect2> <title> Using Template Haskell </title>
5089 The data types and monadic constructor functions for Template Haskell are in the library
5090 <literal>Language.Haskell.THSyntax</literal>.
5094 You can only run a function at compile time if it is imported from another module. That is,
5095 you can't define a function in a module, and call it from within a splice in the same module.
5096 (It would make sense to do so, but it's hard to implement.)
5100 You can only run a function at compile time if it is imported
5101 from another module <emphasis>that is not part of a mutually-recursive group of modules
5102 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5103 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5104 splice is to be run.</para>
5106 For example, when compiling module A,
5107 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5108 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5112 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5115 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5116 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5117 compiles and runs a program, and then looks at the result. So it's important that
5118 the program it compiles produces results whose representations are identical to
5119 those of the compiler itself.
5123 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5124 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5129 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5130 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5131 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5138 -- Import our template "pr"
5139 import Printf ( pr )
5141 -- The splice operator $ takes the Haskell source code
5142 -- generated at compile time by "pr" and splices it into
5143 -- the argument of "putStrLn".
5144 main = putStrLn ( $(pr "Hello") )
5150 -- Skeletal printf from the paper.
5151 -- It needs to be in a separate module to the one where
5152 -- you intend to use it.
5154 -- Import some Template Haskell syntax
5155 import Language.Haskell.TH
5157 -- Describe a format string
5158 data Format = D | S | L String
5160 -- Parse a format string. This is left largely to you
5161 -- as we are here interested in building our first ever
5162 -- Template Haskell program and not in building printf.
5163 parse :: String -> [Format]
5166 -- Generate Haskell source code from a parsed representation
5167 -- of the format string. This code will be spliced into
5168 -- the module which calls "pr", at compile time.
5169 gen :: [Format] -> Q Exp
5170 gen [D] = [| \n -> show n |]
5171 gen [S] = [| \s -> s |]
5172 gen [L s] = stringE s
5174 -- Here we generate the Haskell code for the splice
5175 -- from an input format string.
5176 pr :: String -> Q Exp
5177 pr s = gen (parse s)
5180 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5183 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5186 <para>Run "main.exe" and here is your output:</para>
5196 <title>Using Template Haskell with Profiling</title>
5197 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5199 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5200 interpreter to run the splice expressions. The bytecode interpreter
5201 runs the compiled expression on top of the same runtime on which GHC
5202 itself is running; this means that the compiled code referred to by
5203 the interpreted expression must be compatible with this runtime, and
5204 in particular this means that object code that is compiled for
5205 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5206 expression, because profiled object code is only compatible with the
5207 profiling version of the runtime.</para>
5209 <para>This causes difficulties if you have a multi-module program
5210 containing Template Haskell code and you need to compile it for
5211 profiling, because GHC cannot load the profiled object code and use it
5212 when executing the splices. Fortunately GHC provides a workaround.
5213 The basic idea is to compile the program twice:</para>
5217 <para>Compile the program or library first the normal way, without
5218 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5221 <para>Then compile it again with <option>-prof</option>, and
5222 additionally use <option>-osuf
5223 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5224 to name the object files differently (you can choose any suffix
5225 that isn't the normal object suffix here). GHC will automatically
5226 load the object files built in the first step when executing splice
5227 expressions. If you omit the <option>-osuf</option> flag when
5228 building with <option>-prof</option> and Template Haskell is used,
5229 GHC will emit an error message. </para>
5234 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5235 <para>Quasi-quotation allows patterns and expressions to be written using
5236 programmer-defined concrete syntax; the motivation behind the extension and
5237 several examples are documented in
5238 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5239 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5240 2007). The example below shows how to write a quasiquoter for a simple
5241 expression language.</para>
5244 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5245 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5246 functions for quoting expressions and patterns, respectively. The first argument
5247 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5248 context of the quasi-quotation statement determines which of the two parsers is
5249 called: if the quasi-quotation occurs in an expression context, the expression
5250 parser is called, and if it occurs in a pattern context, the pattern parser is
5254 Note that in the example we make use of an antiquoted
5255 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5256 (this syntax for anti-quotation was defined by the parser's
5257 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5258 integer value argument of the constructor <literal>IntExpr</literal> when
5259 pattern matching. Please see the referenced paper for further details regarding
5260 anti-quotation as well as the description of a technique that uses SYB to
5261 leverage a single parser of type <literal>String -> a</literal> to generate both
5262 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5263 pattern parser that returns a value of type <literal>Q Pat</literal>.
5266 <para>In general, a quasi-quote has the form
5267 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5268 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5269 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5270 can be arbitrary, and may contain newlines.
5273 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5274 the example, <literal>expr</literal> cannot be defined
5275 in <literal>Main.hs</literal> where it is used, but must be imported.
5286 main = do { print $ eval [$expr|1 + 2|]
5288 { [$expr|'int:n|] -> print n
5297 import qualified Language.Haskell.TH as TH
5298 import Language.Haskell.TH.Quasi
5300 data Expr = IntExpr Integer
5301 | AntiIntExpr String
5302 | BinopExpr BinOp Expr Expr
5304 deriving(Show, Typeable, Data)
5310 deriving(Show, Typeable, Data)
5312 eval :: Expr -> Integer
5313 eval (IntExpr n) = n
5314 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5321 expr = QuasiQuoter parseExprExp parseExprPat
5323 -- Parse an Expr, returning its representation as
5324 -- either a Q Exp or a Q Pat. See the referenced paper
5325 -- for how to use SYB to do this by writing a single
5326 -- parser of type String -> Expr instead of two
5327 -- separate parsers.
5329 parseExprExp :: String -> Q Exp
5332 parseExprPat :: String -> Q Pat
5336 <para>Now run the compiler:
5339 $ ghc --make -XQuasiQuotes Main.hs -o main
5342 <para>Run "main" and here is your output:</para>
5354 <!-- ===================== Arrow notation =================== -->
5356 <sect1 id="arrow-notation">
5357 <title>Arrow notation
5360 <para>Arrows are a generalization of monads introduced by John Hughes.
5361 For more details, see
5366 “Generalising Monads to Arrows”,
5367 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5368 pp67–111, May 2000.
5374 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5375 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5381 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5382 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5388 and the arrows web page at
5389 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5390 With the <option>-XArrows</option> flag, GHC supports the arrow
5391 notation described in the second of these papers.
5392 What follows is a brief introduction to the notation;
5393 it won't make much sense unless you've read Hughes's paper.
5394 This notation is translated to ordinary Haskell,
5395 using combinators from the
5396 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5400 <para>The extension adds a new kind of expression for defining arrows:
5402 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5403 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5405 where <literal>proc</literal> is a new keyword.
5406 The variables of the pattern are bound in the body of the
5407 <literal>proc</literal>-expression,
5408 which is a new sort of thing called a <firstterm>command</firstterm>.
5409 The syntax of commands is as follows:
5411 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5412 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5413 | <replaceable>cmd</replaceable><superscript>0</superscript>
5415 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5416 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5417 infix operators as for expressions, and
5419 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5420 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5421 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5422 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5423 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5424 | <replaceable>fcmd</replaceable>
5426 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5427 | ( <replaceable>cmd</replaceable> )
5428 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5430 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5431 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5432 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5433 | <replaceable>cmd</replaceable>
5435 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5436 except that the bodies are commands instead of expressions.
5440 Commands produce values, but (like monadic computations)
5441 may yield more than one value,
5442 or none, and may do other things as well.
5443 For the most part, familiarity with monadic notation is a good guide to
5445 However the values of expressions, even monadic ones,
5446 are determined by the values of the variables they contain;
5447 this is not necessarily the case for commands.
5451 A simple example of the new notation is the expression
5453 proc x -> f -< x+1
5455 We call this a <firstterm>procedure</firstterm> or
5456 <firstterm>arrow abstraction</firstterm>.
5457 As with a lambda expression, the variable <literal>x</literal>
5458 is a new variable bound within the <literal>proc</literal>-expression.
5459 It refers to the input to the arrow.
5460 In the above example, <literal>-<</literal> is not an identifier but an
5461 new reserved symbol used for building commands from an expression of arrow
5462 type and an expression to be fed as input to that arrow.
5463 (The weird look will make more sense later.)
5464 It may be read as analogue of application for arrows.
5465 The above example is equivalent to the Haskell expression
5467 arr (\ x -> x+1) >>> f
5469 That would make no sense if the expression to the left of
5470 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5471 More generally, the expression to the left of <literal>-<</literal>
5472 may not involve any <firstterm>local variable</firstterm>,
5473 i.e. a variable bound in the current arrow abstraction.
5474 For such a situation there is a variant <literal>-<<</literal>, as in
5476 proc x -> f x -<< x+1
5478 which is equivalent to
5480 arr (\ x -> (f x, x+1)) >>> app
5482 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5484 Such an arrow is equivalent to a monad, so if you're using this form
5485 you may find a monadic formulation more convenient.
5489 <title>do-notation for commands</title>
5492 Another form of command is a form of <literal>do</literal>-notation.
5493 For example, you can write
5502 You can read this much like ordinary <literal>do</literal>-notation,
5503 but with commands in place of monadic expressions.
5504 The first line sends the value of <literal>x+1</literal> as an input to
5505 the arrow <literal>f</literal>, and matches its output against
5506 <literal>y</literal>.
5507 In the next line, the output is discarded.
5508 The arrow <function>returnA</function> is defined in the
5509 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5510 module as <literal>arr id</literal>.
5511 The above example is treated as an abbreviation for
5513 arr (\ x -> (x, x)) >>>
5514 first (arr (\ x -> x+1) >>> f) >>>
5515 arr (\ (y, x) -> (y, (x, y))) >>>
5516 first (arr (\ y -> 2*y) >>> g) >>>
5518 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5519 first (arr (\ (x, z) -> x*z) >>> h) >>>
5520 arr (\ (t, z) -> t+z) >>>
5523 Note that variables not used later in the composition are projected out.
5524 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5526 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5527 module, this reduces to
5529 arr (\ x -> (x+1, x)) >>>
5531 arr (\ (y, x) -> (2*y, (x, y))) >>>
5533 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5535 arr (\ (t, z) -> t+z)
5537 which is what you might have written by hand.
5538 With arrow notation, GHC keeps track of all those tuples of variables for you.
5542 Note that although the above translation suggests that
5543 <literal>let</literal>-bound variables like <literal>z</literal> must be
5544 monomorphic, the actual translation produces Core,
5545 so polymorphic variables are allowed.
5549 It's also possible to have mutually recursive bindings,
5550 using the new <literal>rec</literal> keyword, as in the following example:
5552 counter :: ArrowCircuit a => a Bool Int
5553 counter = proc reset -> do
5554 rec output <- returnA -< if reset then 0 else next
5555 next <- delay 0 -< output+1
5556 returnA -< output
5558 The translation of such forms uses the <function>loop</function> combinator,
5559 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5565 <title>Conditional commands</title>
5568 In the previous example, we used a conditional expression to construct the
5570 Sometimes we want to conditionally execute different commands, as in
5577 which is translated to
5579 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5580 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5582 Since the translation uses <function>|||</function>,
5583 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5587 There are also <literal>case</literal> commands, like
5593 y <- h -< (x1, x2)
5597 The syntax is the same as for <literal>case</literal> expressions,
5598 except that the bodies of the alternatives are commands rather than expressions.
5599 The translation is similar to that of <literal>if</literal> commands.
5605 <title>Defining your own control structures</title>
5608 As we're seen, arrow notation provides constructs,
5609 modelled on those for expressions,
5610 for sequencing, value recursion and conditionals.
5611 But suitable combinators,
5612 which you can define in ordinary Haskell,
5613 may also be used to build new commands out of existing ones.
5614 The basic idea is that a command defines an arrow from environments to values.
5615 These environments assign values to the free local variables of the command.
5616 Thus combinators that produce arrows from arrows
5617 may also be used to build commands from commands.
5618 For example, the <literal>ArrowChoice</literal> class includes a combinator
5620 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5622 so we can use it to build commands:
5624 expr' = proc x -> do
5627 symbol Plus -< ()
5628 y <- term -< ()
5631 symbol Minus -< ()
5632 y <- term -< ()
5635 (The <literal>do</literal> on the first line is needed to prevent the first
5636 <literal><+> ...</literal> from being interpreted as part of the
5637 expression on the previous line.)
5638 This is equivalent to
5640 expr' = (proc x -> returnA -< x)
5641 <+> (proc x -> do
5642 symbol Plus -< ()
5643 y <- term -< ()
5645 <+> (proc x -> do
5646 symbol Minus -< ()
5647 y <- term -< ()
5650 It is essential that this operator be polymorphic in <literal>e</literal>
5651 (representing the environment input to the command
5652 and thence to its subcommands)
5653 and satisfy the corresponding naturality property
5655 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5657 at least for strict <literal>k</literal>.
5658 (This should be automatic if you're not using <function>seq</function>.)
5659 This ensures that environments seen by the subcommands are environments
5660 of the whole command,
5661 and also allows the translation to safely trim these environments.
5662 The operator must also not use any variable defined within the current
5667 We could define our own operator
5669 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5670 untilA body cond = proc x ->
5671 if cond x then returnA -< ()
5674 untilA body cond -< x
5676 and use it in the same way.
5677 Of course this infix syntax only makes sense for binary operators;
5678 there is also a more general syntax involving special brackets:
5682 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5689 <title>Primitive constructs</title>
5692 Some operators will need to pass additional inputs to their subcommands.
5693 For example, in an arrow type supporting exceptions,
5694 the operator that attaches an exception handler will wish to pass the
5695 exception that occurred to the handler.
5696 Such an operator might have a type
5698 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5700 where <literal>Ex</literal> is the type of exceptions handled.
5701 You could then use this with arrow notation by writing a command
5703 body `handleA` \ ex -> handler
5705 so that if an exception is raised in the command <literal>body</literal>,
5706 the variable <literal>ex</literal> is bound to the value of the exception
5707 and the command <literal>handler</literal>,
5708 which typically refers to <literal>ex</literal>, is entered.
5709 Though the syntax here looks like a functional lambda,
5710 we are talking about commands, and something different is going on.
5711 The input to the arrow represented by a command consists of values for
5712 the free local variables in the command, plus a stack of anonymous values.
5713 In all the prior examples, this stack was empty.
5714 In the second argument to <function>handleA</function>,
5715 this stack consists of one value, the value of the exception.
5716 The command form of lambda merely gives this value a name.
5721 the values on the stack are paired to the right of the environment.
5722 So operators like <function>handleA</function> that pass
5723 extra inputs to their subcommands can be designed for use with the notation
5724 by pairing the values with the environment in this way.
5725 More precisely, the type of each argument of the operator (and its result)
5726 should have the form
5728 a (...(e,t1), ... tn) t
5730 where <replaceable>e</replaceable> is a polymorphic variable
5731 (representing the environment)
5732 and <replaceable>ti</replaceable> are the types of the values on the stack,
5733 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5734 The polymorphic variable <replaceable>e</replaceable> must not occur in
5735 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5736 <replaceable>t</replaceable>.
5737 However the arrows involved need not be the same.
5738 Here are some more examples of suitable operators:
5740 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5741 runReader :: ... => a e c -> a' (e,State) c
5742 runState :: ... => a e c -> a' (e,State) (c,State)
5744 We can supply the extra input required by commands built with the last two
5745 by applying them to ordinary expressions, as in
5749 (|runReader (do { ... })|) s
5751 which adds <literal>s</literal> to the stack of inputs to the command
5752 built using <function>runReader</function>.
5756 The command versions of lambda abstraction and application are analogous to
5757 the expression versions.
5758 In particular, the beta and eta rules describe equivalences of commands.
5759 These three features (operators, lambda abstraction and application)
5760 are the core of the notation; everything else can be built using them,
5761 though the results would be somewhat clumsy.
5762 For example, we could simulate <literal>do</literal>-notation by defining
5764 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5765 u `bind` f = returnA &&& u >>> f
5767 bind_ :: Arrow a => a e b -> a e c -> a e c
5768 u `bind_` f = u `bind` (arr fst >>> f)
5770 We could simulate <literal>if</literal> by defining
5772 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5773 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5780 <title>Differences with the paper</title>
5785 <para>Instead of a single form of arrow application (arrow tail) with two
5786 translations, the implementation provides two forms
5787 <quote><literal>-<</literal></quote> (first-order)
5788 and <quote><literal>-<<</literal></quote> (higher-order).
5793 <para>User-defined operators are flagged with banana brackets instead of
5794 a new <literal>form</literal> keyword.
5803 <title>Portability</title>
5806 Although only GHC implements arrow notation directly,
5807 there is also a preprocessor
5809 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5810 that translates arrow notation into Haskell 98
5811 for use with other Haskell systems.
5812 You would still want to check arrow programs with GHC;
5813 tracing type errors in the preprocessor output is not easy.
5814 Modules intended for both GHC and the preprocessor must observe some
5815 additional restrictions:
5820 The module must import
5821 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5827 The preprocessor cannot cope with other Haskell extensions.
5828 These would have to go in separate modules.
5834 Because the preprocessor targets Haskell (rather than Core),
5835 <literal>let</literal>-bound variables are monomorphic.
5846 <!-- ==================== BANG PATTERNS ================= -->
5848 <sect1 id="bang-patterns">
5849 <title>Bang patterns
5850 <indexterm><primary>Bang patterns</primary></indexterm>
5852 <para>GHC supports an extension of pattern matching called <emphasis>bang
5853 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5855 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5856 prime feature description</ulink> contains more discussion and examples
5857 than the material below.
5860 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5863 <sect2 id="bang-patterns-informal">
5864 <title>Informal description of bang patterns
5867 The main idea is to add a single new production to the syntax of patterns:
5871 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5872 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5877 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5878 whereas without the bang it would be lazy.
5879 Bang patterns can be nested of course:
5883 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5884 <literal>y</literal>.
5885 A bang only really has an effect if it precedes a variable or wild-card pattern:
5890 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5891 forces evaluation anyway does nothing.
5893 Bang patterns work in <literal>case</literal> expressions too, of course:
5895 g5 x = let y = f x in body
5896 g6 x = case f x of { y -> body }
5897 g7 x = case f x of { !y -> body }
5899 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5900 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5901 result, and then evaluates <literal>body</literal>.
5903 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5904 definitions too. For example:
5908 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5909 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5910 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5911 in a function argument <literal>![x,y]</literal> means the
5912 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5913 is part of the syntax of <literal>let</literal> bindings.
5918 <sect2 id="bang-patterns-sem">
5919 <title>Syntax and semantics
5923 We add a single new production to the syntax of patterns:
5927 There is one problem with syntactic ambiguity. Consider:
5931 Is this a definition of the infix function "<literal>(!)</literal>",
5932 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5933 ambiguity in favour of the latter. If you want to define
5934 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5939 The semantics of Haskell pattern matching is described in <ulink
5940 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5941 Section 3.17.2</ulink> of the Haskell Report. To this description add
5942 one extra item 10, saying:
5943 <itemizedlist><listitem><para>Matching
5944 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5945 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5946 <listitem><para>otherwise, <literal>pat</literal> is matched against
5947 <literal>v</literal></para></listitem>
5949 </para></listitem></itemizedlist>
5950 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5951 Section 3.17.3</ulink>, add a new case (t):
5953 case v of { !pat -> e; _ -> e' }
5954 = v `seq` case v of { pat -> e; _ -> e' }
5957 That leaves let expressions, whose translation is given in
5958 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5960 of the Haskell Report.
5961 In the translation box, first apply
5962 the following transformation: for each pattern <literal>pi</literal> that is of
5963 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5964 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5965 have a bang at the top, apply the rules in the existing box.
5967 <para>The effect of the let rule is to force complete matching of the pattern
5968 <literal>qi</literal> before evaluation of the body is begun. The bang is
5969 retained in the translated form in case <literal>qi</literal> is a variable,
5977 The let-binding can be recursive. However, it is much more common for
5978 the let-binding to be non-recursive, in which case the following law holds:
5979 <literal>(let !p = rhs in body)</literal>
5981 <literal>(case rhs of !p -> body)</literal>
5984 A pattern with a bang at the outermost level is not allowed at the top level of
5990 <!-- ==================== ASSERTIONS ================= -->
5992 <sect1 id="assertions">
5994 <indexterm><primary>Assertions</primary></indexterm>
5998 If you want to make use of assertions in your standard Haskell code, you
5999 could define a function like the following:
6005 assert :: Bool -> a -> a
6006 assert False x = error "assertion failed!"
6013 which works, but gives you back a less than useful error message --
6014 an assertion failed, but which and where?
6018 One way out is to define an extended <function>assert</function> function which also
6019 takes a descriptive string to include in the error message and
6020 perhaps combine this with the use of a pre-processor which inserts
6021 the source location where <function>assert</function> was used.
6025 Ghc offers a helping hand here, doing all of this for you. For every
6026 use of <function>assert</function> in the user's source:
6032 kelvinToC :: Double -> Double
6033 kelvinToC k = assert (k >= 0.0) (k+273.15)
6039 Ghc will rewrite this to also include the source location where the
6046 assert pred val ==> assertError "Main.hs|15" pred val
6052 The rewrite is only performed by the compiler when it spots
6053 applications of <function>Control.Exception.assert</function>, so you
6054 can still define and use your own versions of
6055 <function>assert</function>, should you so wish. If not, import
6056 <literal>Control.Exception</literal> to make use
6057 <function>assert</function> in your code.
6061 GHC ignores assertions when optimisation is turned on with the
6062 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6063 <literal>assert pred e</literal> will be rewritten to
6064 <literal>e</literal>. You can also disable assertions using the
6065 <option>-fignore-asserts</option>
6066 option<indexterm><primary><option>-fignore-asserts</option></primary>
6067 </indexterm>.</para>
6070 Assertion failures can be caught, see the documentation for the
6071 <literal>Control.Exception</literal> library for the details.
6077 <!-- =============================== PRAGMAS =========================== -->
6079 <sect1 id="pragmas">
6080 <title>Pragmas</title>
6082 <indexterm><primary>pragma</primary></indexterm>
6084 <para>GHC supports several pragmas, or instructions to the
6085 compiler placed in the source code. Pragmas don't normally affect
6086 the meaning of the program, but they might affect the efficiency
6087 of the generated code.</para>
6089 <para>Pragmas all take the form
6091 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6093 where <replaceable>word</replaceable> indicates the type of
6094 pragma, and is followed optionally by information specific to that
6095 type of pragma. Case is ignored in
6096 <replaceable>word</replaceable>. The various values for
6097 <replaceable>word</replaceable> that GHC understands are described
6098 in the following sections; any pragma encountered with an
6099 unrecognised <replaceable>word</replaceable> is (silently)
6100 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6101 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6103 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6104 pragma must precede the <literal>module</literal> keyword in the file.
6105 There can be as many file-header pragmas as you please, and they can be
6106 preceded or followed by comments.</para>
6108 <sect2 id="language-pragma">
6109 <title>LANGUAGE pragma</title>
6111 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6112 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6114 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6116 It is the intention that all Haskell compilers support the
6117 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6118 all extensions are supported by all compilers, of
6119 course. The <literal>LANGUAGE</literal> pragma should be used instead
6120 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6122 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6124 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6126 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6128 <para>Every language extension can also be turned into a command-line flag
6129 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6130 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6133 <para>A list of all supported language extensions can be obtained by invoking
6134 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6136 <para>Any extension from the <literal>Extension</literal> type defined in
6138 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6139 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6143 <sect2 id="options-pragma">
6144 <title>OPTIONS_GHC pragma</title>
6145 <indexterm><primary>OPTIONS_GHC</primary>
6147 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6150 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6151 additional options that are given to the compiler when compiling
6152 this source file. See <xref linkend="source-file-options"/> for
6155 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6156 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6159 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6161 <sect2 id="include-pragma">
6162 <title>INCLUDE pragma</title>
6164 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6165 of C header files that should be <literal>#include</literal>'d into
6166 the C source code generated by the compiler for the current module (if
6167 compiling via C). For example:</para>
6170 {-# INCLUDE "foo.h" #-}
6171 {-# INCLUDE <stdio.h> #-}</programlisting>
6173 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6175 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6176 to the <option>-#include</option> option (<xref
6177 linkend="options-C-compiler" />), because the
6178 <literal>INCLUDE</literal> pragma is understood by other
6179 compilers. Yet another alternative is to add the include file to each
6180 <literal>foreign import</literal> declaration in your code, but we
6181 don't recommend using this approach with GHC.</para>
6184 <sect2 id="warning-deprecated-pragma">
6185 <title>WARNING and DEPRECATED pragmas</title>
6186 <indexterm><primary>WARNING</primary></indexterm>
6187 <indexterm><primary>DEPRECATED</primary></indexterm>
6189 <para>The WARNING pragma allows you to attach an arbitrary warning
6190 to a particular function, class, or type.
6191 A DEPRECATED pragma lets you specify that
6192 a particular function, class, or type is deprecated.
6193 There are two ways of using these pragmas.
6197 <para>You can work on an entire module thus:</para>
6199 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6204 module Wibble {-# WARNING "This is an unstable interface." #-} where
6207 <para>When you compile any module that import
6208 <literal>Wibble</literal>, GHC will print the specified
6213 <para>You can attach a warning to a function, class, type, or data constructor, with the
6214 following top-level declarations:</para>
6216 {-# DEPRECATED f, C, T "Don't use these" #-}
6217 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6219 <para>When you compile any module that imports and uses any
6220 of the specified entities, GHC will print the specified
6222 <para> You can only attach to entities declared at top level in the module
6223 being compiled, and you can only use unqualified names in the list of
6224 entities. A capitalised name, such as <literal>T</literal>
6225 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6226 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6227 both are in scope. If both are in scope, there is currently no way to
6228 specify one without the other (c.f. fixities
6229 <xref linkend="infix-tycons"/>).</para>
6232 Warnings and deprecations are not reported for
6233 (a) uses within the defining module, and
6234 (b) uses in an export list.
6235 The latter reduces spurious complaints within a library
6236 in which one module gathers together and re-exports
6237 the exports of several others.
6239 <para>You can suppress the warnings with the flag
6240 <option>-fno-warn-warnings-deprecations</option>.</para>
6243 <sect2 id="inline-noinline-pragma">
6244 <title>INLINE and NOINLINE pragmas</title>
6246 <para>These pragmas control the inlining of function
6249 <sect3 id="inline-pragma">
6250 <title>INLINE pragma</title>
6251 <indexterm><primary>INLINE</primary></indexterm>
6253 <para>GHC (with <option>-O</option>, as always) tries to
6254 inline (or “unfold”) functions/values that are
6255 “small enough,” thus avoiding the call overhead
6256 and possibly exposing other more-wonderful optimisations.
6257 Normally, if GHC decides a function is “too
6258 expensive” to inline, it will not do so, nor will it
6259 export that unfolding for other modules to use.</para>
6261 <para>The sledgehammer you can bring to bear is the
6262 <literal>INLINE</literal><indexterm><primary>INLINE
6263 pragma</primary></indexterm> pragma, used thusly:</para>
6266 key_function :: Int -> String -> (Bool, Double)
6267 {-# INLINE key_function #-}
6270 <para>The major effect of an <literal>INLINE</literal> pragma
6271 is to declare a function's “cost” to be very low.
6272 The normal unfolding machinery will then be very keen to
6273 inline it. However, an <literal>INLINE</literal> pragma for a
6274 function "<literal>f</literal>" has a number of other effects:
6277 No functions are inlined into <literal>f</literal>. Otherwise
6278 GHC might inline a big function into <literal>f</literal>'s right hand side,
6279 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6282 The float-in, float-out, and common-sub-expression transformations are not
6283 applied to the body of <literal>f</literal>.
6286 An INLINE function is not worker/wrappered by strictness analysis.
6287 It's going to be inlined wholesale instead.
6290 All of these effects are aimed at ensuring that what gets inlined is
6291 exactly what you asked for, no more and no less.
6293 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6294 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6295 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6296 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6297 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6298 when there is no choice even an INLINE function can be selected, in which case
6299 the INLINE pragma is ignored.
6300 For example, for a self-recursive function, the loop breaker can only be the function
6301 itself, so an INLINE pragma is always ignored.</para>
6303 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6304 function can be put anywhere its type signature could be
6307 <para><literal>INLINE</literal> pragmas are a particularly
6309 <literal>then</literal>/<literal>return</literal> (or
6310 <literal>bind</literal>/<literal>unit</literal>) functions in
6311 a monad. For example, in GHC's own
6312 <literal>UniqueSupply</literal> monad code, we have:</para>
6315 {-# INLINE thenUs #-}
6316 {-# INLINE returnUs #-}
6319 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6320 linkend="noinline-pragma"/>).</para>
6322 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6323 so if you want your code to be HBC-compatible you'll have to surround
6324 the pragma with C pre-processor directives
6325 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6329 <sect3 id="noinline-pragma">
6330 <title>NOINLINE pragma</title>
6332 <indexterm><primary>NOINLINE</primary></indexterm>
6333 <indexterm><primary>NOTINLINE</primary></indexterm>
6335 <para>The <literal>NOINLINE</literal> pragma does exactly what
6336 you'd expect: it stops the named function from being inlined
6337 by the compiler. You shouldn't ever need to do this, unless
6338 you're very cautious about code size.</para>
6340 <para><literal>NOTINLINE</literal> is a synonym for
6341 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6342 specified by Haskell 98 as the standard way to disable
6343 inlining, so it should be used if you want your code to be
6347 <sect3 id="phase-control">
6348 <title>Phase control</title>
6350 <para> Sometimes you want to control exactly when in GHC's
6351 pipeline the INLINE pragma is switched on. Inlining happens
6352 only during runs of the <emphasis>simplifier</emphasis>. Each
6353 run of the simplifier has a different <emphasis>phase
6354 number</emphasis>; the phase number decreases towards zero.
6355 If you use <option>-dverbose-core2core</option> you'll see the
6356 sequence of phase numbers for successive runs of the
6357 simplifier. In an INLINE pragma you can optionally specify a
6361 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6362 <literal>f</literal>
6363 until phase <literal>k</literal>, but from phase
6364 <literal>k</literal> onwards be very keen to inline it.
6367 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6368 <literal>f</literal>
6369 until phase <literal>k</literal>, but from phase
6370 <literal>k</literal> onwards do not inline it.
6373 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6374 <literal>f</literal>
6375 until phase <literal>k</literal>, but from phase
6376 <literal>k</literal> onwards be willing to inline it (as if
6377 there was no pragma).
6380 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6381 <literal>f</literal>
6382 until phase <literal>k</literal>, but from phase
6383 <literal>k</literal> onwards do not inline it.
6386 The same information is summarised here:
6388 -- Before phase 2 Phase 2 and later
6389 {-# INLINE [2] f #-} -- No Yes
6390 {-# INLINE [~2] f #-} -- Yes No
6391 {-# NOINLINE [2] f #-} -- No Maybe
6392 {-# NOINLINE [~2] f #-} -- Maybe No
6394 {-# INLINE f #-} -- Yes Yes
6395 {-# NOINLINE f #-} -- No No
6397 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6398 function body is small, or it is applied to interesting-looking arguments etc).
6399 Another way to understand the semantics is this:
6401 <listitem><para>For both INLINE and NOINLINE, the phase number says
6402 when inlining is allowed at all.</para></listitem>
6403 <listitem><para>The INLINE pragma has the additional effect of making the
6404 function body look small, so that when inlining is allowed it is very likely to
6409 <para>The same phase-numbering control is available for RULES
6410 (<xref linkend="rewrite-rules"/>).</para>
6414 <sect2 id="line-pragma">
6415 <title>LINE pragma</title>
6417 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6418 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6419 <para>This pragma is similar to C's <literal>#line</literal>
6420 pragma, and is mainly for use in automatically generated Haskell
6421 code. It lets you specify the line number and filename of the
6422 original code; for example</para>
6424 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6426 <para>if you'd generated the current file from something called
6427 <filename>Foo.vhs</filename> and this line corresponds to line
6428 42 in the original. GHC will adjust its error messages to refer
6429 to the line/file named in the <literal>LINE</literal>
6434 <title>RULES pragma</title>
6436 <para>The RULES pragma lets you specify rewrite rules. It is
6437 described in <xref linkend="rewrite-rules"/>.</para>
6440 <sect2 id="specialize-pragma">
6441 <title>SPECIALIZE pragma</title>
6443 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6444 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6445 <indexterm><primary>overloading, death to</primary></indexterm>
6447 <para>(UK spelling also accepted.) For key overloaded
6448 functions, you can create extra versions (NB: more code space)
6449 specialised to particular types. Thus, if you have an
6450 overloaded function:</para>
6453 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6456 <para>If it is heavily used on lists with
6457 <literal>Widget</literal> keys, you could specialise it as
6461 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6464 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6465 be put anywhere its type signature could be put.</para>
6467 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6468 (a) a specialised version of the function and (b) a rewrite rule
6469 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6470 un-specialised function into a call to the specialised one.</para>
6472 <para>The type in a SPECIALIZE pragma can be any type that is less
6473 polymorphic than the type of the original function. In concrete terms,
6474 if the original function is <literal>f</literal> then the pragma
6476 {-# SPECIALIZE f :: <type> #-}
6478 is valid if and only if the definition
6480 f_spec :: <type>
6483 is valid. Here are some examples (where we only give the type signature
6484 for the original function, not its code):
6486 f :: Eq a => a -> b -> b
6487 {-# SPECIALISE f :: Int -> b -> b #-}
6489 g :: (Eq a, Ix b) => a -> b -> b
6490 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6492 h :: Eq a => a -> a -> a
6493 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6495 The last of these examples will generate a
6496 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6497 well. If you use this kind of specialisation, let us know how well it works.
6500 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6501 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6502 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6503 The <literal>INLINE</literal> pragma affects the specialised version of the
6504 function (only), and applies even if the function is recursive. The motivating
6507 -- A GADT for arrays with type-indexed representation
6509 ArrInt :: !Int -> ByteArray# -> Arr Int
6510 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6512 (!:) :: Arr e -> Int -> e
6513 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6514 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6515 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6516 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6518 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6519 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6520 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6521 the specialised function will be inlined. It has two calls to
6522 <literal>(!:)</literal>,
6523 both at type <literal>Int</literal>. Both these calls fire the first
6524 specialisation, whose body is also inlined. The result is a type-based
6525 unrolling of the indexing function.</para>
6526 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6527 on an ordinarily-recursive function.</para>
6529 <para>Note: In earlier versions of GHC, it was possible to provide your own
6530 specialised function for a given type:
6533 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6536 This feature has been removed, as it is now subsumed by the
6537 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6541 <sect2 id="specialize-instance-pragma">
6542 <title>SPECIALIZE instance pragma
6546 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6547 <indexterm><primary>overloading, death to</primary></indexterm>
6548 Same idea, except for instance declarations. For example:
6551 instance (Eq a) => Eq (Foo a) where {
6552 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6556 The pragma must occur inside the <literal>where</literal> part
6557 of the instance declaration.
6560 Compatible with HBC, by the way, except perhaps in the placement
6566 <sect2 id="unpack-pragma">
6567 <title>UNPACK pragma</title>
6569 <indexterm><primary>UNPACK</primary></indexterm>
6571 <para>The <literal>UNPACK</literal> indicates to the compiler
6572 that it should unpack the contents of a constructor field into
6573 the constructor itself, removing a level of indirection. For
6577 data T = T {-# UNPACK #-} !Float
6578 {-# UNPACK #-} !Float
6581 <para>will create a constructor <literal>T</literal> containing
6582 two unboxed floats. This may not always be an optimisation: if
6583 the <function>T</function> constructor is scrutinised and the
6584 floats passed to a non-strict function for example, they will
6585 have to be reboxed (this is done automatically by the
6588 <para>Unpacking constructor fields should only be used in
6589 conjunction with <option>-O</option>, in order to expose
6590 unfoldings to the compiler so the reboxing can be removed as
6591 often as possible. For example:</para>
6595 f (T f1 f2) = f1 + f2
6598 <para>The compiler will avoid reboxing <function>f1</function>
6599 and <function>f2</function> by inlining <function>+</function>
6600 on floats, but only when <option>-O</option> is on.</para>
6602 <para>Any single-constructor data is eligible for unpacking; for
6606 data T = T {-# UNPACK #-} !(Int,Int)
6609 <para>will store the two <literal>Int</literal>s directly in the
6610 <function>T</function> constructor, by flattening the pair.
6611 Multi-level unpacking is also supported:
6614 data T = T {-# UNPACK #-} !S
6615 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6618 will store two unboxed <literal>Int#</literal>s
6619 directly in the <function>T</function> constructor. The
6620 unpacker can see through newtypes, too.</para>
6622 <para>If a field cannot be unpacked, you will not get a warning,
6623 so it might be an idea to check the generated code with
6624 <option>-ddump-simpl</option>.</para>
6626 <para>See also the <option>-funbox-strict-fields</option> flag,
6627 which essentially has the effect of adding
6628 <literal>{-# UNPACK #-}</literal> to every strict
6629 constructor field.</para>
6632 <sect2 id="source-pragma">
6633 <title>SOURCE pragma</title>
6635 <indexterm><primary>SOURCE</primary></indexterm>
6636 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6637 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6643 <!-- ======================= REWRITE RULES ======================== -->
6645 <sect1 id="rewrite-rules">
6646 <title>Rewrite rules
6648 <indexterm><primary>RULES pragma</primary></indexterm>
6649 <indexterm><primary>pragma, RULES</primary></indexterm>
6650 <indexterm><primary>rewrite rules</primary></indexterm></title>
6653 The programmer can specify rewrite rules as part of the source program
6654 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6655 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6656 and (b) the <option>-fno-rewrite-rules</option> flag
6657 (<xref linkend="options-f"/>) is not specified, and (c) the
6658 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6667 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6672 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6673 If you need more information, then <option>-ddump-rule-firings</option> shows you
6674 each individual rule firing in detail.
6678 <title>Syntax</title>
6681 From a syntactic point of view:
6687 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6688 may be generated by the layout rule).
6694 The layout rule applies in a pragma.
6695 Currently no new indentation level
6696 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6697 you must lay out the starting in the same column as the enclosing definitions.
6700 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6701 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6704 Furthermore, the closing <literal>#-}</literal>
6705 should start in a column to the right of the opening <literal>{-#</literal>.
6711 Each rule has a name, enclosed in double quotes. The name itself has
6712 no significance at all. It is only used when reporting how many times the rule fired.
6718 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6719 immediately after the name of the rule. Thus:
6722 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6725 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6726 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6735 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6736 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6737 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6738 by spaces, just like in a type <literal>forall</literal>.
6744 A pattern variable may optionally have a type signature.
6745 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6746 For example, here is the <literal>foldr/build</literal> rule:
6749 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6750 foldr k z (build g) = g k z
6753 Since <function>g</function> has a polymorphic type, it must have a type signature.
6760 The left hand side of a rule must consist of a top-level variable applied
6761 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6764 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6765 "wrong2" forall f. f True = True
6768 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6775 A rule does not need to be in the same module as (any of) the
6776 variables it mentions, though of course they need to be in scope.
6782 Rules are automatically exported from a module, just as instance declarations are.
6793 <title>Semantics</title>
6796 From a semantic point of view:
6802 Rules are only applied if you use the <option>-O</option> flag.
6808 Rules are regarded as left-to-right rewrite rules.
6809 When GHC finds an expression that is a substitution instance of the LHS
6810 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6811 By "a substitution instance" we mean that the LHS can be made equal to the
6812 expression by substituting for the pattern variables.
6819 The LHS and RHS of a rule are typechecked, and must have the
6827 GHC makes absolutely no attempt to verify that the LHS and RHS
6828 of a rule have the same meaning. That is undecidable in general, and
6829 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6836 GHC makes no attempt to make sure that the rules are confluent or
6837 terminating. For example:
6840 "loop" forall x y. f x y = f y x
6843 This rule will cause the compiler to go into an infinite loop.
6850 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6856 GHC currently uses a very simple, syntactic, matching algorithm
6857 for matching a rule LHS with an expression. It seeks a substitution
6858 which makes the LHS and expression syntactically equal modulo alpha
6859 conversion. The pattern (rule), but not the expression, is eta-expanded if
6860 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6861 But not beta conversion (that's called higher-order matching).
6865 Matching is carried out on GHC's intermediate language, which includes
6866 type abstractions and applications. So a rule only matches if the
6867 types match too. See <xref linkend="rule-spec"/> below.
6873 GHC keeps trying to apply the rules as it optimises the program.
6874 For example, consider:
6883 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6884 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6885 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6886 not be substituted, and the rule would not fire.
6893 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6894 results. Consider this (artificial) example
6897 {-# RULES "f" f True = False #-}
6903 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
6908 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
6910 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
6911 would have been a better chance that <literal>f</literal>'s RULE might fire.
6914 The way to get predictable behaviour is to use a NOINLINE
6915 pragma on <literal>f</literal>, to ensure
6916 that it is not inlined until its RULEs have had a chance to fire.
6922 All rules are implicitly exported from the module, and are therefore
6923 in force in any module that imports the module that defined the rule, directly
6924 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6925 in force when compiling A.) The situation is very similar to that for instance
6937 <title>List fusion</title>
6940 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6941 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6942 intermediate list should be eliminated entirely.
6946 The following are good producers:
6958 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6964 Explicit lists (e.g. <literal>[True, False]</literal>)
6970 The cons constructor (e.g <literal>3:4:[]</literal>)
6976 <function>++</function>
6982 <function>map</function>
6988 <function>take</function>, <function>filter</function>
6994 <function>iterate</function>, <function>repeat</function>
7000 <function>zip</function>, <function>zipWith</function>
7009 The following are good consumers:
7021 <function>array</function> (on its second argument)
7027 <function>++</function> (on its first argument)
7033 <function>foldr</function>
7039 <function>map</function>
7045 <function>take</function>, <function>filter</function>
7051 <function>concat</function>
7057 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7063 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7064 will fuse with one but not the other)
7070 <function>partition</function>
7076 <function>head</function>
7082 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7088 <function>sequence_</function>
7094 <function>msum</function>
7100 <function>sortBy</function>
7109 So, for example, the following should generate no intermediate lists:
7112 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7118 This list could readily be extended; if there are Prelude functions that you use
7119 a lot which are not included, please tell us.
7123 If you want to write your own good consumers or producers, look at the
7124 Prelude definitions of the above functions to see how to do so.
7129 <sect2 id="rule-spec">
7130 <title>Specialisation
7134 Rewrite rules can be used to get the same effect as a feature
7135 present in earlier versions of GHC.
7136 For example, suppose that:
7139 genericLookup :: Ord a => Table a b -> a -> b
7140 intLookup :: Table Int b -> Int -> b
7143 where <function>intLookup</function> is an implementation of
7144 <function>genericLookup</function> that works very fast for
7145 keys of type <literal>Int</literal>. You might wish
7146 to tell GHC to use <function>intLookup</function> instead of
7147 <function>genericLookup</function> whenever the latter was called with
7148 type <literal>Table Int b -> Int -> b</literal>.
7149 It used to be possible to write
7152 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7155 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7158 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7161 This slightly odd-looking rule instructs GHC to replace
7162 <function>genericLookup</function> by <function>intLookup</function>
7163 <emphasis>whenever the types match</emphasis>.
7164 What is more, this rule does not need to be in the same
7165 file as <function>genericLookup</function>, unlike the
7166 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7167 have an original definition available to specialise).
7170 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7171 <function>intLookup</function> really behaves as a specialised version
7172 of <function>genericLookup</function>!!!</para>
7174 <para>An example in which using <literal>RULES</literal> for
7175 specialisation will Win Big:
7178 toDouble :: Real a => a -> Double
7179 toDouble = fromRational . toRational
7181 {-# RULES "toDouble/Int" toDouble = i2d #-}
7182 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7185 The <function>i2d</function> function is virtually one machine
7186 instruction; the default conversion—via an intermediate
7187 <literal>Rational</literal>—is obscenely expensive by
7194 <title>Controlling what's going on</title>
7202 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7208 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7209 If you add <option>-dppr-debug</option> you get a more detailed listing.
7215 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7218 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7219 {-# INLINE build #-}
7223 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7224 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7225 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7226 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7233 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7234 see how to write rules that will do fusion and yet give an efficient
7235 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7245 <sect2 id="core-pragma">
7246 <title>CORE pragma</title>
7248 <indexterm><primary>CORE pragma</primary></indexterm>
7249 <indexterm><primary>pragma, CORE</primary></indexterm>
7250 <indexterm><primary>core, annotation</primary></indexterm>
7253 The external core format supports <quote>Note</quote> annotations;
7254 the <literal>CORE</literal> pragma gives a way to specify what these
7255 should be in your Haskell source code. Syntactically, core
7256 annotations are attached to expressions and take a Haskell string
7257 literal as an argument. The following function definition shows an
7261 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7264 Semantically, this is equivalent to:
7272 However, when external core is generated (via
7273 <option>-fext-core</option>), there will be Notes attached to the
7274 expressions <function>show</function> and <varname>x</varname>.
7275 The core function declaration for <function>f</function> is:
7279 f :: %forall a . GHCziShow.ZCTShow a ->
7280 a -> GHCziBase.ZMZN GHCziBase.Char =
7281 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7283 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7285 (tpl1::GHCziBase.Int ->
7287 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7289 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7290 (tpl3::GHCziBase.ZMZN a ->
7291 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7299 Here, we can see that the function <function>show</function> (which
7300 has been expanded out to a case expression over the Show dictionary)
7301 has a <literal>%note</literal> attached to it, as does the
7302 expression <varname>eta</varname> (which used to be called
7303 <varname>x</varname>).
7310 <sect1 id="special-ids">
7311 <title>Special built-in functions</title>
7312 <para>GHC has a few built-in functions with special behaviour. These
7313 are now described in the module <ulink
7314 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7315 in the library documentation.</para>
7319 <sect1 id="generic-classes">
7320 <title>Generic classes</title>
7323 The ideas behind this extension are described in detail in "Derivable type classes",
7324 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7325 An example will give the idea:
7333 fromBin :: [Int] -> (a, [Int])
7335 toBin {| Unit |} Unit = []
7336 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7337 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7338 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7340 fromBin {| Unit |} bs = (Unit, bs)
7341 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7342 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7343 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7344 (y,bs'') = fromBin bs'
7347 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7348 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7349 which are defined thus in the library module <literal>Generics</literal>:
7353 data a :+: b = Inl a | Inr b
7354 data a :*: b = a :*: b
7357 Now you can make a data type into an instance of Bin like this:
7359 instance (Bin a, Bin b) => Bin (a,b)
7360 instance Bin a => Bin [a]
7362 That is, just leave off the "where" clause. Of course, you can put in the
7363 where clause and over-ride whichever methods you please.
7367 <title> Using generics </title>
7368 <para>To use generics you need to</para>
7371 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7372 <option>-XGenerics</option> (to generate extra per-data-type code),
7373 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7377 <para>Import the module <literal>Generics</literal> from the
7378 <literal>lang</literal> package. This import brings into
7379 scope the data types <literal>Unit</literal>,
7380 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7381 don't need this import if you don't mention these types
7382 explicitly; for example, if you are simply giving instance
7383 declarations.)</para>
7388 <sect2> <title> Changes wrt the paper </title>
7390 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7391 can be written infix (indeed, you can now use
7392 any operator starting in a colon as an infix type constructor). Also note that
7393 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7394 Finally, note that the syntax of the type patterns in the class declaration
7395 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7396 alone would ambiguous when they appear on right hand sides (an extension we
7397 anticipate wanting).
7401 <sect2> <title>Terminology and restrictions</title>
7403 Terminology. A "generic default method" in a class declaration
7404 is one that is defined using type patterns as above.
7405 A "polymorphic default method" is a default method defined as in Haskell 98.
7406 A "generic class declaration" is a class declaration with at least one
7407 generic default method.
7415 Alas, we do not yet implement the stuff about constructor names and
7422 A generic class can have only one parameter; you can't have a generic
7423 multi-parameter class.
7429 A default method must be defined entirely using type patterns, or entirely
7430 without. So this is illegal:
7433 op :: a -> (a, Bool)
7434 op {| Unit |} Unit = (Unit, True)
7437 However it is perfectly OK for some methods of a generic class to have
7438 generic default methods and others to have polymorphic default methods.
7444 The type variable(s) in the type pattern for a generic method declaration
7445 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:
7449 op {| p :*: q |} (x :*: y) = op (x :: p)
7457 The type patterns in a generic default method must take one of the forms:
7463 where "a" and "b" are type variables. Furthermore, all the type patterns for
7464 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7465 must use the same type variables. So this is illegal:
7469 op {| a :+: b |} (Inl x) = True
7470 op {| p :+: q |} (Inr y) = False
7472 The type patterns must be identical, even in equations for different methods of the class.
7473 So this too is illegal:
7477 op1 {| a :*: b |} (x :*: y) = True
7480 op2 {| p :*: q |} (x :*: y) = False
7482 (The reason for this restriction is that we gather all the equations for a particular type constructor
7483 into a single generic instance declaration.)
7489 A generic method declaration must give a case for each of the three type constructors.
7495 The type for a generic method can be built only from:
7497 <listitem> <para> Function arrows </para> </listitem>
7498 <listitem> <para> Type variables </para> </listitem>
7499 <listitem> <para> Tuples </para> </listitem>
7500 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7502 Here are some example type signatures for generic methods:
7505 op2 :: Bool -> (a,Bool)
7506 op3 :: [Int] -> a -> a
7509 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7513 This restriction is an implementation restriction: we just haven't got around to
7514 implementing the necessary bidirectional maps over arbitrary type constructors.
7515 It would be relatively easy to add specific type constructors, such as Maybe and list,
7516 to the ones that are allowed.</para>
7521 In an instance declaration for a generic class, the idea is that the compiler
7522 will fill in the methods for you, based on the generic templates. However it can only
7527 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7532 No constructor of the instance type has unboxed fields.
7536 (Of course, these things can only arise if you are already using GHC extensions.)
7537 However, you can still give an instance declarations for types which break these rules,
7538 provided you give explicit code to override any generic default methods.
7546 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7547 what the compiler does with generic declarations.
7552 <sect2> <title> Another example </title>
7554 Just to finish with, here's another example I rather like:
7558 nCons {| Unit |} _ = 1
7559 nCons {| a :*: b |} _ = 1
7560 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7563 tag {| Unit |} _ = 1
7564 tag {| a :*: b |} _ = 1
7565 tag {| a :+: b |} (Inl x) = tag x
7566 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7572 <sect1 id="monomorphism">
7573 <title>Control over monomorphism</title>
7575 <para>GHC supports two flags that control the way in which generalisation is
7576 carried out at let and where bindings.
7580 <title>Switching off the dreaded Monomorphism Restriction</title>
7581 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7583 <para>Haskell's monomorphism restriction (see
7584 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7586 of the Haskell Report)
7587 can be completely switched off by
7588 <option>-XNoMonomorphismRestriction</option>.
7593 <title>Monomorphic pattern bindings</title>
7594 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7595 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7597 <para> As an experimental change, we are exploring the possibility of
7598 making pattern bindings monomorphic; that is, not generalised at all.
7599 A pattern binding is a binding whose LHS has no function arguments,
7600 and is not a simple variable. For example:
7602 f x = x -- Not a pattern binding
7603 f = \x -> x -- Not a pattern binding
7604 f :: Int -> Int = \x -> x -- Not a pattern binding
7606 (g,h) = e -- A pattern binding
7607 (f) = e -- A pattern binding
7608 [x] = e -- A pattern binding
7610 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7611 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7620 ;;; Local Variables: ***
7622 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7623 ;;; ispell-local-dictionary: "british" ***
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