1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individaully.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
137 <para> These two flags control how generalisation is done.
138 See <xref linkend="monomorphism"/>.
145 <option>-XExtendedDefaultRules</option>:
146 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
149 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
150 Independent of the <option>-fglasgow-exts</option>
157 <option>-XOverlappingInstances</option>
158 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
161 <option>-XUndecidableInstances</option>
162 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
165 <option>-XIncoherentInstances</option>
166 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
169 <option>-fcontext-stack=N</option>
170 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
173 <para> See <xref linkend="instance-decls"/>. Only relevant
174 if you also use <option>-fglasgow-exts</option>.</para>
180 <option>-finline-phase</option>
181 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
184 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
185 you also use <option>-fglasgow-exts</option>.</para>
191 <option>-XArrows</option>
192 <indexterm><primary><option>-XArrows</option></primary></indexterm>
195 <para>See <xref linkend="arrow-notation"/>. Independent of
196 <option>-fglasgow-exts</option>.</para>
198 <para>New reserved words/symbols: <literal>rec</literal>,
199 <literal>proc</literal>, <literal>-<</literal>,
200 <literal>>-</literal>, <literal>-<<</literal>,
201 <literal>>>-</literal>.</para>
203 <para>Other syntax stolen: <literal>(|</literal>,
204 <literal>|)</literal>.</para>
210 <option>-XGenerics</option>
211 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
214 <para>See <xref linkend="generic-classes"/>. Independent of
215 <option>-fglasgow-exts</option>.</para>
220 <term><option>-XNoImplicitPrelude</option></term>
222 <para><indexterm><primary>-XNoImplicitPrelude
223 option</primary></indexterm> GHC normally imports
224 <filename>Prelude.hi</filename> files for you. If you'd
225 rather it didn't, then give it a
226 <option>-XNoImplicitPrelude</option> option. The idea is
227 that you can then import a Prelude of your own. (But don't
228 call it <literal>Prelude</literal>; the Haskell module
229 namespace is flat, and you must not conflict with any
230 Prelude module.)</para>
232 <para>Even though you have not imported the Prelude, most of
233 the built-in syntax still refers to the built-in Haskell
234 Prelude types and values, as specified by the Haskell
235 Report. For example, the type <literal>[Int]</literal>
236 still means <literal>Prelude.[] Int</literal>; tuples
237 continue to refer to the standard Prelude tuples; the
238 translation for list comprehensions continues to use
239 <literal>Prelude.map</literal> etc.</para>
241 <para>However, <option>-XNoImplicitPrelude</option> does
242 change the handling of certain built-in syntax: see <xref
243 linkend="rebindable-syntax"/>.</para>
248 <term><option>-XImplicitParams</option></term>
250 <para>Enables implicit parameters (see <xref
251 linkend="implicit-parameters"/>). Currently also implied by
252 <option>-fglasgow-exts</option>.</para>
255 <literal>?<replaceable>varid</replaceable></literal>,
256 <literal>%<replaceable>varid</replaceable></literal>.</para>
261 <term><option>-XOverloadedStrings</option></term>
263 <para>Enables overloaded string literals (see <xref
264 linkend="overloaded-strings"/>).</para>
269 <term><option>-XScopedTypeVariables</option></term>
271 <para>Enables lexically-scoped type variables (see <xref
272 linkend="scoped-type-variables"/>). Implied by
273 <option>-fglasgow-exts</option>.</para>
278 <term><option>-XTemplateHaskell</option></term>
280 <para>Enables Template Haskell (see <xref
281 linkend="template-haskell"/>). This flag must
282 be given explicitly; it is no longer implied by
283 <option>-fglasgow-exts</option>.</para>
285 <para>Syntax stolen: <literal>[|</literal>,
286 <literal>[e|</literal>, <literal>[p|</literal>,
287 <literal>[d|</literal>, <literal>[t|</literal>,
288 <literal>$(</literal>,
289 <literal>$<replaceable>varid</replaceable></literal>.</para>
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>fptools/ghc/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 SGML
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.
370 Primitive (unboxed) types cannot be defined in Haskell, and are
371 therefore built into the language and compiler. Primitive types are
372 always unlifted; that is, a value of a primitive type cannot be
373 bottom. We use the convention that primitive types, values, and
374 operations have a <literal>#</literal> suffix.
378 Primitive values are often represented by a simple bit-pattern, such
379 as <literal>Int#</literal>, <literal>Float#</literal>,
380 <literal>Double#</literal>. But this is not necessarily the case:
381 a primitive value might be represented by a pointer to a
382 heap-allocated object. Examples include
383 <literal>Array#</literal>, the type of primitive arrays. A
384 primitive array is heap-allocated because it is too big a value to fit
385 in a register, and would be too expensive to copy around; in a sense,
386 it is accidental that it is represented by a pointer. If a pointer
387 represents a primitive value, then it really does point to that value:
388 no unevaluated thunks, no indirections…nothing can be at the
389 other end of the pointer than the primitive value.
390 A numerically-intensive program using unboxed types can
391 go a <emphasis>lot</emphasis> faster than its “standard”
392 counterpart—we saw a threefold speedup on one example.
396 There are some restrictions on the use of primitive types:
398 <listitem><para>The main restriction
399 is that you can't pass a primitive value to a polymorphic
400 function or store one in a polymorphic data type. This rules out
401 things like <literal>[Int#]</literal> (i.e. lists of primitive
402 integers). The reason for this restriction is that polymorphic
403 arguments and constructor fields are assumed to be pointers: if an
404 unboxed integer is stored in one of these, the garbage collector would
405 attempt to follow it, leading to unpredictable space leaks. Or a
406 <function>seq</function> operation on the polymorphic component may
407 attempt to dereference the pointer, with disastrous results. Even
408 worse, the unboxed value might be larger than a pointer
409 (<literal>Double#</literal> for instance).
412 <listitem><para> You cannot define a newtype whose representation type
413 (the argument type of the data constructor) is an unboxed type. Thus,
419 <listitem><para> You cannot bind a variable with an unboxed type
420 in a <emphasis>top-level</emphasis> binding.
422 <listitem><para> You cannot bind a variable with an unboxed type
423 in a <emphasis>recursive</emphasis> binding.
425 <listitem><para> You may bind unboxed variables in a (non-recursive,
426 non-top-level) pattern binding, but any such variable causes the entire
428 to become strict. For example:
430 data Foo = Foo Int Int#
432 f x = let (Foo a b, w) = ..rhs.. in ..body..
434 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
436 is strict, and the program behaves as if you had written
438 data Foo = Foo Int Int#
440 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
449 <sect2 id="unboxed-tuples">
450 <title>Unboxed Tuples
454 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
455 they're available by default with <option>-fglasgow-exts</option>. An
456 unboxed tuple looks like this:
468 where <literal>e_1..e_n</literal> are expressions of any
469 type (primitive or non-primitive). The type of an unboxed tuple looks
474 Unboxed tuples are used for functions that need to return multiple
475 values, but they avoid the heap allocation normally associated with
476 using fully-fledged tuples. When an unboxed tuple is returned, the
477 components are put directly into registers or on the stack; the
478 unboxed tuple itself does not have a composite representation. Many
479 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
481 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
482 tuples to avoid unnecessary allocation during sequences of operations.
486 There are some pretty stringent restrictions on the use of unboxed tuples:
491 Values of unboxed tuple types are subject to the same restrictions as
492 other unboxed types; i.e. they may not be stored in polymorphic data
493 structures or passed to polymorphic functions.
500 No variable can have an unboxed tuple type, nor may a constructor or function
501 argument have an unboxed tuple type. The following are all illegal:
505 data Foo = Foo (# Int, Int #)
507 f :: (# Int, Int #) -> (# Int, Int #)
510 g :: (# Int, Int #) -> Int
513 h x = let y = (# x,x #) in ...
520 The typical use of unboxed tuples is simply to return multiple values,
521 binding those multiple results with a <literal>case</literal> expression, thus:
523 f x y = (# x+1, y-1 #)
524 g x = case f x x of { (# a, b #) -> a + b }
526 You can have an unboxed tuple in a pattern binding, thus
528 f x = let (# p,q #) = h x in ..body..
530 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
531 the resulting binding is lazy like any other Haskell pattern binding. The
532 above example desugars like this:
534 f x = let t = case h x o f{ (# p,q #) -> (p,q)
539 Indeed, the bindings can even be recursive.
546 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
548 <sect1 id="syntax-extns">
549 <title>Syntactic extensions</title>
551 <!-- ====================== HIERARCHICAL MODULES ======================= -->
553 <sect2 id="hierarchical-modules">
554 <title>Hierarchical Modules</title>
556 <para>GHC supports a small extension to the syntax of module
557 names: a module name is allowed to contain a dot
558 <literal>‘.’</literal>. This is also known as the
559 “hierarchical module namespace” extension, because
560 it extends the normally flat Haskell module namespace into a
561 more flexible hierarchy of modules.</para>
563 <para>This extension has very little impact on the language
564 itself; modules names are <emphasis>always</emphasis> fully
565 qualified, so you can just think of the fully qualified module
566 name as <quote>the module name</quote>. In particular, this
567 means that the full module name must be given after the
568 <literal>module</literal> keyword at the beginning of the
569 module; for example, the module <literal>A.B.C</literal> must
572 <programlisting>module A.B.C</programlisting>
575 <para>It is a common strategy to use the <literal>as</literal>
576 keyword to save some typing when using qualified names with
577 hierarchical modules. For example:</para>
580 import qualified Control.Monad.ST.Strict as ST
583 <para>For details on how GHC searches for source and interface
584 files in the presence of hierarchical modules, see <xref
585 linkend="search-path"/>.</para>
587 <para>GHC comes with a large collection of libraries arranged
588 hierarchically; see the accompanying <ulink
589 url="../libraries/index.html">library
590 documentation</ulink>. More libraries to install are available
592 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
595 <!-- ====================== PATTERN GUARDS ======================= -->
597 <sect2 id="pattern-guards">
598 <title>Pattern guards</title>
601 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
602 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.)
606 Suppose we have an abstract data type of finite maps, with a
610 lookup :: FiniteMap -> Int -> Maybe Int
613 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
614 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
618 clunky env var1 var2 | ok1 && ok2 = val1 + val2
619 | otherwise = var1 + var2
630 The auxiliary functions are
634 maybeToBool :: Maybe a -> Bool
635 maybeToBool (Just x) = True
636 maybeToBool Nothing = False
638 expectJust :: Maybe a -> a
639 expectJust (Just x) = x
640 expectJust Nothing = error "Unexpected Nothing"
644 What is <function>clunky</function> doing? The guard <literal>ok1 &&
645 ok2</literal> checks that both lookups succeed, using
646 <function>maybeToBool</function> to convert the <function>Maybe</function>
647 types to booleans. The (lazily evaluated) <function>expectJust</function>
648 calls extract the values from the results of the lookups, and binds the
649 returned values to <varname>val1</varname> and <varname>val2</varname>
650 respectively. If either lookup fails, then clunky takes the
651 <literal>otherwise</literal> case and returns the sum of its arguments.
655 This is certainly legal Haskell, but it is a tremendously verbose and
656 un-obvious way to achieve the desired effect. Arguably, a more direct way
657 to write clunky would be to use case expressions:
661 clunky env var1 var2 = case lookup env var1 of
663 Just val1 -> case lookup env var2 of
665 Just val2 -> val1 + val2
671 This is a bit shorter, but hardly better. Of course, we can rewrite any set
672 of pattern-matching, guarded equations as case expressions; that is
673 precisely what the compiler does when compiling equations! The reason that
674 Haskell provides guarded equations is because they allow us to write down
675 the cases we want to consider, one at a time, independently of each other.
676 This structure is hidden in the case version. Two of the right-hand sides
677 are really the same (<function>fail</function>), and the whole expression
678 tends to become more and more indented.
682 Here is how I would write clunky:
687 | Just val1 <- lookup env var1
688 , Just val2 <- lookup env var2
690 ...other equations for clunky...
694 The semantics should be clear enough. The qualifiers are matched in order.
695 For a <literal><-</literal> qualifier, which I call a pattern guard, the
696 right hand side is evaluated and matched against the pattern on the left.
697 If the match fails then the whole guard fails and the next equation is
698 tried. If it succeeds, then the appropriate binding takes place, and the
699 next qualifier is matched, in the augmented environment. Unlike list
700 comprehensions, however, the type of the expression to the right of the
701 <literal><-</literal> is the same as the type of the pattern to its
702 left. The bindings introduced by pattern guards scope over all the
703 remaining guard qualifiers, and over the right hand side of the equation.
707 Just as with list comprehensions, boolean expressions can be freely mixed
708 with among the pattern guards. For example:
719 Haskell's current guards therefore emerge as a special case, in which the
720 qualifier list has just one element, a boolean expression.
724 <!-- ===================== View patterns =================== -->
726 <sect2 id="view-patterns">
731 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
732 More information and examples of view patterns can be found on the
733 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
738 View patterns are somewhat like pattern guards that can be nested inside
739 of other patterns. They are a convenient way of pattern-matching
740 against values of abstract types. For example, in a programming language
741 implementation, we might represent the syntax of the types of the
750 view :: Type -> TypeView
752 -- additional operations for constructing Typ's ...
755 The representation of Typ is held abstract, permitting implementations
756 to use a fancy representation (e.g., hash-consing to managage sharing).
758 Without view patterns, using this signature a little inconvenient:
760 size :: Typ -> Integer
761 size t = case view t of
763 Arrow t1 t2 -> size t1 + size t2
766 It is necessary to iterate the case, rather than using an equational
767 function definition. And the situation is even worse when the matching
768 against <literal>t</literal> is buried deep inside another pattern.
772 View patterns permit calling the view function inside the pattern and
773 matching against the result:
775 size (view -> Unit) = 1
776 size (view -> Arrow t1 t2) = size t1 + size t2
779 That is, we add a new form of pattern, written
780 <replaceable>expression</replaceable> <literal>-></literal>
781 <replaceable>pattern</replaceable> that means "apply the expression to
782 whatever we're trying to match against, and then match the result of
783 that application against the pattern". The expression can be any Haskell
784 expression of function type, and view patterns can be used wherever
789 The semantics of a pattern <literal>(</literal>
790 <replaceable>exp</replaceable> <literal>-></literal>
791 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
797 <para>The variables bound by the view pattern are the variables bound by
798 <replaceable>pat</replaceable>.
802 Any variables in <replaceable>exp</replaceable> are bound occurrences,
803 but variables bound "to the left" in a pattern are in scope. This
804 feature permits, for example, one argument to a function to be used in
805 the view of another argument. For example, the function
806 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
807 written using view patterns as follows:
810 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
811 ...other equations for clunky...
816 More precisely, the scoping rules are:
820 In a single pattern, variables bound by patterns to the left of a view
821 pattern expression are in scope. For example:
823 example :: Maybe ((String -> Integer,Integer), String) -> Bool
824 example Just ((f,_), f -> 4) = True
827 Additionally, in function definitions, variables bound by matching earlier curried
828 arguments may be used in view pattern expressions in later arguments:
830 example :: (String -> Integer) -> String -> Bool
831 example f (f -> 4) = True
833 That is, the scoping is the same as it would be if the curried arguments
834 were collected into a tuple.
840 In mutually recursive bindings, such as <literal>let</literal>,
841 <literal>where</literal>, or the top level, view patterns in one
842 declaration may not mention variables bound by other declarations. That
843 is, each declaration must be self-contained. For example, the following
844 program is not allowed:
851 restriction in the future; the only cost is that type checking patterns
852 would get a little more complicated.)
862 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
863 <replaceable>T1</replaceable> <literal>-></literal>
864 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
865 a <replaceable>T2</replaceable>, then the whole view pattern matches a
866 <replaceable>T1</replaceable>.
869 <listitem><para> Matching: To the equations in Section 3.17.3 of the
870 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
871 Report</ulink>, add the following:
873 case v of { (e -> p) -> e1 ; _ -> e2 }
875 case (e v) of { p -> e1 ; _ -> e2 }
877 That is, to match a variable <replaceable>v</replaceable> against a pattern
878 <literal>(</literal> <replaceable>exp</replaceable>
879 <literal>-></literal> <replaceable>pat</replaceable>
880 <literal>)</literal>, evaluate <literal>(</literal>
881 <replaceable>exp</replaceable> <replaceable> v</replaceable>
882 <literal>)</literal> and match the result against
883 <replaceable>pat</replaceable>.
886 <listitem><para> Efficiency: When the same view function is applied in
887 multiple branches of a function definition or a case expression (e.g.,
888 in <literal>size</literal> above), GHC makes an attempt to collect these
889 applications into a single nested case expression, so that the view
890 function is only applied once. Pattern compilation in GHC follows the
891 matrix algorithm described in Chapter 4 of <ulink
892 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
893 Implementation of Functional Programming Languages</ulink>. When the
894 top rows of the first column of a matrix are all view patterns with the
895 "same" expression, these patterns are transformed into a single nested
896 case. This includes, for example, adjacent view patterns that line up
899 f ((view -> A, p1), p2) = e1
900 f ((view -> B, p3), p4) = e2
904 <para> The current notion of when two view pattern expressions are "the
905 same" is very restricted: it is not even full syntactic equality.
906 However, it does include variables, literals, applications, and tuples;
907 e.g., two instances of <literal>view ("hi", "there")</literal> will be
908 collected. However, the current implementation does not compare up to
909 alpha-equivalence, so two instances of <literal>(x, view x ->
910 y)</literal> will not be coalesced.
920 <!-- ===================== Recursive do-notation =================== -->
922 <sect2 id="mdo-notation">
923 <title>The recursive do-notation
926 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
927 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
928 by Levent Erkok, John Launchbury,
929 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
930 This paper is essential reading for anyone making non-trivial use of mdo-notation,
931 and we do not repeat it here.
934 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
935 that is, the variables bound in a do-expression are visible only in the textually following
936 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
937 group. It turns out that several applications can benefit from recursive bindings in
938 the do-notation, and this extension provides the necessary syntactic support.
941 Here is a simple (yet contrived) example:
944 import Control.Monad.Fix
946 justOnes = mdo xs <- Just (1:xs)
950 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
954 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
957 class Monad m => MonadFix m where
958 mfix :: (a -> m a) -> m a
961 The function <literal>mfix</literal>
962 dictates how the required recursion operation should be performed. For example,
963 <literal>justOnes</literal> desugars as follows:
965 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
967 For full details of the way in which mdo is typechecked and desugared, see
968 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
969 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
972 If recursive bindings are required for a monad,
973 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
974 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
975 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
976 for Haskell's internal state monad (strict and lazy, respectively).
979 Here are some important points in using the recursive-do notation:
982 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
983 than <literal>do</literal>).
987 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
988 <literal>-fglasgow-exts</literal>.
992 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
993 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
994 be distinct (Section 3.3 of the paper).
998 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
999 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
1000 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
1001 and improve termination (Section 3.2 of the paper).
1007 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb/">http://www.cse.ogi.edu/PacSoft/projects/rmb/</ulink>
1008 contains up to date information on recursive monadic bindings.
1012 Historical note: The old implementation of the mdo-notation (and most
1013 of the existing documents) used the name
1014 <literal>MonadRec</literal> for the class and the corresponding library.
1015 This name is not supported by GHC.
1021 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1023 <sect2 id="parallel-list-comprehensions">
1024 <title>Parallel List Comprehensions</title>
1025 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1027 <indexterm><primary>parallel list comprehensions</primary>
1030 <para>Parallel list comprehensions are a natural extension to list
1031 comprehensions. List comprehensions can be thought of as a nice
1032 syntax for writing maps and filters. Parallel comprehensions
1033 extend this to include the zipWith family.</para>
1035 <para>A parallel list comprehension has multiple independent
1036 branches of qualifier lists, each separated by a `|' symbol. For
1037 example, the following zips together two lists:</para>
1040 [ (x, y) | x <- xs | y <- ys ]
1043 <para>The behavior of parallel list comprehensions follows that of
1044 zip, in that the resulting list will have the same length as the
1045 shortest branch.</para>
1047 <para>We can define parallel list comprehensions by translation to
1048 regular comprehensions. Here's the basic idea:</para>
1050 <para>Given a parallel comprehension of the form: </para>
1053 [ e | p1 <- e11, p2 <- e12, ...
1054 | q1 <- e21, q2 <- e22, ...
1059 <para>This will be translated to: </para>
1062 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1063 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1068 <para>where `zipN' is the appropriate zip for the given number of
1073 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1075 <sect2 id="generalised-list-comprehensions">
1076 <title>Generalised (SQL-Like) List Comprehensions</title>
1077 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1079 <indexterm><primary>extended list comprehensions</primary>
1081 <indexterm><primary>group</primary></indexterm>
1082 <indexterm><primary>sql</primary></indexterm>
1085 <para>Generalised list comprehensions are a further enhancement to the
1086 list comprehension syntatic sugar to allow operations such as sorting
1087 and grouping which are familiar from SQL. They are fully described in the
1088 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1089 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1090 except that the syntax we use differs slightly from the paper.</para>
1091 <para>Here is an example:
1093 employees = [ ("Simon", "MS", 80)
1094 , ("Erik", "MS", 100)
1095 , ("Phil", "Ed", 40)
1096 , ("Gordon", "Ed", 45)
1097 , ("Paul", "Yale", 60)]
1099 output = [ (the dept, sum salary)
1100 | (name, dept, salary) <- employees
1101 , then group by dept
1102 , then sortWith by (sum salary)
1105 In this example, the list <literal>output</literal> would take on
1109 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1112 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1113 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1114 function that is exported by <literal>GHC.Exts</literal>.)</para>
1116 <para>There are five new forms of compehension qualifier,
1117 all introduced by the (existing) keyword <literal>then</literal>:
1125 This statement requires that <literal>f</literal> have the type <literal>
1126 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1127 motivating example, as this form is used to apply <literal>take 5</literal>.
1138 This form is similar to the previous one, but allows you to create a function
1139 which will be passed as the first argument to f. As a consequence f must have
1140 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1141 from the type, this function lets f "project out" some information
1142 from the elements of the list it is transforming.</para>
1144 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1145 is supplied with a function that lets it find out the <literal>sum salary</literal>
1146 for any item in the list comprehension it transforms.</para>
1154 then group by e using f
1157 <para>This is the most general of the grouping-type statements. In this form,
1158 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1159 As with the <literal>then f by e</literal> case above, the first argument
1160 is a function supplied to f by the compiler which lets it compute e on every
1161 element of the list being transformed. However, unlike the non-grouping case,
1162 f additionally partitions the list into a number of sublists: this means that
1163 at every point after this statement, binders occuring before it in the comprehension
1164 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1165 this, let's look at an example:</para>
1168 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1169 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1170 groupRuns f = groupBy (\x y -> f x == f y)
1172 output = [ (the x, y)
1173 | x <- ([1..3] ++ [1..2])
1175 , then group by x using groupRuns ]
1178 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1181 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1184 <para>Note that we have used the <literal>the</literal> function to change the type
1185 of x from a list to its original numeric type. The variable y, in contrast, is left
1186 unchanged from the list form introduced by the grouping.</para>
1196 <para>This form of grouping is essentially the same as the one described above. However,
1197 since no function to use for the grouping has been supplied it will fall back on the
1198 <literal>groupWith</literal> function defined in
1199 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1200 is the form of the group statement that we made use of in the opening example.</para>
1211 <para>With this form of the group statement, f is required to simply have the type
1212 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1213 comprehension so far directly. An example of this form is as follows:</para>
1219 , then group using inits]
1222 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1225 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1233 <!-- ===================== REBINDABLE SYNTAX =================== -->
1235 <sect2 id="rebindable-syntax">
1236 <title>Rebindable syntax</title>
1238 <para>GHC allows most kinds of built-in syntax to be rebound by
1239 the user, to facilitate replacing the <literal>Prelude</literal>
1240 with a home-grown version, for example.</para>
1242 <para>You may want to define your own numeric class
1243 hierarchy. It completely defeats that purpose if the
1244 literal "1" means "<literal>Prelude.fromInteger
1245 1</literal>", which is what the Haskell Report specifies.
1246 So the <option>-XNoImplicitPrelude</option> flag causes
1247 the following pieces of built-in syntax to refer to
1248 <emphasis>whatever is in scope</emphasis>, not the Prelude
1253 <para>An integer literal <literal>368</literal> means
1254 "<literal>fromInteger (368::Integer)</literal>", rather than
1255 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1258 <listitem><para>Fractional literals are handed in just the same way,
1259 except that the translation is
1260 <literal>fromRational (3.68::Rational)</literal>.
1263 <listitem><para>The equality test in an overloaded numeric pattern
1264 uses whatever <literal>(==)</literal> is in scope.
1267 <listitem><para>The subtraction operation, and the
1268 greater-than-or-equal test, in <literal>n+k</literal> patterns
1269 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1273 <para>Negation (e.g. "<literal>- (f x)</literal>")
1274 means "<literal>negate (f x)</literal>", both in numeric
1275 patterns, and expressions.
1279 <para>"Do" notation is translated using whatever
1280 functions <literal>(>>=)</literal>,
1281 <literal>(>>)</literal>, and <literal>fail</literal>,
1282 are in scope (not the Prelude
1283 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1284 comprehensions, are unaffected. </para></listitem>
1288 notation (see <xref linkend="arrow-notation"/>)
1289 uses whatever <literal>arr</literal>,
1290 <literal>(>>>)</literal>, <literal>first</literal>,
1291 <literal>app</literal>, <literal>(|||)</literal> and
1292 <literal>loop</literal> functions are in scope. But unlike the
1293 other constructs, the types of these functions must match the
1294 Prelude types very closely. Details are in flux; if you want
1298 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1299 even if that is a little unexpected. For emample, the
1300 static semantics of the literal <literal>368</literal>
1301 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1302 <literal>fromInteger</literal> to have any of the types:
1304 fromInteger :: Integer -> Integer
1305 fromInteger :: forall a. Foo a => Integer -> a
1306 fromInteger :: Num a => a -> Integer
1307 fromInteger :: Integer -> Bool -> Bool
1311 <para>Be warned: this is an experimental facility, with
1312 fewer checks than usual. Use <literal>-dcore-lint</literal>
1313 to typecheck the desugared program. If Core Lint is happy
1314 you should be all right.</para>
1318 <sect2 id="postfix-operators">
1319 <title>Postfix operators</title>
1322 GHC allows a small extension to the syntax of left operator sections, which
1323 allows you to define postfix operators. The extension is this: the left section
1327 is equivalent (from the point of view of both type checking and execution) to the expression
1331 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1332 The strict Haskell 98 interpretation is that the section is equivalent to
1336 That is, the operator must be a function of two arguments. GHC allows it to
1337 take only one argument, and that in turn allows you to write the function
1340 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1341 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1342 change their behaviour, of course.)
1344 <para>The extension does not extend to the left-hand side of function
1345 definitions; you must define such a function in prefix form.</para>
1349 <sect2 id="disambiguate-fields">
1350 <title>Record field disambiguation</title>
1352 In record construction and record pattern matching
1353 it is entirely unambiguous which field is referred to, even if there are two different
1354 data types in scope with a common field name. For example:
1357 data S = MkS { x :: Int, y :: Bool }
1362 data T = MkT { x :: Int }
1364 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1366 ok2 n = MkT { x = n+1 } -- Unambiguous
1368 bad1 k = k { x = 3 } -- Ambiguous
1369 bad2 k = x k -- Ambiguous
1371 Even though there are two <literal>x</literal>'s in scope,
1372 it is clear that the <literal>x</literal> in the pattern in the
1373 definition of <literal>ok1</literal> can only mean the field
1374 <literal>x</literal> from type <literal>S</literal>. Similarly for
1375 the function <literal>ok2</literal>. However, in the record update
1376 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1377 it is not clear which of the two types is intended.
1380 Haskell 98 regards all four as ambiguous, but with the
1381 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1382 the former two. The rules are precisely the same as those for instance
1383 declarations in Haskell 98, where the method names on the left-hand side
1384 of the method bindings in an instance declaration refer unambiguously
1385 to the method of that class (provided they are in scope at all), even
1386 if there are other variables in scope with the same name.
1387 This reduces the clutter of qualified names when you import two
1388 records from different modules that use the same field name.
1392 <!-- ===================== Record puns =================== -->
1394 <sect2 id="record-puns">
1399 Record puns are enabled by the flag <literal>-XRecordPuns</literal>.
1403 When using records, it is common to write a pattern that binds a
1404 variable with the same name as a record field, such as:
1407 data C = C {a :: Int}
1413 Record punning permits the variable name to be elided, so one can simply
1420 to mean the same pattern as above. That is, in a record pattern, the
1421 pattern <literal>a</literal> expands into the pattern <literal>a =
1422 a</literal> for the same name <literal>a</literal>.
1426 Note that puns and other patterns can be mixed in the same record:
1428 data C = C {a :: Int, b :: Int}
1429 f (C {a, b = 4}) = a
1431 and that puns can be used wherever record patterns occur (e.g. in
1432 <literal>let</literal> bindings or at the top-level).
1436 Record punning can also be used in an expression, writing, for example,
1442 let a = 1 in C {a = a}
1445 Note that this expansion is purely syntactic, so the record pun
1446 expression refers to the nearest enclosing variable that is spelled the
1447 same as the field name.
1452 <!-- ===================== Record wildcards =================== -->
1454 <sect2 id="record-wildcards">
1455 <title>Record wildcards
1459 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1463 For records with many fields, it can be tiresome to write out each field
1464 individually in a record pattern, as in
1466 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1467 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1472 Record wildcard syntax permits a (<literal>..</literal>) in a record
1473 pattern, where each elided field <literal>f</literal> is replaced by the
1474 pattern <literal>f = f</literal>. For example, the above pattern can be
1477 f (C {a = 1, ..}) = b + c + d
1482 Note that wildcards can be mixed with other patterns, including puns
1483 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1484 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1485 wherever record patterns occur, including in <literal>let</literal>
1486 bindings and at the top-level. For example, the top-level binding
1490 defines <literal>b</literal>, <literal>c</literal>, and
1491 <literal>d</literal>.
1495 Record wildcards can also be used in expressions, writing, for example,
1498 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1504 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1507 Note that this expansion is purely syntactic, so the record wildcard
1508 expression refers to the nearest enclosing variables that are spelled
1509 the same as the omitted field names.
1514 <!-- ===================== Local fixity declarations =================== -->
1516 <sect2 id="local-fixity-declarations">
1517 <title>Local Fixity Declarations
1520 <para>A careful reading of the Haskell 98 Report reveals that fixity
1521 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1522 <literal>infixr</literal>) are permitted to appear inside local bindings
1523 such those introduced by <literal>let</literal> and
1524 <literal>where</literal>. However, the Haskell Report does not specify
1525 the semantics of such bindings very precisely.
1528 <para>In GHC, a fixity declaration may accompany a local binding:
1535 and the fixity declaration applies wherever the binding is in scope.
1536 For example, in a <literal>let</literal>, it applies in the right-hand
1537 sides of other <literal>let</literal>-bindings and the body of the
1538 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1539 expressions (<xref linkend="mdo-notation"/>), the local fixity
1540 declarations of aA <literal>let</literal> statement scope over other
1541 statements in the group, just as the bound name does.
1544 Moreover, a local fixity declatation *must* accompany a local binding of
1545 that name: it is not possible to revise the fixity of name bound
1548 let infixr 9 $ in ...
1551 Because local fixity declarations are technically Haskell 98, no flag is
1552 necessary to enable them.
1558 <!-- TYPE SYSTEM EXTENSIONS -->
1559 <sect1 id="data-type-extensions">
1560 <title>Extensions to data types and type synonyms</title>
1562 <sect2 id="nullary-types">
1563 <title>Data types with no constructors</title>
1565 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1566 a data type with no constructors. For example:</para>
1570 data T a -- T :: * -> *
1573 <para>Syntactically, the declaration lacks the "= constrs" part. The
1574 type can be parameterised over types of any kind, but if the kind is
1575 not <literal>*</literal> then an explicit kind annotation must be used
1576 (see <xref linkend="kinding"/>).</para>
1578 <para>Such data types have only one value, namely bottom.
1579 Nevertheless, they can be useful when defining "phantom types".</para>
1582 <sect2 id="infix-tycons">
1583 <title>Infix type constructors, classes, and type variables</title>
1586 GHC allows type constructors, classes, and type variables to be operators, and
1587 to be written infix, very much like expressions. More specifically:
1590 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1591 The lexical syntax is the same as that for data constructors.
1594 Data type and type-synonym declarations can be written infix, parenthesised
1595 if you want further arguments. E.g.
1597 data a :*: b = Foo a b
1598 type a :+: b = Either a b
1599 class a :=: b where ...
1601 data (a :**: b) x = Baz a b x
1602 type (a :++: b) y = Either (a,b) y
1606 Types, and class constraints, can be written infix. For example
1609 f :: (a :=: b) => a -> b
1613 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1614 The lexical syntax is the same as that for variable operators, excluding "(.)",
1615 "(!)", and "(*)". In a binding position, the operator must be
1616 parenthesised. For example:
1618 type T (+) = Int + Int
1622 liftA2 :: Arrow (~>)
1623 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1629 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1630 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1633 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1634 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1635 sets the fixity for a data constructor and the corresponding type constructor. For example:
1639 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1640 and similarly for <literal>:*:</literal>.
1641 <literal>Int `a` Bool</literal>.
1644 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1651 <sect2 id="type-synonyms">
1652 <title>Liberalised type synonyms</title>
1655 Type synonyms are like macros at the type level, and
1656 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1657 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1659 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1660 in a type synonym, thus:
1662 type Discard a = forall b. Show b => a -> b -> (a, String)
1667 g :: Discard Int -> (Int,String) -- A rank-2 type
1674 You can write an unboxed tuple in a type synonym:
1676 type Pr = (# Int, Int #)
1684 You can apply a type synonym to a forall type:
1686 type Foo a = a -> a -> Bool
1688 f :: Foo (forall b. b->b)
1690 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1692 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1697 You can apply a type synonym to a partially applied type synonym:
1699 type Generic i o = forall x. i x -> o x
1702 foo :: Generic Id []
1704 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1706 foo :: forall x. x -> [x]
1714 GHC currently does kind checking before expanding synonyms (though even that
1718 After expanding type synonyms, GHC does validity checking on types, looking for
1719 the following mal-formedness which isn't detected simply by kind checking:
1722 Type constructor applied to a type involving for-alls.
1725 Unboxed tuple on left of an arrow.
1728 Partially-applied type synonym.
1732 this will be rejected:
1734 type Pr = (# Int, Int #)
1739 because GHC does not allow unboxed tuples on the left of a function arrow.
1744 <sect2 id="existential-quantification">
1745 <title>Existentially quantified data constructors
1749 The idea of using existential quantification in data type declarations
1750 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1751 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1752 London, 1991). It was later formalised by Laufer and Odersky
1753 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1754 TOPLAS, 16(5), pp1411-1430, 1994).
1755 It's been in Lennart
1756 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1757 proved very useful. Here's the idea. Consider the declaration:
1763 data Foo = forall a. MkFoo a (a -> Bool)
1770 The data type <literal>Foo</literal> has two constructors with types:
1776 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1783 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1784 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1785 For example, the following expression is fine:
1791 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1797 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1798 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1799 isUpper</function> packages a character with a compatible function. These
1800 two things are each of type <literal>Foo</literal> and can be put in a list.
1804 What can we do with a value of type <literal>Foo</literal>?. In particular,
1805 what happens when we pattern-match on <function>MkFoo</function>?
1811 f (MkFoo val fn) = ???
1817 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1818 are compatible, the only (useful) thing we can do with them is to
1819 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1826 f (MkFoo val fn) = fn val
1832 What this allows us to do is to package heterogenous values
1833 together with a bunch of functions that manipulate them, and then treat
1834 that collection of packages in a uniform manner. You can express
1835 quite a bit of object-oriented-like programming this way.
1838 <sect3 id="existential">
1839 <title>Why existential?
1843 What has this to do with <emphasis>existential</emphasis> quantification?
1844 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1850 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1856 But Haskell programmers can safely think of the ordinary
1857 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1858 adding a new existential quantification construct.
1863 <sect3 id="existential-with-context">
1864 <title>Existentials and type classes</title>
1867 An easy extension is to allow
1868 arbitrary contexts before the constructor. For example:
1874 data Baz = forall a. Eq a => Baz1 a a
1875 | forall b. Show b => Baz2 b (b -> b)
1881 The two constructors have the types you'd expect:
1887 Baz1 :: forall a. Eq a => a -> a -> Baz
1888 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1894 But when pattern matching on <function>Baz1</function> the matched values can be compared
1895 for equality, and when pattern matching on <function>Baz2</function> the first matched
1896 value can be converted to a string (as well as applying the function to it).
1897 So this program is legal:
1904 f (Baz1 p q) | p == q = "Yes"
1906 f (Baz2 v fn) = show (fn v)
1912 Operationally, in a dictionary-passing implementation, the
1913 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1914 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1915 extract it on pattern matching.
1920 <sect3 id="existential-records">
1921 <title>Record Constructors</title>
1924 GHC allows existentials to be used with records syntax as well. For example:
1927 data Counter a = forall self. NewCounter
1929 , _inc :: self -> self
1930 , _display :: self -> IO ()
1934 Here <literal>tag</literal> is a public field, with a well-typed selector
1935 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1936 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1937 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1938 compile-time error. In other words, <emphasis>GHC defines a record selector function
1939 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1940 (This example used an underscore in the fields for which record selectors
1941 will not be defined, but that is only programming style; GHC ignores them.)
1945 To make use of these hidden fields, we need to create some helper functions:
1948 inc :: Counter a -> Counter a
1949 inc (NewCounter x i d t) = NewCounter
1950 { _this = i x, _inc = i, _display = d, tag = t }
1952 display :: Counter a -> IO ()
1953 display NewCounter{ _this = x, _display = d } = d x
1956 Now we can define counters with different underlying implementations:
1959 counterA :: Counter String
1960 counterA = NewCounter
1961 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1963 counterB :: Counter String
1964 counterB = NewCounter
1965 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1968 display (inc counterA) -- prints "1"
1969 display (inc (inc counterB)) -- prints "##"
1972 At the moment, record update syntax is only supported for Haskell 98 data types,
1973 so the following function does <emphasis>not</emphasis> work:
1976 -- This is invalid; use explicit NewCounter instead for now
1977 setTag :: Counter a -> a -> Counter a
1978 setTag obj t = obj{ tag = t }
1987 <title>Restrictions</title>
1990 There are several restrictions on the ways in which existentially-quantified
1991 constructors can be use.
2000 When pattern matching, each pattern match introduces a new,
2001 distinct, type for each existential type variable. These types cannot
2002 be unified with any other type, nor can they escape from the scope of
2003 the pattern match. For example, these fragments are incorrect:
2011 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2012 is the result of <function>f1</function>. One way to see why this is wrong is to
2013 ask what type <function>f1</function> has:
2017 f1 :: Foo -> a -- Weird!
2021 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2026 f1 :: forall a. Foo -> a -- Wrong!
2030 The original program is just plain wrong. Here's another sort of error
2034 f2 (Baz1 a b) (Baz1 p q) = a==q
2038 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2039 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2040 from the two <function>Baz1</function> constructors.
2048 You can't pattern-match on an existentially quantified
2049 constructor in a <literal>let</literal> or <literal>where</literal> group of
2050 bindings. So this is illegal:
2054 f3 x = a==b where { Baz1 a b = x }
2057 Instead, use a <literal>case</literal> expression:
2060 f3 x = case x of Baz1 a b -> a==b
2063 In general, you can only pattern-match
2064 on an existentially-quantified constructor in a <literal>case</literal> expression or
2065 in the patterns of a function definition.
2067 The reason for this restriction is really an implementation one.
2068 Type-checking binding groups is already a nightmare without
2069 existentials complicating the picture. Also an existential pattern
2070 binding at the top level of a module doesn't make sense, because it's
2071 not clear how to prevent the existentially-quantified type "escaping".
2072 So for now, there's a simple-to-state restriction. We'll see how
2080 You can't use existential quantification for <literal>newtype</literal>
2081 declarations. So this is illegal:
2085 newtype T = forall a. Ord a => MkT a
2089 Reason: a value of type <literal>T</literal> must be represented as a
2090 pair of a dictionary for <literal>Ord t</literal> and a value of type
2091 <literal>t</literal>. That contradicts the idea that
2092 <literal>newtype</literal> should have no concrete representation.
2093 You can get just the same efficiency and effect by using
2094 <literal>data</literal> instead of <literal>newtype</literal>. If
2095 there is no overloading involved, then there is more of a case for
2096 allowing an existentially-quantified <literal>newtype</literal>,
2097 because the <literal>data</literal> version does carry an
2098 implementation cost, but single-field existentially quantified
2099 constructors aren't much use. So the simple restriction (no
2100 existential stuff on <literal>newtype</literal>) stands, unless there
2101 are convincing reasons to change it.
2109 You can't use <literal>deriving</literal> to define instances of a
2110 data type with existentially quantified data constructors.
2112 Reason: in most cases it would not make sense. For example:;
2115 data T = forall a. MkT [a] deriving( Eq )
2118 To derive <literal>Eq</literal> in the standard way we would need to have equality
2119 between the single component of two <function>MkT</function> constructors:
2123 (MkT a) == (MkT b) = ???
2126 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2127 It's just about possible to imagine examples in which the derived instance
2128 would make sense, but it seems altogether simpler simply to prohibit such
2129 declarations. Define your own instances!
2140 <!-- ====================== Generalised algebraic data types ======================= -->
2142 <sect2 id="gadt-style">
2143 <title>Declaring data types with explicit constructor signatures</title>
2145 <para>GHC allows you to declare an algebraic data type by
2146 giving the type signatures of constructors explicitly. For example:
2150 Just :: a -> Maybe a
2152 The form is called a "GADT-style declaration"
2153 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2154 can only be declared using this form.</para>
2155 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2156 For example, these two declarations are equivalent:
2158 data Foo = forall a. MkFoo a (a -> Bool)
2159 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2162 <para>Any data type that can be declared in standard Haskell-98 syntax
2163 can also be declared using GADT-style syntax.
2164 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2165 they treat class constraints on the data constructors differently.
2166 Specifically, if the constructor is given a type-class context, that
2167 context is made available by pattern matching. For example:
2170 MkSet :: Eq a => [a] -> Set a
2172 makeSet :: Eq a => [a] -> Set a
2173 makeSet xs = MkSet (nub xs)
2175 insert :: a -> Set a -> Set a
2176 insert a (MkSet as) | a `elem` as = MkSet as
2177 | otherwise = MkSet (a:as)
2179 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2180 gives rise to a <literal>(Eq a)</literal>
2181 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2182 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2183 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2184 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2185 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2186 In the example, the equality dictionary is used to satisfy the equality constraint
2187 generated by the call to <literal>elem</literal>, so that the type of
2188 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2191 For example, one possible application is to reify dictionaries:
2193 data NumInst a where
2194 MkNumInst :: Num a => NumInst a
2196 intInst :: NumInst Int
2199 plus :: NumInst a -> a -> a -> a
2200 plus MkNumInst p q = p + q
2202 Here, a value of type <literal>NumInst a</literal> is equivalent
2203 to an explicit <literal>(Num a)</literal> dictionary.
2206 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2207 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2211 = Num a => MkNumInst (NumInst a)
2213 Notice that, unlike the situation when declaring an existental, there is
2214 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2215 data type's univerally quantified type variable <literal>a</literal>.
2216 A constructor may have both universal and existential type variables: for example,
2217 the following two declarations are equivalent:
2220 = forall b. (Num a, Eq b) => MkT1 a b
2222 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2225 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2226 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2227 In Haskell 98 the definition
2229 data Eq a => Set' a = MkSet' [a]
2231 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2232 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2233 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2234 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2235 GHC's behaviour is much more useful, as well as much more intuitive.
2239 The rest of this section gives further details about GADT-style data
2244 The result type of each data constructor must begin with the type constructor being defined.
2245 If the result type of all constructors
2246 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2247 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2248 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2252 The type signature of
2253 each constructor is independent, and is implicitly universally quantified as usual.
2254 Different constructors may have different universally-quantified type variables
2255 and different type-class constraints.
2256 For example, this is fine:
2259 T1 :: Eq b => b -> T b
2260 T2 :: (Show c, Ix c) => c -> [c] -> T c
2265 Unlike a Haskell-98-style
2266 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2267 have no scope. Indeed, one can write a kind signature instead:
2269 data Set :: * -> * where ...
2271 or even a mixture of the two:
2273 data Foo a :: (* -> *) -> * where ...
2275 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2278 data Foo a (b :: * -> *) where ...
2284 You can use strictness annotations, in the obvious places
2285 in the constructor type:
2288 Lit :: !Int -> Term Int
2289 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2290 Pair :: Term a -> Term b -> Term (a,b)
2295 You can use a <literal>deriving</literal> clause on a GADT-style data type
2296 declaration. For example, these two declarations are equivalent
2298 data Maybe1 a where {
2299 Nothing1 :: Maybe1 a ;
2300 Just1 :: a -> Maybe1 a
2301 } deriving( Eq, Ord )
2303 data Maybe2 a = Nothing2 | Just2 a
2309 You can use record syntax on a GADT-style data type declaration:
2313 Adult { name :: String, children :: [Person] } :: Person
2314 Child { name :: String } :: Person
2316 As usual, for every constructor that has a field <literal>f</literal>, the type of
2317 field <literal>f</literal> must be the same (modulo alpha conversion).
2320 At the moment, record updates are not yet possible with GADT-style declarations,
2321 so support is limited to record construction, selection and pattern matching.
2324 aPerson = Adult { name = "Fred", children = [] }
2326 shortName :: Person -> Bool
2327 hasChildren (Adult { children = kids }) = not (null kids)
2328 hasChildren (Child {}) = False
2333 As in the case of existentials declared using the Haskell-98-like record syntax
2334 (<xref linkend="existential-records"/>),
2335 record-selector functions are generated only for those fields that have well-typed
2337 Here is the example of that section, in GADT-style syntax:
2339 data Counter a where
2340 NewCounter { _this :: self
2341 , _inc :: self -> self
2342 , _display :: self -> IO ()
2347 As before, only one selector function is generated here, that for <literal>tag</literal>.
2348 Nevertheless, you can still use all the field names in pattern matching and record construction.
2350 </itemizedlist></para>
2354 <title>Generalised Algebraic Data Types (GADTs)</title>
2356 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2357 by allowing constructors to have richer return types. Here is an example:
2360 Lit :: Int -> Term Int
2361 Succ :: Term Int -> Term Int
2362 IsZero :: Term Int -> Term Bool
2363 If :: Term Bool -> Term a -> Term a -> Term a
2364 Pair :: Term a -> Term b -> Term (a,b)
2366 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2367 case with ordinary data types. This generality allows us to
2368 write a well-typed <literal>eval</literal> function
2369 for these <literal>Terms</literal>:
2373 eval (Succ t) = 1 + eval t
2374 eval (IsZero t) = eval t == 0
2375 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2376 eval (Pair e1 e2) = (eval e1, eval e2)
2378 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2379 For example, in the right hand side of the equation
2384 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2385 A precise specification of the type rules is beyond what this user manual aspires to,
2386 but the design closely follows that described in
2388 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2389 unification-based type inference for GADTs</ulink>,
2391 The general principle is this: <emphasis>type refinement is only carried out
2392 based on user-supplied type annotations</emphasis>.
2393 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2394 and lots of obscure error messages will
2395 occur. However, the refinement is quite general. For example, if we had:
2397 eval :: Term a -> a -> a
2398 eval (Lit i) j = i+j
2400 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2401 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2402 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2405 These and many other examples are given in papers by Hongwei Xi, and
2406 Tim Sheard. There is a longer introduction
2407 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2409 <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
2410 may use different notation to that implemented in GHC.
2413 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2414 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2417 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2418 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2419 The result type of each constructor must begin with the type constructor being defined,
2420 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2421 For example, in the <literal>Term</literal> data
2422 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2423 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
2428 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2429 an ordinary data type.
2433 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2437 Lit { val :: Int } :: Term Int
2438 Succ { num :: Term Int } :: Term Int
2439 Pred { num :: Term Int } :: Term Int
2440 IsZero { arg :: Term Int } :: Term Bool
2441 Pair { arg1 :: Term a
2444 If { cnd :: Term Bool
2449 However, for GADTs there is the following additional constraint:
2450 every constructor that has a field <literal>f</literal> must have
2451 the same result type (modulo alpha conversion)
2452 Hence, in the above example, we cannot merge the <literal>num</literal>
2453 and <literal>arg</literal> fields above into a
2454 single name. Although their field types are both <literal>Term Int</literal>,
2455 their selector functions actually have different types:
2458 num :: Term Int -> Term Int
2459 arg :: Term Bool -> Term Int
2469 <!-- ====================== End of Generalised algebraic data types ======================= -->
2471 <sect1 id="deriving">
2472 <title>Extensions to the "deriving" mechanism</title>
2474 <sect2 id="deriving-inferred">
2475 <title>Inferred context for deriving clauses</title>
2478 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2481 data T0 f a = MkT0 a deriving( Eq )
2482 data T1 f a = MkT1 (f a) deriving( Eq )
2483 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2485 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2487 instance Eq a => Eq (T0 f a) where ...
2488 instance Eq (f a) => Eq (T1 f a) where ...
2489 instance Eq (f (f a)) => Eq (T2 f a) where ...
2491 The first of these is obviously fine. The second is still fine, although less obviously.
2492 The third is not Haskell 98, and risks losing termination of instances.
2495 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2496 each constraint in the inferred instance context must consist only of type variables,
2497 with no repetitions.
2500 This rule is applied regardless of flags. If you want a more exotic context, you can write
2501 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2505 <sect2 id="stand-alone-deriving">
2506 <title>Stand-alone deriving declarations</title>
2509 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2511 data Foo a = Bar a | Baz String
2513 deriving instance Eq a => Eq (Foo a)
2515 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2516 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2517 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2518 exactly as you would in an ordinary instance declaration.
2519 (In contrast the context is inferred in a <literal>deriving</literal> clause
2520 attached to a data type declaration.) These <literal>deriving instance</literal>
2521 rules obey the same rules concerning form and termination as ordinary instance declarations,
2522 controlled by the same flags; see <xref linkend="instance-decls"/>. </para>
2524 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2525 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2528 newtype Foo a = MkFoo (State Int a)
2530 deriving instance MonadState Int Foo
2532 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2533 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2539 <sect2 id="deriving-typeable">
2540 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2543 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2544 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2545 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2546 classes <literal>Eq</literal>, <literal>Ord</literal>,
2547 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2550 GHC extends this list with two more classes that may be automatically derived
2551 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2552 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2553 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2554 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2556 <para>An instance of <literal>Typeable</literal> can only be derived if the
2557 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2558 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2560 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2561 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2563 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2564 are used, and only <literal>Typeable1</literal> up to
2565 <literal>Typeable7</literal> are provided in the library.)
2566 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2567 class, whose kind suits that of the data type constructor, and
2568 then writing the data type instance by hand.
2572 <sect2 id="newtype-deriving">
2573 <title>Generalised derived instances for newtypes</title>
2576 When you define an abstract type using <literal>newtype</literal>, you may want
2577 the new type to inherit some instances from its representation. In
2578 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2579 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2580 other classes you have to write an explicit instance declaration. For
2581 example, if you define
2584 newtype Dollars = Dollars Int
2587 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2588 explicitly define an instance of <literal>Num</literal>:
2591 instance Num Dollars where
2592 Dollars a + Dollars b = Dollars (a+b)
2595 All the instance does is apply and remove the <literal>newtype</literal>
2596 constructor. It is particularly galling that, since the constructor
2597 doesn't appear at run-time, this instance declaration defines a
2598 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2599 dictionary, only slower!
2603 <sect3> <title> Generalising the deriving clause </title>
2605 GHC now permits such instances to be derived instead,
2606 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2609 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2612 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2613 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2614 derives an instance declaration of the form
2617 instance Num Int => Num Dollars
2620 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2624 We can also derive instances of constructor classes in a similar
2625 way. For example, suppose we have implemented state and failure monad
2626 transformers, such that
2629 instance Monad m => Monad (State s m)
2630 instance Monad m => Monad (Failure m)
2632 In Haskell 98, we can define a parsing monad by
2634 type Parser tok m a = State [tok] (Failure m) a
2637 which is automatically a monad thanks to the instance declarations
2638 above. With the extension, we can make the parser type abstract,
2639 without needing to write an instance of class <literal>Monad</literal>, via
2642 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2645 In this case the derived instance declaration is of the form
2647 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2650 Notice that, since <literal>Monad</literal> is a constructor class, the
2651 instance is a <emphasis>partial application</emphasis> of the new type, not the
2652 entire left hand side. We can imagine that the type declaration is
2653 "eta-converted" to generate the context of the instance
2658 We can even derive instances of multi-parameter classes, provided the
2659 newtype is the last class parameter. In this case, a ``partial
2660 application'' of the class appears in the <literal>deriving</literal>
2661 clause. For example, given the class
2664 class StateMonad s m | m -> s where ...
2665 instance Monad m => StateMonad s (State s m) where ...
2667 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2669 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2670 deriving (Monad, StateMonad [tok])
2673 The derived instance is obtained by completing the application of the
2674 class to the new type:
2677 instance StateMonad [tok] (State [tok] (Failure m)) =>
2678 StateMonad [tok] (Parser tok m)
2683 As a result of this extension, all derived instances in newtype
2684 declarations are treated uniformly (and implemented just by reusing
2685 the dictionary for the representation type), <emphasis>except</emphasis>
2686 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2687 the newtype and its representation.
2691 <sect3> <title> A more precise specification </title>
2693 Derived instance declarations are constructed as follows. Consider the
2694 declaration (after expansion of any type synonyms)
2697 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2703 The <literal>ci</literal> are partial applications of
2704 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2705 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2708 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2711 The type <literal>t</literal> is an arbitrary type.
2714 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2715 nor in the <literal>ci</literal>, and
2718 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2719 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2720 should not "look through" the type or its constructor. You can still
2721 derive these classes for a newtype, but it happens in the usual way, not
2722 via this new mechanism.
2725 Then, for each <literal>ci</literal>, the derived instance
2728 instance ci t => ci (T v1...vk)
2730 As an example which does <emphasis>not</emphasis> work, consider
2732 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2734 Here we cannot derive the instance
2736 instance Monad (State s m) => Monad (NonMonad m)
2739 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2740 and so cannot be "eta-converted" away. It is a good thing that this
2741 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2742 not, in fact, a monad --- for the same reason. Try defining
2743 <literal>>>=</literal> with the correct type: you won't be able to.
2747 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2748 important, since we can only derive instances for the last one. If the
2749 <literal>StateMonad</literal> class above were instead defined as
2752 class StateMonad m s | m -> s where ...
2755 then we would not have been able to derive an instance for the
2756 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2757 classes usually have one "main" parameter for which deriving new
2758 instances is most interesting.
2760 <para>Lastly, all of this applies only for classes other than
2761 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2762 and <literal>Data</literal>, for which the built-in derivation applies (section
2763 4.3.3. of the Haskell Report).
2764 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2765 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2766 the standard method is used or the one described here.)
2773 <!-- TYPE SYSTEM EXTENSIONS -->
2774 <sect1 id="type-class-extensions">
2775 <title>Class and instances declarations</title>
2777 <sect2 id="multi-param-type-classes">
2778 <title>Class declarations</title>
2781 This section, and the next one, documents GHC's type-class extensions.
2782 There's lots of background in the paper <ulink
2783 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2784 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2785 Jones, Erik Meijer).
2788 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2792 <title>Multi-parameter type classes</title>
2794 Multi-parameter type classes are permitted. For example:
2798 class Collection c a where
2799 union :: c a -> c a -> c a
2807 <title>The superclasses of a class declaration</title>
2810 There are no restrictions on the context in a class declaration
2811 (which introduces superclasses), except that the class hierarchy must
2812 be acyclic. So these class declarations are OK:
2816 class Functor (m k) => FiniteMap m k where
2819 class (Monad m, Monad (t m)) => Transform t m where
2820 lift :: m a -> (t m) a
2826 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2827 of "acyclic" involves only the superclass relationships. For example,
2833 op :: D b => a -> b -> b
2836 class C a => D a where { ... }
2840 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2841 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2842 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2849 <sect3 id="class-method-types">
2850 <title>Class method types</title>
2853 Haskell 98 prohibits class method types to mention constraints on the
2854 class type variable, thus:
2857 fromList :: [a] -> s a
2858 elem :: Eq a => a -> s a -> Bool
2860 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2861 contains the constraint <literal>Eq a</literal>, constrains only the
2862 class type variable (in this case <literal>a</literal>).
2863 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2870 <sect2 id="functional-dependencies">
2871 <title>Functional dependencies
2874 <para> Functional dependencies are implemented as described by Mark Jones
2875 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2876 In Proceedings of the 9th European Symposium on Programming,
2877 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2881 Functional dependencies are introduced by a vertical bar in the syntax of a
2882 class declaration; e.g.
2884 class (Monad m) => MonadState s m | m -> s where ...
2886 class Foo a b c | a b -> c where ...
2888 There should be more documentation, but there isn't (yet). Yell if you need it.
2891 <sect3><title>Rules for functional dependencies </title>
2893 In a class declaration, all of the class type variables must be reachable (in the sense
2894 mentioned in <xref linkend="type-restrictions"/>)
2895 from the free variables of each method type.
2899 class Coll s a where
2901 insert :: s -> a -> s
2904 is not OK, because the type of <literal>empty</literal> doesn't mention
2905 <literal>a</literal>. Functional dependencies can make the type variable
2908 class Coll s a | s -> a where
2910 insert :: s -> a -> s
2913 Alternatively <literal>Coll</literal> might be rewritten
2916 class Coll s a where
2918 insert :: s a -> a -> s a
2922 which makes the connection between the type of a collection of
2923 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2924 Occasionally this really doesn't work, in which case you can split the
2932 class CollE s => Coll s a where
2933 insert :: s -> a -> s
2940 <title>Background on functional dependencies</title>
2942 <para>The following description of the motivation and use of functional dependencies is taken
2943 from the Hugs user manual, reproduced here (with minor changes) by kind
2944 permission of Mark Jones.
2947 Consider the following class, intended as part of a
2948 library for collection types:
2950 class Collects e ce where
2952 insert :: e -> ce -> ce
2953 member :: e -> ce -> Bool
2955 The type variable e used here represents the element type, while ce is the type
2956 of the container itself. Within this framework, we might want to define
2957 instances of this class for lists or characteristic functions (both of which
2958 can be used to represent collections of any equality type), bit sets (which can
2959 be used to represent collections of characters), or hash tables (which can be
2960 used to represent any collection whose elements have a hash function). Omitting
2961 standard implementation details, this would lead to the following declarations:
2963 instance Eq e => Collects e [e] where ...
2964 instance Eq e => Collects e (e -> Bool) where ...
2965 instance Collects Char BitSet where ...
2966 instance (Hashable e, Collects a ce)
2967 => Collects e (Array Int ce) where ...
2969 All this looks quite promising; we have a class and a range of interesting
2970 implementations. Unfortunately, there are some serious problems with the class
2971 declaration. First, the empty function has an ambiguous type:
2973 empty :: Collects e ce => ce
2975 By "ambiguous" we mean that there is a type variable e that appears on the left
2976 of the <literal>=></literal> symbol, but not on the right. The problem with
2977 this is that, according to the theoretical foundations of Haskell overloading,
2978 we cannot guarantee a well-defined semantics for any term with an ambiguous
2982 We can sidestep this specific problem by removing the empty member from the
2983 class declaration. However, although the remaining members, insert and member,
2984 do not have ambiguous types, we still run into problems when we try to use
2985 them. For example, consider the following two functions:
2987 f x y = insert x . insert y
2990 for which GHC infers the following types:
2992 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2993 g :: (Collects Bool c, Collects Char c) => c -> c
2995 Notice that the type for f allows the two parameters x and y to be assigned
2996 different types, even though it attempts to insert each of the two values, one
2997 after the other, into the same collection. If we're trying to model collections
2998 that contain only one type of value, then this is clearly an inaccurate
2999 type. Worse still, the definition for g is accepted, without causing a type
3000 error. As a result, the error in this code will not be flagged at the point
3001 where it appears. Instead, it will show up only when we try to use g, which
3002 might even be in a different module.
3005 <sect4><title>An attempt to use constructor classes</title>
3008 Faced with the problems described above, some Haskell programmers might be
3009 tempted to use something like the following version of the class declaration:
3011 class Collects e c where
3013 insert :: e -> c e -> c e
3014 member :: e -> c e -> Bool
3016 The key difference here is that we abstract over the type constructor c that is
3017 used to form the collection type c e, and not over that collection type itself,
3018 represented by ce in the original class declaration. This avoids the immediate
3019 problems that we mentioned above: empty has type <literal>Collects e c => c
3020 e</literal>, which is not ambiguous.
3023 The function f from the previous section has a more accurate type:
3025 f :: (Collects e c) => e -> e -> c e -> c e
3027 The function g from the previous section is now rejected with a type error as
3028 we would hope because the type of f does not allow the two arguments to have
3030 This, then, is an example of a multiple parameter class that does actually work
3031 quite well in practice, without ambiguity problems.
3032 There is, however, a catch. This version of the Collects class is nowhere near
3033 as general as the original class seemed to be: only one of the four instances
3034 for <literal>Collects</literal>
3035 given above can be used with this version of Collects because only one of
3036 them---the instance for lists---has a collection type that can be written in
3037 the form c e, for some type constructor c, and element type e.
3041 <sect4><title>Adding functional dependencies</title>
3044 To get a more useful version of the Collects class, Hugs provides a mechanism
3045 that allows programmers to specify dependencies between the parameters of a
3046 multiple parameter class (For readers with an interest in theoretical
3047 foundations and previous work: The use of dependency information can be seen
3048 both as a generalization of the proposal for `parametric type classes' that was
3049 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3050 later framework for "improvement" of qualified types. The
3051 underlying ideas are also discussed in a more theoretical and abstract setting
3052 in a manuscript [implparam], where they are identified as one point in a
3053 general design space for systems of implicit parameterization.).
3055 To start with an abstract example, consider a declaration such as:
3057 class C a b where ...
3059 which tells us simply that C can be thought of as a binary relation on types
3060 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3061 included in the definition of classes to add information about dependencies
3062 between parameters, as in the following examples:
3064 class D a b | a -> b where ...
3065 class E a b | a -> b, b -> a where ...
3067 The notation <literal>a -> b</literal> used here between the | and where
3068 symbols --- not to be
3069 confused with a function type --- indicates that the a parameter uniquely
3070 determines the b parameter, and might be read as "a determines b." Thus D is
3071 not just a relation, but actually a (partial) function. Similarly, from the two
3072 dependencies that are included in the definition of E, we can see that E
3073 represents a (partial) one-one mapping between types.
3076 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3077 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3078 m>=0, meaning that the y parameters are uniquely determined by the x
3079 parameters. Spaces can be used as separators if more than one variable appears
3080 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3081 annotated with multiple dependencies using commas as separators, as in the
3082 definition of E above. Some dependencies that we can write in this notation are
3083 redundant, and will be rejected because they don't serve any useful
3084 purpose, and may instead indicate an error in the program. Examples of
3085 dependencies like this include <literal>a -> a </literal>,
3086 <literal>a -> a a </literal>,
3087 <literal>a -> </literal>, etc. There can also be
3088 some redundancy if multiple dependencies are given, as in
3089 <literal>a->b</literal>,
3090 <literal>b->c </literal>, <literal>a->c </literal>, and
3091 in which some subset implies the remaining dependencies. Examples like this are
3092 not treated as errors. Note that dependencies appear only in class
3093 declarations, and not in any other part of the language. In particular, the
3094 syntax for instance declarations, class constraints, and types is completely
3098 By including dependencies in a class declaration, we provide a mechanism for
3099 the programmer to specify each multiple parameter class more precisely. The
3100 compiler, on the other hand, is responsible for ensuring that the set of
3101 instances that are in scope at any given point in the program is consistent
3102 with any declared dependencies. For example, the following pair of instance
3103 declarations cannot appear together in the same scope because they violate the
3104 dependency for D, even though either one on its own would be acceptable:
3106 instance D Bool Int where ...
3107 instance D Bool Char where ...
3109 Note also that the following declaration is not allowed, even by itself:
3111 instance D [a] b where ...
3113 The problem here is that this instance would allow one particular choice of [a]
3114 to be associated with more than one choice for b, which contradicts the
3115 dependency specified in the definition of D. More generally, this means that,
3116 in any instance of the form:
3118 instance D t s where ...
3120 for some particular types t and s, the only variables that can appear in s are
3121 the ones that appear in t, and hence, if the type t is known, then s will be
3122 uniquely determined.
3125 The benefit of including dependency information is that it allows us to define
3126 more general multiple parameter classes, without ambiguity problems, and with
3127 the benefit of more accurate types. To illustrate this, we return to the
3128 collection class example, and annotate the original definition of <literal>Collects</literal>
3129 with a simple dependency:
3131 class Collects e ce | ce -> e where
3133 insert :: e -> ce -> ce
3134 member :: e -> ce -> Bool
3136 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3137 determined by the type of the collection ce. Note that both parameters of
3138 Collects are of kind *; there are no constructor classes here. Note too that
3139 all of the instances of Collects that we gave earlier can be used
3140 together with this new definition.
3143 What about the ambiguity problems that we encountered with the original
3144 definition? The empty function still has type Collects e ce => ce, but it is no
3145 longer necessary to regard that as an ambiguous type: Although the variable e
3146 does not appear on the right of the => symbol, the dependency for class
3147 Collects tells us that it is uniquely determined by ce, which does appear on
3148 the right of the => symbol. Hence the context in which empty is used can still
3149 give enough information to determine types for both ce and e, without
3150 ambiguity. More generally, we need only regard a type as ambiguous if it
3151 contains a variable on the left of the => that is not uniquely determined
3152 (either directly or indirectly) by the variables on the right.
3155 Dependencies also help to produce more accurate types for user defined
3156 functions, and hence to provide earlier detection of errors, and less cluttered
3157 types for programmers to work with. Recall the previous definition for a
3160 f x y = insert x y = insert x . insert y
3162 for which we originally obtained a type:
3164 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3166 Given the dependency information that we have for Collects, however, we can
3167 deduce that a and b must be equal because they both appear as the second
3168 parameter in a Collects constraint with the same first parameter c. Hence we
3169 can infer a shorter and more accurate type for f:
3171 f :: (Collects a c) => a -> a -> c -> c
3173 In a similar way, the earlier definition of g will now be flagged as a type error.
3176 Although we have given only a few examples here, it should be clear that the
3177 addition of dependency information can help to make multiple parameter classes
3178 more useful in practice, avoiding ambiguity problems, and allowing more general
3179 sets of instance declarations.
3185 <sect2 id="instance-decls">
3186 <title>Instance declarations</title>
3188 <sect3 id="instance-rules">
3189 <title>Relaxed rules for instance declarations</title>
3191 <para>An instance declaration has the form
3193 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 ...
3195 The part before the "<literal>=></literal>" is the
3196 <emphasis>context</emphasis>, while the part after the
3197 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3201 In Haskell 98 the head of an instance declaration
3202 must be of the form <literal>C (T a1 ... an)</literal>, where
3203 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3204 and the <literal>a1 ... an</literal> are distinct type variables.
3205 Furthermore, the assertions in the context of the instance declaration
3206 must be of the form <literal>C a</literal> where <literal>a</literal>
3207 is a type variable that occurs in the head.
3210 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3211 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3212 the context and head of the instance declaration can each consist of arbitrary
3213 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3217 The Paterson Conditions: for each assertion in the context
3219 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3220 <listitem><para>The assertion has fewer constructors and variables (taken together
3221 and counting repetitions) than the head</para></listitem>
3225 <listitem><para>The Coverage Condition. For each functional dependency,
3226 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3227 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3228 every type variable in
3229 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3230 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3231 substitution mapping each type variable in the class declaration to the
3232 corresponding type in the instance declaration.
3235 These restrictions ensure that context reduction terminates: each reduction
3236 step makes the problem smaller by at least one
3237 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3238 if you give the <option>-fallow-undecidable-instances</option>
3239 flag (<xref linkend="undecidable-instances"/>).
3240 You can find lots of background material about the reason for these
3241 restrictions in the paper <ulink
3242 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3243 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3246 For example, these are OK:
3248 instance C Int [a] -- Multiple parameters
3249 instance Eq (S [a]) -- Structured type in head
3251 -- Repeated type variable in head
3252 instance C4 a a => C4 [a] [a]
3253 instance Stateful (ST s) (MutVar s)
3255 -- Head can consist of type variables only
3257 instance (Eq a, Show b) => C2 a b
3259 -- Non-type variables in context
3260 instance Show (s a) => Show (Sized s a)
3261 instance C2 Int a => C3 Bool [a]
3262 instance C2 Int a => C3 [a] b
3266 -- Context assertion no smaller than head
3267 instance C a => C a where ...
3268 -- (C b b) has more more occurrences of b than the head
3269 instance C b b => Foo [b] where ...
3274 The same restrictions apply to instances generated by
3275 <literal>deriving</literal> clauses. Thus the following is accepted:
3277 data MinHeap h a = H a (h a)
3280 because the derived instance
3282 instance (Show a, Show (h a)) => Show (MinHeap h a)
3284 conforms to the above rules.
3288 A useful idiom permitted by the above rules is as follows.
3289 If one allows overlapping instance declarations then it's quite
3290 convenient to have a "default instance" declaration that applies if
3291 something more specific does not:
3299 <sect3 id="undecidable-instances">
3300 <title>Undecidable instances</title>
3303 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3304 For example, sometimes you might want to use the following to get the
3305 effect of a "class synonym":
3307 class (C1 a, C2 a, C3 a) => C a where { }
3309 instance (C1 a, C2 a, C3 a) => C a where { }
3311 This allows you to write shorter signatures:
3317 f :: (C1 a, C2 a, C3 a) => ...
3319 The restrictions on functional dependencies (<xref
3320 linkend="functional-dependencies"/>) are particularly troublesome.
3321 It is tempting to introduce type variables in the context that do not appear in
3322 the head, something that is excluded by the normal rules. For example:
3324 class HasConverter a b | a -> b where
3327 data Foo a = MkFoo a
3329 instance (HasConverter a b,Show b) => Show (Foo a) where
3330 show (MkFoo value) = show (convert value)
3332 This is dangerous territory, however. Here, for example, is a program that would make the
3337 instance F [a] [[a]]
3338 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3340 Similarly, it can be tempting to lift the coverage condition:
3342 class Mul a b c | a b -> c where
3343 (.*.) :: a -> b -> c
3345 instance Mul Int Int Int where (.*.) = (*)
3346 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3347 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3349 The third instance declaration does not obey the coverage condition;
3350 and indeed the (somewhat strange) definition:
3352 f = \ b x y -> if b then x .*. [y] else y
3354 makes instance inference go into a loop, because it requires the constraint
3355 <literal>(Mul a [b] b)</literal>.
3358 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3359 the experimental flag <option>-XUndecidableInstances</option>
3360 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3361 both the Paterson Conditions and the Coverage Condition
3362 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3363 fixed-depth recursion stack. If you exceed the stack depth you get a
3364 sort of backtrace, and the opportunity to increase the stack depth
3365 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3371 <sect3 id="instance-overlap">
3372 <title>Overlapping instances</title>
3374 In general, <emphasis>GHC requires that that it be unambiguous which instance
3376 should be used to resolve a type-class constraint</emphasis>. This behaviour
3377 can be modified by two flags: <option>-XOverlappingInstances</option>
3378 <indexterm><primary>-XOverlappingInstances
3379 </primary></indexterm>
3380 and <option>-XIncoherentInstances</option>
3381 <indexterm><primary>-XIncoherentInstances
3382 </primary></indexterm>, as this section discusses. Both these
3383 flags are dynamic flags, and can be set on a per-module basis, using
3384 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3386 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3387 it tries to match every instance declaration against the
3389 by instantiating the head of the instance declaration. For example, consider
3392 instance context1 => C Int a where ... -- (A)
3393 instance context2 => C a Bool where ... -- (B)
3394 instance context3 => C Int [a] where ... -- (C)
3395 instance context4 => C Int [Int] where ... -- (D)
3397 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3398 but (C) and (D) do not. When matching, GHC takes
3399 no account of the context of the instance declaration
3400 (<literal>context1</literal> etc).
3401 GHC's default behaviour is that <emphasis>exactly one instance must match the
3402 constraint it is trying to resolve</emphasis>.
3403 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3404 including both declarations (A) and (B), say); an error is only reported if a
3405 particular constraint matches more than one.
3409 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3410 more than one instance to match, provided there is a most specific one. For
3411 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3412 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3413 most-specific match, the program is rejected.
3416 However, GHC is conservative about committing to an overlapping instance. For example:
3421 Suppose that from the RHS of <literal>f</literal> we get the constraint
3422 <literal>C Int [b]</literal>. But
3423 GHC does not commit to instance (C), because in a particular
3424 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3425 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3426 So GHC rejects the program.
3427 (If you add the flag <option>-XIncoherentInstances</option>,
3428 GHC will instead pick (C), without complaining about
3429 the problem of subsequent instantiations.)
3432 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3433 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3434 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3435 it instead. In this case, GHC will refrain from
3436 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3437 as before) but, rather than rejecting the program, it will infer the type
3439 f :: C Int b => [b] -> [b]
3441 That postpones the question of which instance to pick to the
3442 call site for <literal>f</literal>
3443 by which time more is known about the type <literal>b</literal>.
3446 The willingness to be overlapped or incoherent is a property of
3447 the <emphasis>instance declaration</emphasis> itself, controlled by the
3448 presence or otherwise of the <option>-XOverlappingInstances</option>
3449 and <option>-XIncoherentInstances</option> flags when that module is
3450 being defined. Neither flag is required in a module that imports and uses the
3451 instance declaration. Specifically, during the lookup process:
3454 An instance declaration is ignored during the lookup process if (a) a more specific
3455 match is found, and (b) the instance declaration was compiled with
3456 <option>-XOverlappingInstances</option>. The flag setting for the
3457 more-specific instance does not matter.
3460 Suppose an instance declaration does not match the constraint being looked up, but
3461 does unify with it, so that it might match when the constraint is further
3462 instantiated. Usually GHC will regard this as a reason for not committing to
3463 some other constraint. But if the instance declaration was compiled with
3464 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3465 check for that declaration.
3468 These rules make it possible for a library author to design a library that relies on
3469 overlapping instances without the library client having to know.
3472 If an instance declaration is compiled without
3473 <option>-XOverlappingInstances</option>,
3474 then that instance can never be overlapped. This could perhaps be
3475 inconvenient. Perhaps the rule should instead say that the
3476 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3477 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3478 at a usage site should be permitted regardless of how the instance declarations
3479 are compiled, if the <option>-XOverlappingInstances</option> flag is
3480 used at the usage site. (Mind you, the exact usage site can occasionally be
3481 hard to pin down.) We are interested to receive feedback on these points.
3483 <para>The <option>-XIncoherentInstances</option> flag implies the
3484 <option>-XOverlappingInstances</option> flag, but not vice versa.
3489 <title>Type synonyms in the instance head</title>
3492 <emphasis>Unlike Haskell 98, instance heads may use type
3493 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3494 As always, using a type synonym is just shorthand for
3495 writing the RHS of the type synonym definition. For example:
3499 type Point = (Int,Int)
3500 instance C Point where ...
3501 instance C [Point] where ...
3505 is legal. However, if you added
3509 instance C (Int,Int) where ...
3513 as well, then the compiler will complain about the overlapping
3514 (actually, identical) instance declarations. As always, type synonyms
3515 must be fully applied. You cannot, for example, write:
3520 instance Monad P where ...
3524 This design decision is independent of all the others, and easily
3525 reversed, but it makes sense to me.
3533 <sect2 id="overloaded-strings">
3534 <title>Overloaded string literals
3538 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3539 string literal has type <literal>String</literal>, but with overloaded string
3540 literals enabled (with <literal>-XOverloadedStrings</literal>)
3541 a string literal has type <literal>(IsString a) => a</literal>.
3544 This means that the usual string syntax can be used, e.g., for packed strings
3545 and other variations of string like types. String literals behave very much
3546 like integer literals, i.e., they can be used in both expressions and patterns.
3547 If used in a pattern the literal with be replaced by an equality test, in the same
3548 way as an integer literal is.
3551 The class <literal>IsString</literal> is defined as:
3553 class IsString a where
3554 fromString :: String -> a
3556 The only predefined instance is the obvious one to make strings work as usual:
3558 instance IsString [Char] where
3561 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3562 it explicitly (for example, to give an instance declaration for it), you can import it
3563 from module <literal>GHC.Exts</literal>.
3566 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3570 Each type in a default declaration must be an
3571 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3575 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3576 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3577 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3578 <emphasis>or</emphasis> <literal>IsString</literal>.
3587 import GHC.Exts( IsString(..) )
3589 newtype MyString = MyString String deriving (Eq, Show)
3590 instance IsString MyString where
3591 fromString = MyString
3593 greet :: MyString -> MyString
3594 greet "hello" = "world"
3598 print $ greet "hello"
3599 print $ greet "fool"
3603 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3604 to work since it gets translated into an equality comparison.
3610 <sect1 id="other-type-extensions">
3611 <title>Other type system extensions</title>
3613 <sect2 id="type-restrictions">
3614 <title>Type signatures</title>
3616 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3618 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3619 the form <emphasis>(class type-variable)</emphasis> or
3620 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3621 these type signatures are perfectly OK
3624 g :: Ord (T a ()) => ...
3628 GHC imposes the following restrictions on the constraints in a type signature.
3632 forall tv1..tvn (c1, ...,cn) => type
3635 (Here, we write the "foralls" explicitly, although the Haskell source
3636 language omits them; in Haskell 98, all the free type variables of an
3637 explicit source-language type signature are universally quantified,
3638 except for the class type variables in a class declaration. However,
3639 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3648 <emphasis>Each universally quantified type variable
3649 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3651 A type variable <literal>a</literal> is "reachable" if it it appears
3652 in the same constraint as either a type variable free in in
3653 <literal>type</literal>, or another reachable type variable.
3654 A value with a type that does not obey
3655 this reachability restriction cannot be used without introducing
3656 ambiguity; that is why the type is rejected.
3657 Here, for example, is an illegal type:
3661 forall a. Eq a => Int
3665 When a value with this type was used, the constraint <literal>Eq tv</literal>
3666 would be introduced where <literal>tv</literal> is a fresh type variable, and
3667 (in the dictionary-translation implementation) the value would be
3668 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3669 can never know which instance of <literal>Eq</literal> to use because we never
3670 get any more information about <literal>tv</literal>.
3674 that the reachability condition is weaker than saying that <literal>a</literal> is
3675 functionally dependent on a type variable free in
3676 <literal>type</literal> (see <xref
3677 linkend="functional-dependencies"/>). The reason for this is there
3678 might be a "hidden" dependency, in a superclass perhaps. So
3679 "reachable" is a conservative approximation to "functionally dependent".
3680 For example, consider:
3682 class C a b | a -> b where ...
3683 class C a b => D a b where ...
3684 f :: forall a b. D a b => a -> a
3686 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3687 but that is not immediately apparent from <literal>f</literal>'s type.
3693 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3694 universally quantified type variables <literal>tvi</literal></emphasis>.
3696 For example, this type is OK because <literal>C a b</literal> mentions the
3697 universally quantified type variable <literal>b</literal>:
3701 forall a. C a b => burble
3705 The next type is illegal because the constraint <literal>Eq b</literal> does not
3706 mention <literal>a</literal>:
3710 forall a. Eq b => burble
3714 The reason for this restriction is milder than the other one. The
3715 excluded types are never useful or necessary (because the offending
3716 context doesn't need to be witnessed at this point; it can be floated
3717 out). Furthermore, floating them out increases sharing. Lastly,
3718 excluding them is a conservative choice; it leaves a patch of
3719 territory free in case we need it later.
3733 <sect2 id="implicit-parameters">
3734 <title>Implicit parameters</title>
3736 <para> Implicit parameters are implemented as described in
3737 "Implicit parameters: dynamic scoping with static types",
3738 J Lewis, MB Shields, E Meijer, J Launchbury,
3739 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3743 <para>(Most of the following, still rather incomplete, documentation is
3744 due to Jeff Lewis.)</para>
3746 <para>Implicit parameter support is enabled with the option
3747 <option>-XImplicitParams</option>.</para>
3750 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3751 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3752 context. In Haskell, all variables are statically bound. Dynamic
3753 binding of variables is a notion that goes back to Lisp, but was later
3754 discarded in more modern incarnations, such as Scheme. Dynamic binding
3755 can be very confusing in an untyped language, and unfortunately, typed
3756 languages, in particular Hindley-Milner typed languages like Haskell,
3757 only support static scoping of variables.
3760 However, by a simple extension to the type class system of Haskell, we
3761 can support dynamic binding. Basically, we express the use of a
3762 dynamically bound variable as a constraint on the type. These
3763 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3764 function uses a dynamically-bound variable <literal>?x</literal>
3765 of type <literal>t'</literal>". For
3766 example, the following expresses the type of a sort function,
3767 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3769 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3771 The dynamic binding constraints are just a new form of predicate in the type class system.
3774 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3775 where <literal>x</literal> is
3776 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3777 Use of this construct also introduces a new
3778 dynamic-binding constraint in the type of the expression.
3779 For example, the following definition
3780 shows how we can define an implicitly parameterized sort function in
3781 terms of an explicitly parameterized <literal>sortBy</literal> function:
3783 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3785 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3791 <title>Implicit-parameter type constraints</title>
3793 Dynamic binding constraints behave just like other type class
3794 constraints in that they are automatically propagated. Thus, when a
3795 function is used, its implicit parameters are inherited by the
3796 function that called it. For example, our <literal>sort</literal> function might be used
3797 to pick out the least value in a list:
3799 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3800 least xs = head (sort xs)
3802 Without lifting a finger, the <literal>?cmp</literal> parameter is
3803 propagated to become a parameter of <literal>least</literal> as well. With explicit
3804 parameters, the default is that parameters must always be explicit
3805 propagated. With implicit parameters, the default is to always
3809 An implicit-parameter type constraint differs from other type class constraints in the
3810 following way: All uses of a particular implicit parameter must have
3811 the same type. This means that the type of <literal>(?x, ?x)</literal>
3812 is <literal>(?x::a) => (a,a)</literal>, and not
3813 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3817 <para> You can't have an implicit parameter in the context of a class or instance
3818 declaration. For example, both these declarations are illegal:
3820 class (?x::Int) => C a where ...
3821 instance (?x::a) => Foo [a] where ...
3823 Reason: exactly which implicit parameter you pick up depends on exactly where
3824 you invoke a function. But the ``invocation'' of instance declarations is done
3825 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3826 Easiest thing is to outlaw the offending types.</para>
3828 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3830 f :: (?x :: [a]) => Int -> Int
3833 g :: (Read a, Show a) => String -> String
3836 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3837 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3838 quite unambiguous, and fixes the type <literal>a</literal>.
3843 <title>Implicit-parameter bindings</title>
3846 An implicit parameter is <emphasis>bound</emphasis> using the standard
3847 <literal>let</literal> or <literal>where</literal> binding forms.
3848 For example, we define the <literal>min</literal> function by binding
3849 <literal>cmp</literal>.
3852 min = let ?cmp = (<=) in least
3856 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3857 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3858 (including in a list comprehension, or do-notation, or pattern guards),
3859 or a <literal>where</literal> clause.
3860 Note the following points:
3863 An implicit-parameter binding group must be a
3864 collection of simple bindings to implicit-style variables (no
3865 function-style bindings, and no type signatures); these bindings are
3866 neither polymorphic or recursive.
3869 You may not mix implicit-parameter bindings with ordinary bindings in a
3870 single <literal>let</literal>
3871 expression; use two nested <literal>let</literal>s instead.
3872 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3876 You may put multiple implicit-parameter bindings in a
3877 single binding group; but they are <emphasis>not</emphasis> treated
3878 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3879 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3880 parameter. The bindings are not nested, and may be re-ordered without changing
3881 the meaning of the program.
3882 For example, consider:
3884 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3886 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3887 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3889 f :: (?x::Int) => Int -> Int
3897 <sect3><title>Implicit parameters and polymorphic recursion</title>
3900 Consider these two definitions:
3903 len1 xs = let ?acc = 0 in len_acc1 xs
3906 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3911 len2 xs = let ?acc = 0 in len_acc2 xs
3913 len_acc2 :: (?acc :: Int) => [a] -> Int
3915 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3917 The only difference between the two groups is that in the second group
3918 <literal>len_acc</literal> is given a type signature.
3919 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3920 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3921 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3922 has a type signature, the recursive call is made to the
3923 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3924 as an implicit parameter. So we get the following results in GHCi:
3931 Adding a type signature dramatically changes the result! This is a rather
3932 counter-intuitive phenomenon, worth watching out for.
3936 <sect3><title>Implicit parameters and monomorphism</title>
3938 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3939 Haskell Report) to implicit parameters. For example, consider:
3947 Since the binding for <literal>y</literal> falls under the Monomorphism
3948 Restriction it is not generalised, so the type of <literal>y</literal> is
3949 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3950 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3951 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3952 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3953 <literal>y</literal> in the body of the <literal>let</literal> will see the
3954 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3955 <literal>14</literal>.
3960 <!-- ======================= COMMENTED OUT ========================
3962 We intend to remove linear implicit parameters, so I'm at least removing
3963 them from the 6.6 user manual
3965 <sect2 id="linear-implicit-parameters">
3966 <title>Linear implicit parameters</title>
3968 Linear implicit parameters are an idea developed by Koen Claessen,
3969 Mark Shields, and Simon PJ. They address the long-standing
3970 problem that monads seem over-kill for certain sorts of problem, notably:
3973 <listitem> <para> distributing a supply of unique names </para> </listitem>
3974 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3975 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3979 Linear implicit parameters are just like ordinary implicit parameters,
3980 except that they are "linear"; that is, they cannot be copied, and
3981 must be explicitly "split" instead. Linear implicit parameters are
3982 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3983 (The '/' in the '%' suggests the split!)
3988 import GHC.Exts( Splittable )
3990 data NameSupply = ...
3992 splitNS :: NameSupply -> (NameSupply, NameSupply)
3993 newName :: NameSupply -> Name
3995 instance Splittable NameSupply where
3999 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4000 f env (Lam x e) = Lam x' (f env e)
4003 env' = extend env x x'
4004 ...more equations for f...
4006 Notice that the implicit parameter %ns is consumed
4008 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4009 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4013 So the translation done by the type checker makes
4014 the parameter explicit:
4016 f :: NameSupply -> Env -> Expr -> Expr
4017 f ns env (Lam x e) = Lam x' (f ns1 env e)
4019 (ns1,ns2) = splitNS ns
4021 env = extend env x x'
4023 Notice the call to 'split' introduced by the type checker.
4024 How did it know to use 'splitNS'? Because what it really did
4025 was to introduce a call to the overloaded function 'split',
4026 defined by the class <literal>Splittable</literal>:
4028 class Splittable a where
4031 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4032 split for name supplies. But we can simply write
4038 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4040 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4041 <literal>GHC.Exts</literal>.
4046 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4047 are entirely distinct implicit parameters: you
4048 can use them together and they won't interfere with each other. </para>
4051 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4053 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4054 in the context of a class or instance declaration. </para></listitem>
4058 <sect3><title>Warnings</title>
4061 The monomorphism restriction is even more important than usual.
4062 Consider the example above:
4064 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4065 f env (Lam x e) = Lam x' (f env e)
4068 env' = extend env x x'
4070 If we replaced the two occurrences of x' by (newName %ns), which is
4071 usually a harmless thing to do, we get:
4073 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4074 f env (Lam x e) = Lam (newName %ns) (f env e)
4076 env' = extend env x (newName %ns)
4078 But now the name supply is consumed in <emphasis>three</emphasis> places
4079 (the two calls to newName,and the recursive call to f), so
4080 the result is utterly different. Urk! We don't even have
4084 Well, this is an experimental change. With implicit
4085 parameters we have already lost beta reduction anyway, and
4086 (as John Launchbury puts it) we can't sensibly reason about
4087 Haskell programs without knowing their typing.
4092 <sect3><title>Recursive functions</title>
4093 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4096 foo :: %x::T => Int -> [Int]
4098 foo n = %x : foo (n-1)
4100 where T is some type in class Splittable.</para>
4102 Do you get a list of all the same T's or all different T's
4103 (assuming that split gives two distinct T's back)?
4105 If you supply the type signature, taking advantage of polymorphic
4106 recursion, you get what you'd probably expect. Here's the
4107 translated term, where the implicit param is made explicit:
4110 foo x n = let (x1,x2) = split x
4111 in x1 : foo x2 (n-1)
4113 But if you don't supply a type signature, GHC uses the Hindley
4114 Milner trick of using a single monomorphic instance of the function
4115 for the recursive calls. That is what makes Hindley Milner type inference
4116 work. So the translation becomes
4120 foom n = x : foom (n-1)
4124 Result: 'x' is not split, and you get a list of identical T's. So the
4125 semantics of the program depends on whether or not foo has a type signature.
4128 You may say that this is a good reason to dislike linear implicit parameters
4129 and you'd be right. That is why they are an experimental feature.
4135 ================ END OF Linear Implicit Parameters commented out -->
4137 <sect2 id="kinding">
4138 <title>Explicitly-kinded quantification</title>
4141 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4142 to give the kind explicitly as (machine-checked) documentation,
4143 just as it is nice to give a type signature for a function. On some occasions,
4144 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4145 John Hughes had to define the data type:
4147 data Set cxt a = Set [a]
4148 | Unused (cxt a -> ())
4150 The only use for the <literal>Unused</literal> constructor was to force the correct
4151 kind for the type variable <literal>cxt</literal>.
4154 GHC now instead allows you to specify the kind of a type variable directly, wherever
4155 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4158 This flag enables kind signatures in the following places:
4160 <listitem><para><literal>data</literal> declarations:
4162 data Set (cxt :: * -> *) a = Set [a]
4163 </screen></para></listitem>
4164 <listitem><para><literal>type</literal> declarations:
4166 type T (f :: * -> *) = f Int
4167 </screen></para></listitem>
4168 <listitem><para><literal>class</literal> declarations:
4170 class (Eq a) => C (f :: * -> *) a where ...
4171 </screen></para></listitem>
4172 <listitem><para><literal>forall</literal>'s in type signatures:
4174 f :: forall (cxt :: * -> *). Set cxt Int
4175 </screen></para></listitem>
4180 The parentheses are required. Some of the spaces are required too, to
4181 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4182 will get a parse error, because "<literal>::*->*</literal>" is a
4183 single lexeme in Haskell.
4187 As part of the same extension, you can put kind annotations in types
4190 f :: (Int :: *) -> Int
4191 g :: forall a. a -> (a :: *)
4195 atype ::= '(' ctype '::' kind ')
4197 The parentheses are required.
4202 <sect2 id="universal-quantification">
4203 <title>Arbitrary-rank polymorphism
4207 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4208 allows us to say exactly what this means. For example:
4216 g :: forall b. (b -> b)
4218 The two are treated identically.
4222 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4223 explicit universal quantification in
4225 For example, all the following types are legal:
4227 f1 :: forall a b. a -> b -> a
4228 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4230 f2 :: (forall a. a->a) -> Int -> Int
4231 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4233 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4235 f4 :: Int -> (forall a. a -> a)
4237 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4238 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4239 The <literal>forall</literal> makes explicit the universal quantification that
4240 is implicitly added by Haskell.
4243 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4244 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4245 shows, the polymorphic type on the left of the function arrow can be overloaded.
4248 The function <literal>f3</literal> has a rank-3 type;
4249 it has rank-2 types on the left of a function arrow.
4252 GHC has three flags to control higher-rank types:
4255 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argment types.
4258 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4261 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4262 That is, you can nest <literal>forall</literal>s
4263 arbitrarily deep in function arrows.
4264 In particular, a forall-type (also called a "type scheme"),
4265 including an operational type class context, is legal:
4267 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4268 of a function arrow </para> </listitem>
4269 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4270 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4271 field type signatures.</para> </listitem>
4272 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4273 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4277 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4278 a type variable any more!
4287 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4288 the types of the constructor arguments. Here are several examples:
4294 data T a = T1 (forall b. b -> b -> b) a
4296 data MonadT m = MkMonad { return :: forall a. a -> m a,
4297 bind :: forall a b. m a -> (a -> m b) -> m b
4300 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4306 The constructors have rank-2 types:
4312 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4313 MkMonad :: forall m. (forall a. a -> m a)
4314 -> (forall a b. m a -> (a -> m b) -> m b)
4316 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4322 Notice that you don't need to use a <literal>forall</literal> if there's an
4323 explicit context. For example in the first argument of the
4324 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4325 prefixed to the argument type. The implicit <literal>forall</literal>
4326 quantifies all type variables that are not already in scope, and are
4327 mentioned in the type quantified over.
4331 As for type signatures, implicit quantification happens for non-overloaded
4332 types too. So if you write this:
4335 data T a = MkT (Either a b) (b -> b)
4338 it's just as if you had written this:
4341 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4344 That is, since the type variable <literal>b</literal> isn't in scope, it's
4345 implicitly universally quantified. (Arguably, it would be better
4346 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4347 where that is what is wanted. Feedback welcomed.)
4351 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4352 the constructor to suitable values, just as usual. For example,
4363 a3 = MkSwizzle reverse
4366 a4 = let r x = Just x
4373 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4374 mkTs f x y = [T1 f x, T1 f y]
4380 The type of the argument can, as usual, be more general than the type
4381 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4382 does not need the <literal>Ord</literal> constraint.)
4386 When you use pattern matching, the bound variables may now have
4387 polymorphic types. For example:
4393 f :: T a -> a -> (a, Char)
4394 f (T1 w k) x = (w k x, w 'c' 'd')
4396 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4397 g (MkSwizzle s) xs f = s (map f (s xs))
4399 h :: MonadT m -> [m a] -> m [a]
4400 h m [] = return m []
4401 h m (x:xs) = bind m x $ \y ->
4402 bind m (h m xs) $ \ys ->
4409 In the function <function>h</function> we use the record selectors <literal>return</literal>
4410 and <literal>bind</literal> to extract the polymorphic bind and return functions
4411 from the <literal>MonadT</literal> data structure, rather than using pattern
4417 <title>Type inference</title>
4420 In general, type inference for arbitrary-rank types is undecidable.
4421 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4422 to get a decidable algorithm by requiring some help from the programmer.
4423 We do not yet have a formal specification of "some help" but the rule is this:
4426 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4427 provides an explicit polymorphic type for x, or GHC's type inference will assume
4428 that x's type has no foralls in it</emphasis>.
4431 What does it mean to "provide" an explicit type for x? You can do that by
4432 giving a type signature for x directly, using a pattern type signature
4433 (<xref linkend="scoped-type-variables"/>), thus:
4435 \ f :: (forall a. a->a) -> (f True, f 'c')
4437 Alternatively, you can give a type signature to the enclosing
4438 context, which GHC can "push down" to find the type for the variable:
4440 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4442 Here the type signature on the expression can be pushed inwards
4443 to give a type signature for f. Similarly, and more commonly,
4444 one can give a type signature for the function itself:
4446 h :: (forall a. a->a) -> (Bool,Char)
4447 h f = (f True, f 'c')
4449 You don't need to give a type signature if the lambda bound variable
4450 is a constructor argument. Here is an example we saw earlier:
4452 f :: T a -> a -> (a, Char)
4453 f (T1 w k) x = (w k x, w 'c' 'd')
4455 Here we do not need to give a type signature to <literal>w</literal>, because
4456 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4463 <sect3 id="implicit-quant">
4464 <title>Implicit quantification</title>
4467 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4468 user-written types, if and only if there is no explicit <literal>forall</literal>,
4469 GHC finds all the type variables mentioned in the type that are not already
4470 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4474 f :: forall a. a -> a
4481 h :: forall b. a -> b -> b
4487 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4490 f :: (a -> a) -> Int
4492 f :: forall a. (a -> a) -> Int
4494 f :: (forall a. a -> a) -> Int
4497 g :: (Ord a => a -> a) -> Int
4498 -- MEANS the illegal type
4499 g :: forall a. (Ord a => a -> a) -> Int
4501 g :: (forall a. Ord a => a -> a) -> Int
4503 The latter produces an illegal type, which you might think is silly,
4504 but at least the rule is simple. If you want the latter type, you
4505 can write your for-alls explicitly. Indeed, doing so is strongly advised
4512 <sect2 id="impredicative-polymorphism">
4513 <title>Impredicative polymorphism
4515 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4516 enabled with <option>-XImpredicativeTypes</option>.
4518 that you can call a polymorphic function at a polymorphic type, and
4519 parameterise data structures over polymorphic types. For example:
4521 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4522 f (Just g) = Just (g [3], g "hello")
4525 Notice here that the <literal>Maybe</literal> type is parameterised by the
4526 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4529 <para>The technical details of this extension are described in the paper
4530 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4531 type inference for higher-rank types and impredicativity</ulink>,
4532 which appeared at ICFP 2006.
4536 <sect2 id="scoped-type-variables">
4537 <title>Lexically scoped type variables
4541 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4542 which some type signatures are simply impossible to write. For example:
4544 f :: forall a. [a] -> [a]
4550 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4551 the entire definition of <literal>f</literal>.
4552 In particular, it is in scope at the type signature for <varname>ys</varname>.
4553 In Haskell 98 it is not possible to declare
4554 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4555 it becomes possible to do so.
4557 <para>Lexically-scoped type variables are enabled by
4558 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4560 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4561 variables work, compared to earlier releases. Read this section
4565 <title>Overview</title>
4567 <para>The design follows the following principles
4569 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4570 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4571 design.)</para></listitem>
4572 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4573 type variables. This means that every programmer-written type signature
4574 (including one that contains free scoped type variables) denotes a
4575 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4576 checker, and no inference is involved.</para></listitem>
4577 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4578 changing the program.</para></listitem>
4582 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4584 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4585 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4586 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4587 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4591 In Haskell, a programmer-written type signature is implicitly quantified over
4592 its free type variables (<ulink
4593 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4595 of the Haskel Report).
4596 Lexically scoped type variables affect this implicit quantification rules
4597 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4598 quantified. For example, if type variable <literal>a</literal> is in scope,
4601 (e :: a -> a) means (e :: a -> a)
4602 (e :: b -> b) means (e :: forall b. b->b)
4603 (e :: a -> b) means (e :: forall b. a->b)
4611 <sect3 id="decl-type-sigs">
4612 <title>Declaration type signatures</title>
4613 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4614 quantification (using <literal>forall</literal>) brings into scope the
4615 explicitly-quantified
4616 type variables, in the definition of the named function. For example:
4618 f :: forall a. [a] -> [a]
4619 f (x:xs) = xs ++ [ x :: a ]
4621 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4622 the definition of "<literal>f</literal>".
4624 <para>This only happens if:
4626 <listitem><para> The quantification in <literal>f</literal>'s type
4627 signature is explicit. For example:
4630 g (x:xs) = xs ++ [ x :: a ]
4632 This program will be rejected, because "<literal>a</literal>" does not scope
4633 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4634 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4635 quantification rules.
4637 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4638 not a pattern binding.
4641 f1 :: forall a. [a] -> [a]
4642 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4644 f2 :: forall a. [a] -> [a]
4645 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4647 f3 :: forall a. [a] -> [a]
4648 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4650 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4651 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4652 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4653 the type signature brings <literal>a</literal> into scope.
4659 <sect3 id="exp-type-sigs">
4660 <title>Expression type signatures</title>
4662 <para>An expression type signature that has <emphasis>explicit</emphasis>
4663 quantification (using <literal>forall</literal>) brings into scope the
4664 explicitly-quantified
4665 type variables, in the annotated expression. For example:
4667 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4669 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4670 type variable <literal>s</literal> into scope, in the annotated expression
4671 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4676 <sect3 id="pattern-type-sigs">
4677 <title>Pattern type signatures</title>
4679 A type signature may occur in any pattern; this is a <emphasis>pattern type
4680 signature</emphasis>.
4683 -- f and g assume that 'a' is already in scope
4684 f = \(x::Int, y::a) -> x
4686 h ((x,y) :: (Int,Bool)) = (y,x)
4688 In the case where all the type variables in the pattern type signature are
4689 already in scope (i.e. bound by the enclosing context), matters are simple: the
4690 signature simply constrains the type of the pattern in the obvious way.
4693 Unlike expression and declaration type signatures, pattern type signatures are not implictly generalised.
4694 The pattern in a <emphasis>patterm binding</emphasis> may only mention type variables
4695 that are already in scope. For example:
4697 f :: forall a. [a] -> (Int, [a])
4700 (ys::[a], n) = (reverse xs, length xs) -- OK
4701 zs::[a] = xs ++ ys -- OK
4703 Just (v::b) = ... -- Not OK; b is not in scope
4705 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4706 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4710 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4711 type signature may mention a type variable that is not in scope; in this case,
4712 <emphasis>the signature brings that type variable into scope</emphasis>.
4713 This is particularly important for existential data constructors. For example:
4715 data T = forall a. MkT [a]
4718 k (MkT [t::a]) = MkT t3
4722 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4723 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4724 because it is bound by the pattern match. GHC's rule is that in this situation
4725 (and only then), a pattern type signature can mention a type variable that is
4726 not already in scope; the effect is to bring it into scope, standing for the
4727 existentially-bound type variable.
4730 When a pattern type signature binds a type variable in this way, GHC insists that the
4731 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4732 This means that any user-written type signature always stands for a completely known type.
4735 If all this seems a little odd, we think so too. But we must have
4736 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4737 could not name existentially-bound type variables in subsequent type signatures.
4740 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4741 signature is allowed to mention a lexical variable that is not already in
4743 For example, both <literal>f</literal> and <literal>g</literal> would be
4744 illegal if <literal>a</literal> was not already in scope.
4750 <!-- ==================== Commented out part about result type signatures
4752 <sect3 id="result-type-sigs">
4753 <title>Result type signatures</title>
4756 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4759 {- f assumes that 'a' is already in scope -}
4760 f x y :: [a] = [x,y,x]
4762 g = \ x :: [Int] -> [3,4]
4764 h :: forall a. [a] -> a
4768 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4769 the result of the function. Similarly, the body of the lambda in the RHS of
4770 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4771 alternative in <literal>h</literal> is <literal>a</literal>.
4773 <para> A result type signature never brings new type variables into scope.</para>
4775 There are a couple of syntactic wrinkles. First, notice that all three
4776 examples would parse quite differently with parentheses:
4778 {- f assumes that 'a' is already in scope -}
4779 f x (y :: [a]) = [x,y,x]
4781 g = \ (x :: [Int]) -> [3,4]
4783 h :: forall a. [a] -> a
4787 Now the signature is on the <emphasis>pattern</emphasis>; and
4788 <literal>h</literal> would certainly be ill-typed (since the pattern
4789 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4791 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4792 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4793 token or a parenthesised type of some sort). To see why,
4794 consider how one would parse this:
4803 <sect3 id="cls-inst-scoped-tyvars">
4804 <title>Class and instance declarations</title>
4807 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4808 scope over the methods defined in the <literal>where</literal> part. For example:
4826 <sect2 id="typing-binds">
4827 <title>Generalised typing of mutually recursive bindings</title>
4830 The Haskell Report specifies that a group of bindings (at top level, or in a
4831 <literal>let</literal> or <literal>where</literal>) should be sorted into
4832 strongly-connected components, and then type-checked in dependency order
4833 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4834 Report, Section 4.5.1</ulink>).
4835 As each group is type-checked, any binders of the group that
4837 an explicit type signature are put in the type environment with the specified
4839 and all others are monomorphic until the group is generalised
4840 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4843 <para>Following a suggestion of Mark Jones, in his paper
4844 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4846 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4848 <emphasis>the dependency analysis ignores references to variables that have an explicit
4849 type signature</emphasis>.
4850 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4851 typecheck. For example, consider:
4853 f :: Eq a => a -> Bool
4854 f x = (x == x) || g True || g "Yes"
4856 g y = (y <= y) || f True
4858 This is rejected by Haskell 98, but under Jones's scheme the definition for
4859 <literal>g</literal> is typechecked first, separately from that for
4860 <literal>f</literal>,
4861 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4862 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4863 type is generalised, to get
4865 g :: Ord a => a -> Bool
4867 Now, the definition for <literal>f</literal> is typechecked, with this type for
4868 <literal>g</literal> in the type environment.
4872 The same refined dependency analysis also allows the type signatures of
4873 mutually-recursive functions to have different contexts, something that is illegal in
4874 Haskell 98 (Section 4.5.2, last sentence). With
4875 <option>-XRelaxedPolyRec</option>
4876 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4877 type signatures; in practice this means that only variables bound by the same
4878 pattern binding must have the same context. For example, this is fine:
4880 f :: Eq a => a -> Bool
4881 f x = (x == x) || g True
4883 g :: Ord a => a -> Bool
4884 g y = (y <= y) || f True
4889 <sect2 id="type-families">
4890 <title>Type families
4894 GHC supports the definition of type families indexed by types. They may be
4895 seen as an extension of Haskell 98's class-based overloading of values to
4896 types. When type families are declared in classes, they are also known as
4900 There are two forms of type families: data families and type synonym families.
4901 Currently, only the former are fully implemented, while we are still working
4902 on the latter. As a result, the specification of the language extension is
4903 also still to some degree in flux. Hence, a more detailed description of
4904 the language extension and its use is currently available
4905 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4906 wiki page on type families</ulink>. The material will be moved to this user's
4907 guide when it has stabilised.
4910 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4917 <!-- ==================== End of type system extensions ================= -->
4919 <!-- ====================== TEMPLATE HASKELL ======================= -->
4921 <sect1 id="template-haskell">
4922 <title>Template Haskell</title>
4924 <para>Template Haskell allows you to do compile-time meta-programming in
4927 the main technical innovations is discussed in "<ulink
4928 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
4929 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4932 There is a Wiki page about
4933 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
4934 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4938 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4939 Haskell library reference material</ulink>
4940 (look for module <literal>Language.Haskell.TH</literal>).
4941 Many changes to the original design are described in
4942 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4943 Notes on Template Haskell version 2</ulink>.
4944 Not all of these changes are in GHC, however.
4947 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4948 as a worked example to help get you started.
4952 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4953 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4958 <title>Syntax</title>
4960 <para> Template Haskell has the following new syntactic
4961 constructions. You need to use the flag
4962 <option>-XTemplateHaskell</option>
4963 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4964 </indexterm>to switch these syntactic extensions on
4965 (<option>-XTemplateHaskell</option> is no longer implied by
4966 <option>-fglasgow-exts</option>).</para>
4970 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4971 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4972 There must be no space between the "$" and the identifier or parenthesis. This use
4973 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4974 of "." as an infix operator. If you want the infix operator, put spaces around it.
4976 <para> A splice can occur in place of
4978 <listitem><para> an expression; the spliced expression must
4979 have type <literal>Q Exp</literal></para></listitem>
4980 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4983 Inside a splice you can can only call functions defined in imported modules,
4984 not functions defined elsewhere in the same module.</listitem>
4988 A expression quotation is written in Oxford brackets, thus:
4990 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4991 the quotation has type <literal>Q Exp</literal>.</para></listitem>
4992 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4993 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4994 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4995 the quotation has type <literal>Q Typ</literal>.</para></listitem>
4996 </itemizedlist></para></listitem>
4999 A quasi-quotation can appear in either a pattern context or an
5000 expression context and is also written in Oxford brackets:
5002 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5003 where the "..." is an arbitrary string; a full description of the
5004 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5005 </itemizedlist></para></listitem>
5008 A name can be quoted with either one or two prefix single quotes:
5010 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5011 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5012 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5014 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5015 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5018 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, delarations etc. They
5019 may also be given as an argument to the <literal>reify</literal> function.
5025 (Compared to the original paper, there are many differnces of detail.
5026 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5027 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5028 Type splices are not implemented, and neither are pattern splices or quotations.
5032 <sect2> <title> Using Template Haskell </title>
5036 The data types and monadic constructor functions for Template Haskell are in the library
5037 <literal>Language.Haskell.THSyntax</literal>.
5041 You can only run a function at compile time if it is imported from another module. That is,
5042 you can't define a function in a module, and call it from within a splice in the same module.
5043 (It would make sense to do so, but it's hard to implement.)
5047 You can only run a function at compile time if it is imported
5048 from another module <emphasis>that is not part of a mutually-recursive group of modules
5049 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5050 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5051 splice is to be run.</para>
5053 For example, when compiling module A,
5054 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5055 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5059 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5062 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5063 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5064 compiles and runs a program, and then looks at the result. So it's important that
5065 the program it compiles produces results whose representations are identical to
5066 those of the compiler itself.
5070 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5071 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5076 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5077 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5078 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5085 -- Import our template "pr"
5086 import Printf ( pr )
5088 -- The splice operator $ takes the Haskell source code
5089 -- generated at compile time by "pr" and splices it into
5090 -- the argument of "putStrLn".
5091 main = putStrLn ( $(pr "Hello") )
5097 -- Skeletal printf from the paper.
5098 -- It needs to be in a separate module to the one where
5099 -- you intend to use it.
5101 -- Import some Template Haskell syntax
5102 import Language.Haskell.TH
5104 -- Describe a format string
5105 data Format = D | S | L String
5107 -- Parse a format string. This is left largely to you
5108 -- as we are here interested in building our first ever
5109 -- Template Haskell program and not in building printf.
5110 parse :: String -> [Format]
5113 -- Generate Haskell source code from a parsed representation
5114 -- of the format string. This code will be spliced into
5115 -- the module which calls "pr", at compile time.
5116 gen :: [Format] -> Q Exp
5117 gen [D] = [| \n -> show n |]
5118 gen [S] = [| \s -> s |]
5119 gen [L s] = stringE s
5121 -- Here we generate the Haskell code for the splice
5122 -- from an input format string.
5123 pr :: String -> Q Exp
5124 pr s = gen (parse s)
5127 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5130 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5133 <para>Run "main.exe" and here is your output:</para>
5143 <title>Using Template Haskell with Profiling</title>
5144 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5146 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5147 interpreter to run the splice expressions. The bytecode interpreter
5148 runs the compiled expression on top of the same runtime on which GHC
5149 itself is running; this means that the compiled code referred to by
5150 the interpreted expression must be compatible with this runtime, and
5151 in particular this means that object code that is compiled for
5152 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5153 expression, because profiled object code is only compatible with the
5154 profiling version of the runtime.</para>
5156 <para>This causes difficulties if you have a multi-module program
5157 containing Template Haskell code and you need to compile it for
5158 profiling, because GHC cannot load the profiled object code and use it
5159 when executing the splices. Fortunately GHC provides a workaround.
5160 The basic idea is to compile the program twice:</para>
5164 <para>Compile the program or library first the normal way, without
5165 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5168 <para>Then compile it again with <option>-prof</option>, and
5169 additionally use <option>-osuf
5170 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5171 to name the object files differently (you can choose any suffix
5172 that isn't the normal object suffix here). GHC will automatically
5173 load the object files built in the first step when executing splice
5174 expressions. If you omit the <option>-osuf</option> flag when
5175 building with <option>-prof</option> and Template Haskell is used,
5176 GHC will emit an error message. </para>
5181 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5182 <para>Quasi-quotation allows patterns and expressions to be written using
5183 programmer-defined concrete syntax; the motivation behind the extension and
5184 several examples are documented in
5185 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5186 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5187 2007). The example below shows how to write a quasiquoter for a simple
5188 expression language.</para>
5191 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5192 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5193 functions for quoting expressions and patterns, respectively. The first argument
5194 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5195 context of the quasi-quotation statement determines which of the two parsers is
5196 called: if the quasi-quotation occurs in an expression context, the expression
5197 parser is called, and if it occurs in a pattern context, the pattern parser is
5201 Note that in the example we make use of an antiquoted
5202 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5203 (this syntax for anti-quotation was defined by the parser's
5204 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5205 integer value argument of the constructor <literal>IntExpr</literal> when
5206 pattern matching. Please see the referenced paper for further details regarding
5207 anti-quotation as well as the description of a technique that uses SYB to
5208 leverage a single parser of type <literal>String -> a</literal> to generate both
5209 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5210 pattern parser that returns a value of type <literal>Q Pat</literal>.
5213 <para>In general, a quasi-quote has the form
5214 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5215 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5216 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5217 can be arbitrary, and may contain newlines.
5220 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5221 the example, <literal>expr</literal> cannot be defined
5222 in <literal>Main.hs</literal> where it is used, but must be imported.
5233 main = do { print $ eval [$expr|1 + 2|]
5235 { [$expr|'int:n|] -> print n
5244 import qualified Language.Haskell.TH as TH
5245 import Language.Haskell.TH.Quasi
5247 data Expr = IntExpr Integer
5248 | AntiIntExpr String
5249 | BinopExpr BinOp Expr Expr
5251 deriving(Show, Typeable, Data)
5257 deriving(Show, Typeable, Data)
5259 eval :: Expr -> Integer
5260 eval (IntExpr n) = n
5261 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5268 expr = QuasiQuoter parseExprExp parseExprPat
5270 -- Parse an Expr, returning its representation as
5271 -- either a Q Exp or a Q Pat. See the referenced paper
5272 -- for how to use SYB to do this by writing a single
5273 -- parser of type String -> Expr instead of two
5274 -- separate parsers.
5276 parseExprExp :: String -> Q Exp
5279 parseExprPat :: String -> Q Pat
5283 <para>Now run the compiler:
5286 $ ghc --make -XQuasiQuotes Main.hs -o main
5289 <para>Run "main" and here is your output:</para>
5301 <!-- ===================== Arrow notation =================== -->
5303 <sect1 id="arrow-notation">
5304 <title>Arrow notation
5307 <para>Arrows are a generalization of monads introduced by John Hughes.
5308 For more details, see
5313 “Generalising Monads to Arrows”,
5314 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5315 pp67–111, May 2000.
5321 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5322 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5328 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5329 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5335 and the arrows web page at
5336 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5337 With the <option>-XArrows</option> flag, GHC supports the arrow
5338 notation described in the second of these papers.
5339 What follows is a brief introduction to the notation;
5340 it won't make much sense unless you've read Hughes's paper.
5341 This notation is translated to ordinary Haskell,
5342 using combinators from the
5343 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5347 <para>The extension adds a new kind of expression for defining arrows:
5349 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5350 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5352 where <literal>proc</literal> is a new keyword.
5353 The variables of the pattern are bound in the body of the
5354 <literal>proc</literal>-expression,
5355 which is a new sort of thing called a <firstterm>command</firstterm>.
5356 The syntax of commands is as follows:
5358 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5359 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5360 | <replaceable>cmd</replaceable><superscript>0</superscript>
5362 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5363 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5364 infix operators as for expressions, and
5366 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5367 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5368 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5369 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5370 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5371 | <replaceable>fcmd</replaceable>
5373 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5374 | ( <replaceable>cmd</replaceable> )
5375 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5377 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5378 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5379 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5380 | <replaceable>cmd</replaceable>
5382 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5383 except that the bodies are commands instead of expressions.
5387 Commands produce values, but (like monadic computations)
5388 may yield more than one value,
5389 or none, and may do other things as well.
5390 For the most part, familiarity with monadic notation is a good guide to
5392 However the values of expressions, even monadic ones,
5393 are determined by the values of the variables they contain;
5394 this is not necessarily the case for commands.
5398 A simple example of the new notation is the expression
5400 proc x -> f -< x+1
5402 We call this a <firstterm>procedure</firstterm> or
5403 <firstterm>arrow abstraction</firstterm>.
5404 As with a lambda expression, the variable <literal>x</literal>
5405 is a new variable bound within the <literal>proc</literal>-expression.
5406 It refers to the input to the arrow.
5407 In the above example, <literal>-<</literal> is not an identifier but an
5408 new reserved symbol used for building commands from an expression of arrow
5409 type and an expression to be fed as input to that arrow.
5410 (The weird look will make more sense later.)
5411 It may be read as analogue of application for arrows.
5412 The above example is equivalent to the Haskell expression
5414 arr (\ x -> x+1) >>> f
5416 That would make no sense if the expression to the left of
5417 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5418 More generally, the expression to the left of <literal>-<</literal>
5419 may not involve any <firstterm>local variable</firstterm>,
5420 i.e. a variable bound in the current arrow abstraction.
5421 For such a situation there is a variant <literal>-<<</literal>, as in
5423 proc x -> f x -<< x+1
5425 which is equivalent to
5427 arr (\ x -> (f x, x+1)) >>> app
5429 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5431 Such an arrow is equivalent to a monad, so if you're using this form
5432 you may find a monadic formulation more convenient.
5436 <title>do-notation for commands</title>
5439 Another form of command is a form of <literal>do</literal>-notation.
5440 For example, you can write
5449 You can read this much like ordinary <literal>do</literal>-notation,
5450 but with commands in place of monadic expressions.
5451 The first line sends the value of <literal>x+1</literal> as an input to
5452 the arrow <literal>f</literal>, and matches its output against
5453 <literal>y</literal>.
5454 In the next line, the output is discarded.
5455 The arrow <function>returnA</function> is defined in the
5456 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5457 module as <literal>arr id</literal>.
5458 The above example is treated as an abbreviation for
5460 arr (\ x -> (x, x)) >>>
5461 first (arr (\ x -> x+1) >>> f) >>>
5462 arr (\ (y, x) -> (y, (x, y))) >>>
5463 first (arr (\ y -> 2*y) >>> g) >>>
5465 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5466 first (arr (\ (x, z) -> x*z) >>> h) >>>
5467 arr (\ (t, z) -> t+z) >>>
5470 Note that variables not used later in the composition are projected out.
5471 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5473 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5474 module, this reduces to
5476 arr (\ x -> (x+1, x)) >>>
5478 arr (\ (y, x) -> (2*y, (x, y))) >>>
5480 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5482 arr (\ (t, z) -> t+z)
5484 which is what you might have written by hand.
5485 With arrow notation, GHC keeps track of all those tuples of variables for you.
5489 Note that although the above translation suggests that
5490 <literal>let</literal>-bound variables like <literal>z</literal> must be
5491 monomorphic, the actual translation produces Core,
5492 so polymorphic variables are allowed.
5496 It's also possible to have mutually recursive bindings,
5497 using the new <literal>rec</literal> keyword, as in the following example:
5499 counter :: ArrowCircuit a => a Bool Int
5500 counter = proc reset -> do
5501 rec output <- returnA -< if reset then 0 else next
5502 next <- delay 0 -< output+1
5503 returnA -< output
5505 The translation of such forms uses the <function>loop</function> combinator,
5506 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5512 <title>Conditional commands</title>
5515 In the previous example, we used a conditional expression to construct the
5517 Sometimes we want to conditionally execute different commands, as in
5524 which is translated to
5526 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5527 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5529 Since the translation uses <function>|||</function>,
5530 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5534 There are also <literal>case</literal> commands, like
5540 y <- h -< (x1, x2)
5544 The syntax is the same as for <literal>case</literal> expressions,
5545 except that the bodies of the alternatives are commands rather than expressions.
5546 The translation is similar to that of <literal>if</literal> commands.
5552 <title>Defining your own control structures</title>
5555 As we're seen, arrow notation provides constructs,
5556 modelled on those for expressions,
5557 for sequencing, value recursion and conditionals.
5558 But suitable combinators,
5559 which you can define in ordinary Haskell,
5560 may also be used to build new commands out of existing ones.
5561 The basic idea is that a command defines an arrow from environments to values.
5562 These environments assign values to the free local variables of the command.
5563 Thus combinators that produce arrows from arrows
5564 may also be used to build commands from commands.
5565 For example, the <literal>ArrowChoice</literal> class includes a combinator
5567 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5569 so we can use it to build commands:
5571 expr' = proc x -> do
5574 symbol Plus -< ()
5575 y <- term -< ()
5578 symbol Minus -< ()
5579 y <- term -< ()
5582 (The <literal>do</literal> on the first line is needed to prevent the first
5583 <literal><+> ...</literal> from being interpreted as part of the
5584 expression on the previous line.)
5585 This is equivalent to
5587 expr' = (proc x -> returnA -< x)
5588 <+> (proc x -> do
5589 symbol Plus -< ()
5590 y <- term -< ()
5592 <+> (proc x -> do
5593 symbol Minus -< ()
5594 y <- term -< ()
5597 It is essential that this operator be polymorphic in <literal>e</literal>
5598 (representing the environment input to the command
5599 and thence to its subcommands)
5600 and satisfy the corresponding naturality property
5602 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5604 at least for strict <literal>k</literal>.
5605 (This should be automatic if you're not using <function>seq</function>.)
5606 This ensures that environments seen by the subcommands are environments
5607 of the whole command,
5608 and also allows the translation to safely trim these environments.
5609 The operator must also not use any variable defined within the current
5614 We could define our own operator
5616 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5617 untilA body cond = proc x ->
5618 if cond x then returnA -< ()
5621 untilA body cond -< x
5623 and use it in the same way.
5624 Of course this infix syntax only makes sense for binary operators;
5625 there is also a more general syntax involving special brackets:
5629 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5636 <title>Primitive constructs</title>
5639 Some operators will need to pass additional inputs to their subcommands.
5640 For example, in an arrow type supporting exceptions,
5641 the operator that attaches an exception handler will wish to pass the
5642 exception that occurred to the handler.
5643 Such an operator might have a type
5645 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5647 where <literal>Ex</literal> is the type of exceptions handled.
5648 You could then use this with arrow notation by writing a command
5650 body `handleA` \ ex -> handler
5652 so that if an exception is raised in the command <literal>body</literal>,
5653 the variable <literal>ex</literal> is bound to the value of the exception
5654 and the command <literal>handler</literal>,
5655 which typically refers to <literal>ex</literal>, is entered.
5656 Though the syntax here looks like a functional lambda,
5657 we are talking about commands, and something different is going on.
5658 The input to the arrow represented by a command consists of values for
5659 the free local variables in the command, plus a stack of anonymous values.
5660 In all the prior examples, this stack was empty.
5661 In the second argument to <function>handleA</function>,
5662 this stack consists of one value, the value of the exception.
5663 The command form of lambda merely gives this value a name.
5668 the values on the stack are paired to the right of the environment.
5669 So operators like <function>handleA</function> that pass
5670 extra inputs to their subcommands can be designed for use with the notation
5671 by pairing the values with the environment in this way.
5672 More precisely, the type of each argument of the operator (and its result)
5673 should have the form
5675 a (...(e,t1), ... tn) t
5677 where <replaceable>e</replaceable> is a polymorphic variable
5678 (representing the environment)
5679 and <replaceable>ti</replaceable> are the types of the values on the stack,
5680 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5681 The polymorphic variable <replaceable>e</replaceable> must not occur in
5682 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5683 <replaceable>t</replaceable>.
5684 However the arrows involved need not be the same.
5685 Here are some more examples of suitable operators:
5687 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5688 runReader :: ... => a e c -> a' (e,State) c
5689 runState :: ... => a e c -> a' (e,State) (c,State)
5691 We can supply the extra input required by commands built with the last two
5692 by applying them to ordinary expressions, as in
5696 (|runReader (do { ... })|) s
5698 which adds <literal>s</literal> to the stack of inputs to the command
5699 built using <function>runReader</function>.
5703 The command versions of lambda abstraction and application are analogous to
5704 the expression versions.
5705 In particular, the beta and eta rules describe equivalences of commands.
5706 These three features (operators, lambda abstraction and application)
5707 are the core of the notation; everything else can be built using them,
5708 though the results would be somewhat clumsy.
5709 For example, we could simulate <literal>do</literal>-notation by defining
5711 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5712 u `bind` f = returnA &&& u >>> f
5714 bind_ :: Arrow a => a e b -> a e c -> a e c
5715 u `bind_` f = u `bind` (arr fst >>> f)
5717 We could simulate <literal>if</literal> by defining
5719 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5720 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5727 <title>Differences with the paper</title>
5732 <para>Instead of a single form of arrow application (arrow tail) with two
5733 translations, the implementation provides two forms
5734 <quote><literal>-<</literal></quote> (first-order)
5735 and <quote><literal>-<<</literal></quote> (higher-order).
5740 <para>User-defined operators are flagged with banana brackets instead of
5741 a new <literal>form</literal> keyword.
5750 <title>Portability</title>
5753 Although only GHC implements arrow notation directly,
5754 there is also a preprocessor
5756 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5757 that translates arrow notation into Haskell 98
5758 for use with other Haskell systems.
5759 You would still want to check arrow programs with GHC;
5760 tracing type errors in the preprocessor output is not easy.
5761 Modules intended for both GHC and the preprocessor must observe some
5762 additional restrictions:
5767 The module must import
5768 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5774 The preprocessor cannot cope with other Haskell extensions.
5775 These would have to go in separate modules.
5781 Because the preprocessor targets Haskell (rather than Core),
5782 <literal>let</literal>-bound variables are monomorphic.
5793 <!-- ==================== BANG PATTERNS ================= -->
5795 <sect1 id="bang-patterns">
5796 <title>Bang patterns
5797 <indexterm><primary>Bang patterns</primary></indexterm>
5799 <para>GHC supports an extension of pattern matching called <emphasis>bang
5800 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5802 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5803 prime feature description</ulink> contains more discussion and examples
5804 than the material below.
5807 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5810 <sect2 id="bang-patterns-informal">
5811 <title>Informal description of bang patterns
5814 The main idea is to add a single new production to the syntax of patterns:
5818 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5819 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5824 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5825 whereas without the bang it would be lazy.
5826 Bang patterns can be nested of course:
5830 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5831 <literal>y</literal>.
5832 A bang only really has an effect if it precedes a variable or wild-card pattern:
5837 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5838 forces evaluation anyway does nothing.
5840 Bang patterns work in <literal>case</literal> expressions too, of course:
5842 g5 x = let y = f x in body
5843 g6 x = case f x of { y -> body }
5844 g7 x = case f x of { !y -> body }
5846 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5847 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5848 result, and then evaluates <literal>body</literal>.
5850 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5851 definitions too. For example:
5855 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5856 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5857 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5858 in a function argument <literal>![x,y]</literal> means the
5859 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5860 is part of the syntax of <literal>let</literal> bindings.
5865 <sect2 id="bang-patterns-sem">
5866 <title>Syntax and semantics
5870 We add a single new production to the syntax of patterns:
5874 There is one problem with syntactic ambiguity. Consider:
5878 Is this a definition of the infix function "<literal>(!)</literal>",
5879 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5880 ambiguity in favour of the latter. If you want to define
5881 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5886 The semantics of Haskell pattern matching is described in <ulink
5887 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5888 Section 3.17.2</ulink> of the Haskell Report. To this description add
5889 one extra item 10, saying:
5890 <itemizedlist><listitem><para>Matching
5891 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5892 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5893 <listitem><para>otherwise, <literal>pat</literal> is matched against
5894 <literal>v</literal></para></listitem>
5896 </para></listitem></itemizedlist>
5897 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5898 Section 3.17.3</ulink>, add a new case (t):
5900 case v of { !pat -> e; _ -> e' }
5901 = v `seq` case v of { pat -> e; _ -> e' }
5904 That leaves let expressions, whose translation is given in
5905 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5907 of the Haskell Report.
5908 In the translation box, first apply
5909 the following transformation: for each pattern <literal>pi</literal> that is of
5910 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5911 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5912 have a bang at the top, apply the rules in the existing box.
5914 <para>The effect of the let rule is to force complete matching of the pattern
5915 <literal>qi</literal> before evaluation of the body is begun. The bang is
5916 retained in the translated form in case <literal>qi</literal> is a variable,
5924 The let-binding can be recursive. However, it is much more common for
5925 the let-binding to be non-recursive, in which case the following law holds:
5926 <literal>(let !p = rhs in body)</literal>
5928 <literal>(case rhs of !p -> body)</literal>
5931 A pattern with a bang at the outermost level is not allowed at the top level of
5937 <!-- ==================== ASSERTIONS ================= -->
5939 <sect1 id="assertions">
5941 <indexterm><primary>Assertions</primary></indexterm>
5945 If you want to make use of assertions in your standard Haskell code, you
5946 could define a function like the following:
5952 assert :: Bool -> a -> a
5953 assert False x = error "assertion failed!"
5960 which works, but gives you back a less than useful error message --
5961 an assertion failed, but which and where?
5965 One way out is to define an extended <function>assert</function> function which also
5966 takes a descriptive string to include in the error message and
5967 perhaps combine this with the use of a pre-processor which inserts
5968 the source location where <function>assert</function> was used.
5972 Ghc offers a helping hand here, doing all of this for you. For every
5973 use of <function>assert</function> in the user's source:
5979 kelvinToC :: Double -> Double
5980 kelvinToC k = assert (k >= 0.0) (k+273.15)
5986 Ghc will rewrite this to also include the source location where the
5993 assert pred val ==> assertError "Main.hs|15" pred val
5999 The rewrite is only performed by the compiler when it spots
6000 applications of <function>Control.Exception.assert</function>, so you
6001 can still define and use your own versions of
6002 <function>assert</function>, should you so wish. If not, import
6003 <literal>Control.Exception</literal> to make use
6004 <function>assert</function> in your code.
6008 GHC ignores assertions when optimisation is turned on with the
6009 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6010 <literal>assert pred e</literal> will be rewritten to
6011 <literal>e</literal>. You can also disable assertions using the
6012 <option>-fignore-asserts</option>
6013 option<indexterm><primary><option>-fignore-asserts</option></primary>
6014 </indexterm>.</para>
6017 Assertion failures can be caught, see the documentation for the
6018 <literal>Control.Exception</literal> library for the details.
6024 <!-- =============================== PRAGMAS =========================== -->
6026 <sect1 id="pragmas">
6027 <title>Pragmas</title>
6029 <indexterm><primary>pragma</primary></indexterm>
6031 <para>GHC supports several pragmas, or instructions to the
6032 compiler placed in the source code. Pragmas don't normally affect
6033 the meaning of the program, but they might affect the efficiency
6034 of the generated code.</para>
6036 <para>Pragmas all take the form
6038 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6040 where <replaceable>word</replaceable> indicates the type of
6041 pragma, and is followed optionally by information specific to that
6042 type of pragma. Case is ignored in
6043 <replaceable>word</replaceable>. The various values for
6044 <replaceable>word</replaceable> that GHC understands are described
6045 in the following sections; any pragma encountered with an
6046 unrecognised <replaceable>word</replaceable> is (silently)
6049 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6050 pragma must precede the <literal>module</literal> keyword in the file.
6051 There can be as many file-header pragmas as you please, and they can be
6052 preceded or followed by comments.</para>
6054 <sect2 id="language-pragma">
6055 <title>LANGUAGE pragma</title>
6057 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6058 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6060 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6062 It is the intention that all Haskell compilers support the
6063 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6064 all extensions are supported by all compilers, of
6065 course. The <literal>LANGUAGE</literal> pragma should be used instead
6066 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6068 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6070 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6072 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6074 <para>Every language extension can also be turned into a command-line flag
6075 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6076 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6079 <para>A list of all supported language extensions can be obtained by invoking
6080 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6082 <para>Any extension from the <literal>Extension</literal> type defined in
6084 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6085 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6089 <sect2 id="options-pragma">
6090 <title>OPTIONS_GHC pragma</title>
6091 <indexterm><primary>OPTIONS_GHC</primary>
6093 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6096 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6097 additional options that are given to the compiler when compiling
6098 this source file. See <xref linkend="source-file-options"/> for
6101 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6102 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6105 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6107 <sect2 id="include-pragma">
6108 <title>INCLUDE pragma</title>
6110 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6111 of C header files that should be <literal>#include</literal>'d into
6112 the C source code generated by the compiler for the current module (if
6113 compiling via C). For example:</para>
6116 {-# INCLUDE "foo.h" #-}
6117 {-# INCLUDE <stdio.h> #-}</programlisting>
6119 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6121 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6122 to the <option>-#include</option> option (<xref
6123 linkend="options-C-compiler" />), because the
6124 <literal>INCLUDE</literal> pragma is understood by other
6125 compilers. Yet another alternative is to add the include file to each
6126 <literal>foreign import</literal> declaration in your code, but we
6127 don't recommend using this approach with GHC.</para>
6130 <sect2 id="deprecated-pragma">
6131 <title>DEPRECATED pragma</title>
6132 <indexterm><primary>DEPRECATED</primary>
6135 <para>The DEPRECATED pragma lets you specify that a particular
6136 function, class, or type, is deprecated. There are two
6141 <para>You can deprecate an entire module thus:</para>
6143 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6146 <para>When you compile any module that import
6147 <literal>Wibble</literal>, GHC will print the specified
6152 <para>You can deprecate a function, class, type, or data constructor, with the
6153 following top-level declaration:</para>
6155 {-# DEPRECATED f, C, T "Don't use these" #-}
6157 <para>When you compile any module that imports and uses any
6158 of the specified entities, GHC will print the specified
6160 <para> You can only deprecate entities declared at top level in the module
6161 being compiled, and you can only use unqualified names in the list of
6162 entities being deprecated. A capitalised name, such as <literal>T</literal>
6163 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6164 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6165 both are in scope. If both are in scope, there is currently no way to deprecate
6166 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
6169 Any use of the deprecated item, or of anything from a deprecated
6170 module, will be flagged with an appropriate message. However,
6171 deprecations are not reported for
6172 (a) uses of a deprecated function within its defining module, and
6173 (b) uses of a deprecated function in an export list.
6174 The latter reduces spurious complaints within a library
6175 in which one module gathers together and re-exports
6176 the exports of several others.
6178 <para>You can suppress the warnings with the flag
6179 <option>-fno-warn-deprecations</option>.</para>
6182 <sect2 id="inline-noinline-pragma">
6183 <title>INLINE and NOINLINE pragmas</title>
6185 <para>These pragmas control the inlining of function
6188 <sect3 id="inline-pragma">
6189 <title>INLINE pragma</title>
6190 <indexterm><primary>INLINE</primary></indexterm>
6192 <para>GHC (with <option>-O</option>, as always) tries to
6193 inline (or “unfold”) functions/values that are
6194 “small enough,” thus avoiding the call overhead
6195 and possibly exposing other more-wonderful optimisations.
6196 Normally, if GHC decides a function is “too
6197 expensive” to inline, it will not do so, nor will it
6198 export that unfolding for other modules to use.</para>
6200 <para>The sledgehammer you can bring to bear is the
6201 <literal>INLINE</literal><indexterm><primary>INLINE
6202 pragma</primary></indexterm> pragma, used thusly:</para>
6205 key_function :: Int -> String -> (Bool, Double)
6207 #ifdef __GLASGOW_HASKELL__
6208 {-# INLINE key_function #-}
6212 <para>(You don't need to do the C pre-processor carry-on
6213 unless you're going to stick the code through HBC—it
6214 doesn't like <literal>INLINE</literal> pragmas.)</para>
6216 <para>The major effect of an <literal>INLINE</literal> pragma
6217 is to declare a function's “cost” to be very low.
6218 The normal unfolding machinery will then be very keen to
6219 inline it. However, an <literal>INLINE</literal> pragma for a
6220 function "<literal>f</literal>" has a number of other effects:
6223 No funtions are inlined into <literal>f</literal>. Otherwise
6224 GHC might inline a big function into <literal>f</literal>'s right hand side,
6225 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6228 The float-in, float-out, and common-sub-expression transformations are not
6229 applied to the body of <literal>f</literal>.
6232 An INLINE function is not worker/wrappered by strictness analysis.
6233 It's going to be inlined wholesale instead.
6236 All of these effects are aimed at ensuring that what gets inlined is
6237 exactly what you asked for, no more and no less.
6239 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6240 function can be put anywhere its type signature could be
6243 <para><literal>INLINE</literal> pragmas are a particularly
6245 <literal>then</literal>/<literal>return</literal> (or
6246 <literal>bind</literal>/<literal>unit</literal>) functions in
6247 a monad. For example, in GHC's own
6248 <literal>UniqueSupply</literal> monad code, we have:</para>
6251 #ifdef __GLASGOW_HASKELL__
6252 {-# INLINE thenUs #-}
6253 {-# INLINE returnUs #-}
6257 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6258 linkend="noinline-pragma"/>).</para>
6261 <sect3 id="noinline-pragma">
6262 <title>NOINLINE pragma</title>
6264 <indexterm><primary>NOINLINE</primary></indexterm>
6265 <indexterm><primary>NOTINLINE</primary></indexterm>
6267 <para>The <literal>NOINLINE</literal> pragma does exactly what
6268 you'd expect: it stops the named function from being inlined
6269 by the compiler. You shouldn't ever need to do this, unless
6270 you're very cautious about code size.</para>
6272 <para><literal>NOTINLINE</literal> is a synonym for
6273 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6274 specified by Haskell 98 as the standard way to disable
6275 inlining, so it should be used if you want your code to be
6279 <sect3 id="phase-control">
6280 <title>Phase control</title>
6282 <para> Sometimes you want to control exactly when in GHC's
6283 pipeline the INLINE pragma is switched on. Inlining happens
6284 only during runs of the <emphasis>simplifier</emphasis>. Each
6285 run of the simplifier has a different <emphasis>phase
6286 number</emphasis>; the phase number decreases towards zero.
6287 If you use <option>-dverbose-core2core</option> you'll see the
6288 sequence of phase numbers for successive runs of the
6289 simplifier. In an INLINE pragma you can optionally specify a
6293 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6294 <literal>f</literal>
6295 until phase <literal>k</literal>, but from phase
6296 <literal>k</literal> onwards be very keen to inline it.
6299 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6300 <literal>f</literal>
6301 until phase <literal>k</literal>, but from phase
6302 <literal>k</literal> onwards do not inline it.
6305 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6306 <literal>f</literal>
6307 until phase <literal>k</literal>, but from phase
6308 <literal>k</literal> onwards be willing to inline it (as if
6309 there was no pragma).
6312 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6313 <literal>f</literal>
6314 until phase <literal>k</literal>, but from phase
6315 <literal>k</literal> onwards do not inline it.
6318 The same information is summarised here:
6320 -- Before phase 2 Phase 2 and later
6321 {-# INLINE [2] f #-} -- No Yes
6322 {-# INLINE [~2] f #-} -- Yes No
6323 {-# NOINLINE [2] f #-} -- No Maybe
6324 {-# NOINLINE [~2] f #-} -- Maybe No
6326 {-# INLINE f #-} -- Yes Yes
6327 {-# NOINLINE f #-} -- No No
6329 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6330 function body is small, or it is applied to interesting-looking arguments etc).
6331 Another way to understand the semantics is this:
6333 <listitem><para>For both INLINE and NOINLINE, the phase number says
6334 when inlining is allowed at all.</para></listitem>
6335 <listitem><para>The INLINE pragma has the additional effect of making the
6336 function body look small, so that when inlining is allowed it is very likely to
6341 <para>The same phase-numbering control is available for RULES
6342 (<xref linkend="rewrite-rules"/>).</para>
6346 <sect2 id="line-pragma">
6347 <title>LINE pragma</title>
6349 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6350 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6351 <para>This pragma is similar to C's <literal>#line</literal>
6352 pragma, and is mainly for use in automatically generated Haskell
6353 code. It lets you specify the line number and filename of the
6354 original code; for example</para>
6356 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6358 <para>if you'd generated the current file from something called
6359 <filename>Foo.vhs</filename> and this line corresponds to line
6360 42 in the original. GHC will adjust its error messages to refer
6361 to the line/file named in the <literal>LINE</literal>
6366 <title>RULES pragma</title>
6368 <para>The RULES pragma lets you specify rewrite rules. It is
6369 described in <xref linkend="rewrite-rules"/>.</para>
6372 <sect2 id="specialize-pragma">
6373 <title>SPECIALIZE pragma</title>
6375 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6376 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6377 <indexterm><primary>overloading, death to</primary></indexterm>
6379 <para>(UK spelling also accepted.) For key overloaded
6380 functions, you can create extra versions (NB: more code space)
6381 specialised to particular types. Thus, if you have an
6382 overloaded function:</para>
6385 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6388 <para>If it is heavily used on lists with
6389 <literal>Widget</literal> keys, you could specialise it as
6393 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6396 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6397 be put anywhere its type signature could be put.</para>
6399 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6400 (a) a specialised version of the function and (b) a rewrite rule
6401 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6402 un-specialised function into a call to the specialised one.</para>
6404 <para>The type in a SPECIALIZE pragma can be any type that is less
6405 polymorphic than the type of the original function. In concrete terms,
6406 if the original function is <literal>f</literal> then the pragma
6408 {-# SPECIALIZE f :: <type> #-}
6410 is valid if and only if the definition
6412 f_spec :: <type>
6415 is valid. Here are some examples (where we only give the type signature
6416 for the original function, not its code):
6418 f :: Eq a => a -> b -> b
6419 {-# SPECIALISE f :: Int -> b -> b #-}
6421 g :: (Eq a, Ix b) => a -> b -> b
6422 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6424 h :: Eq a => a -> a -> a
6425 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6427 The last of these examples will generate a
6428 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6429 well. If you use this kind of specialisation, let us know how well it works.
6432 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6433 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6434 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6435 The <literal>INLINE</literal> pragma affects the specialised version of the
6436 function (only), and applies even if the function is recursive. The motivating
6439 -- A GADT for arrays with type-indexed representation
6441 ArrInt :: !Int -> ByteArray# -> Arr Int
6442 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6444 (!:) :: Arr e -> Int -> e
6445 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6446 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6447 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6448 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6450 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6451 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6452 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6453 the specialised function will be inlined. It has two calls to
6454 <literal>(!:)</literal>,
6455 both at type <literal>Int</literal>. Both these calls fire the first
6456 specialisation, whose body is also inlined. The result is a type-based
6457 unrolling of the indexing function.</para>
6458 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6459 on an ordinarily-recursive function.</para>
6461 <para>Note: In earlier versions of GHC, it was possible to provide your own
6462 specialised function for a given type:
6465 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6468 This feature has been removed, as it is now subsumed by the
6469 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6473 <sect2 id="specialize-instance-pragma">
6474 <title>SPECIALIZE instance pragma
6478 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6479 <indexterm><primary>overloading, death to</primary></indexterm>
6480 Same idea, except for instance declarations. For example:
6483 instance (Eq a) => Eq (Foo a) where {
6484 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6488 The pragma must occur inside the <literal>where</literal> part
6489 of the instance declaration.
6492 Compatible with HBC, by the way, except perhaps in the placement
6498 <sect2 id="unpack-pragma">
6499 <title>UNPACK pragma</title>
6501 <indexterm><primary>UNPACK</primary></indexterm>
6503 <para>The <literal>UNPACK</literal> indicates to the compiler
6504 that it should unpack the contents of a constructor field into
6505 the constructor itself, removing a level of indirection. For
6509 data T = T {-# UNPACK #-} !Float
6510 {-# UNPACK #-} !Float
6513 <para>will create a constructor <literal>T</literal> containing
6514 two unboxed floats. This may not always be an optimisation: if
6515 the <function>T</function> constructor is scrutinised and the
6516 floats passed to a non-strict function for example, they will
6517 have to be reboxed (this is done automatically by the
6520 <para>Unpacking constructor fields should only be used in
6521 conjunction with <option>-O</option>, in order to expose
6522 unfoldings to the compiler so the reboxing can be removed as
6523 often as possible. For example:</para>
6527 f (T f1 f2) = f1 + f2
6530 <para>The compiler will avoid reboxing <function>f1</function>
6531 and <function>f2</function> by inlining <function>+</function>
6532 on floats, but only when <option>-O</option> is on.</para>
6534 <para>Any single-constructor data is eligible for unpacking; for
6538 data T = T {-# UNPACK #-} !(Int,Int)
6541 <para>will store the two <literal>Int</literal>s directly in the
6542 <function>T</function> constructor, by flattening the pair.
6543 Multi-level unpacking is also supported:
6546 data T = T {-# UNPACK #-} !S
6547 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6550 will store two unboxed <literal>Int#</literal>s
6551 directly in the <function>T</function> constructor. The
6552 unpacker can see through newtypes, too.</para>
6554 <para>If a field cannot be unpacked, you will not get a warning,
6555 so it might be an idea to check the generated code with
6556 <option>-ddump-simpl</option>.</para>
6558 <para>See also the <option>-funbox-strict-fields</option> flag,
6559 which essentially has the effect of adding
6560 <literal>{-# UNPACK #-}</literal> to every strict
6561 constructor field.</para>
6564 <sect2 id="source-pragma">
6565 <title>SOURCE pragma</title>
6567 <indexterm><primary>SOURCE</primary></indexterm>
6568 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6569 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6575 <!-- ======================= REWRITE RULES ======================== -->
6577 <sect1 id="rewrite-rules">
6578 <title>Rewrite rules
6580 <indexterm><primary>RULES pragma</primary></indexterm>
6581 <indexterm><primary>pragma, RULES</primary></indexterm>
6582 <indexterm><primary>rewrite rules</primary></indexterm></title>
6585 The programmer can specify rewrite rules as part of the source program
6586 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6587 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6588 and (b) the <option>-frules-off</option> flag
6589 (<xref linkend="options-f"/>) is not specified, and (c) the
6590 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6599 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6606 <title>Syntax</title>
6609 From a syntactic point of view:
6615 There may be zero or more rules in a <literal>RULES</literal> pragma.
6622 Each rule has a name, enclosed in double quotes. The name itself has
6623 no significance at all. It is only used when reporting how many times the rule fired.
6629 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6630 immediately after the name of the rule. Thus:
6633 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6636 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6637 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6646 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
6647 is set, so you must lay out your rules starting in the same column as the
6648 enclosing definitions.
6655 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6656 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6657 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6658 by spaces, just like in a type <literal>forall</literal>.
6664 A pattern variable may optionally have a type signature.
6665 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6666 For example, here is the <literal>foldr/build</literal> rule:
6669 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6670 foldr k z (build g) = g k z
6673 Since <function>g</function> has a polymorphic type, it must have a type signature.
6680 The left hand side of a rule must consist of a top-level variable applied
6681 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6684 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6685 "wrong2" forall f. f True = True
6688 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6695 A rule does not need to be in the same module as (any of) the
6696 variables it mentions, though of course they need to be in scope.
6702 Rules are automatically exported from a module, just as instance declarations are.
6713 <title>Semantics</title>
6716 From a semantic point of view:
6722 Rules are only applied if you use the <option>-O</option> flag.
6728 Rules are regarded as left-to-right rewrite rules.
6729 When GHC finds an expression that is a substitution instance of the LHS
6730 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6731 By "a substitution instance" we mean that the LHS can be made equal to the
6732 expression by substituting for the pattern variables.
6739 The LHS and RHS of a rule are typechecked, and must have the
6747 GHC makes absolutely no attempt to verify that the LHS and RHS
6748 of a rule have the same meaning. That is undecidable in general, and
6749 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6756 GHC makes no attempt to make sure that the rules are confluent or
6757 terminating. For example:
6760 "loop" forall x,y. f x y = f y x
6763 This rule will cause the compiler to go into an infinite loop.
6770 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6776 GHC currently uses a very simple, syntactic, matching algorithm
6777 for matching a rule LHS with an expression. It seeks a substitution
6778 which makes the LHS and expression syntactically equal modulo alpha
6779 conversion. The pattern (rule), but not the expression, is eta-expanded if
6780 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6781 But not beta conversion (that's called higher-order matching).
6785 Matching is carried out on GHC's intermediate language, which includes
6786 type abstractions and applications. So a rule only matches if the
6787 types match too. See <xref linkend="rule-spec"/> below.
6793 GHC keeps trying to apply the rules as it optimises the program.
6794 For example, consider:
6803 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6804 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6805 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6806 not be substituted, and the rule would not fire.
6813 In the earlier phases of compilation, GHC inlines <emphasis>nothing
6814 that appears on the LHS of a rule</emphasis>, because once you have substituted
6815 for something you can't match against it (given the simple minded
6816 matching). So if you write the rule
6819 "map/map" forall f,g. map f . map g = map (f.g)
6822 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
6823 It will only match something written with explicit use of ".".
6824 Well, not quite. It <emphasis>will</emphasis> match the expression
6830 where <function>wibble</function> is defined:
6833 wibble f g = map f . map g
6836 because <function>wibble</function> will be inlined (it's small).
6838 Later on in compilation, GHC starts inlining even things on the
6839 LHS of rules, but still leaves the rules enabled. This inlining
6840 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
6847 All rules are implicitly exported from the module, and are therefore
6848 in force in any module that imports the module that defined the rule, directly
6849 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6850 in force when compiling A.) The situation is very similar to that for instance
6862 <title>List fusion</title>
6865 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6866 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6867 intermediate list should be eliminated entirely.
6871 The following are good producers:
6883 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6889 Explicit lists (e.g. <literal>[True, False]</literal>)
6895 The cons constructor (e.g <literal>3:4:[]</literal>)
6901 <function>++</function>
6907 <function>map</function>
6913 <function>take</function>, <function>filter</function>
6919 <function>iterate</function>, <function>repeat</function>
6925 <function>zip</function>, <function>zipWith</function>
6934 The following are good consumers:
6946 <function>array</function> (on its second argument)
6952 <function>++</function> (on its first argument)
6958 <function>foldr</function>
6964 <function>map</function>
6970 <function>take</function>, <function>filter</function>
6976 <function>concat</function>
6982 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6988 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6989 will fuse with one but not the other)
6995 <function>partition</function>
7001 <function>head</function>
7007 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7013 <function>sequence_</function>
7019 <function>msum</function>
7025 <function>sortBy</function>
7034 So, for example, the following should generate no intermediate lists:
7037 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7043 This list could readily be extended; if there are Prelude functions that you use
7044 a lot which are not included, please tell us.
7048 If you want to write your own good consumers or producers, look at the
7049 Prelude definitions of the above functions to see how to do so.
7054 <sect2 id="rule-spec">
7055 <title>Specialisation
7059 Rewrite rules can be used to get the same effect as a feature
7060 present in earlier versions of GHC.
7061 For example, suppose that:
7064 genericLookup :: Ord a => Table a b -> a -> b
7065 intLookup :: Table Int b -> Int -> b
7068 where <function>intLookup</function> is an implementation of
7069 <function>genericLookup</function> that works very fast for
7070 keys of type <literal>Int</literal>. You might wish
7071 to tell GHC to use <function>intLookup</function> instead of
7072 <function>genericLookup</function> whenever the latter was called with
7073 type <literal>Table Int b -> Int -> b</literal>.
7074 It used to be possible to write
7077 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7080 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7083 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7086 This slightly odd-looking rule instructs GHC to replace
7087 <function>genericLookup</function> by <function>intLookup</function>
7088 <emphasis>whenever the types match</emphasis>.
7089 What is more, this rule does not need to be in the same
7090 file as <function>genericLookup</function>, unlike the
7091 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7092 have an original definition available to specialise).
7095 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7096 <function>intLookup</function> really behaves as a specialised version
7097 of <function>genericLookup</function>!!!</para>
7099 <para>An example in which using <literal>RULES</literal> for
7100 specialisation will Win Big:
7103 toDouble :: Real a => a -> Double
7104 toDouble = fromRational . toRational
7106 {-# RULES "toDouble/Int" toDouble = i2d #-}
7107 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7110 The <function>i2d</function> function is virtually one machine
7111 instruction; the default conversion—via an intermediate
7112 <literal>Rational</literal>—is obscenely expensive by
7119 <title>Controlling what's going on</title>
7127 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7133 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7134 If you add <option>-dppr-debug</option> you get a more detailed listing.
7140 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7143 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7144 {-# INLINE build #-}
7148 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7149 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7150 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7151 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7158 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7159 see how to write rules that will do fusion and yet give an efficient
7160 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7170 <sect2 id="core-pragma">
7171 <title>CORE pragma</title>
7173 <indexterm><primary>CORE pragma</primary></indexterm>
7174 <indexterm><primary>pragma, CORE</primary></indexterm>
7175 <indexterm><primary>core, annotation</primary></indexterm>
7178 The external core format supports <quote>Note</quote> annotations;
7179 the <literal>CORE</literal> pragma gives a way to specify what these
7180 should be in your Haskell source code. Syntactically, core
7181 annotations are attached to expressions and take a Haskell string
7182 literal as an argument. The following function definition shows an
7186 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7189 Semantically, this is equivalent to:
7197 However, when external for is generated (via
7198 <option>-fext-core</option>), there will be Notes attached to the
7199 expressions <function>show</function> and <varname>x</varname>.
7200 The core function declaration for <function>f</function> is:
7204 f :: %forall a . GHCziShow.ZCTShow a ->
7205 a -> GHCziBase.ZMZN GHCziBase.Char =
7206 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7208 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7210 (tpl1::GHCziBase.Int ->
7212 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7214 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7215 (tpl3::GHCziBase.ZMZN a ->
7216 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7224 Here, we can see that the function <function>show</function> (which
7225 has been expanded out to a case expression over the Show dictionary)
7226 has a <literal>%note</literal> attached to it, as does the
7227 expression <varname>eta</varname> (which used to be called
7228 <varname>x</varname>).
7235 <sect1 id="special-ids">
7236 <title>Special built-in functions</title>
7237 <para>GHC has a few built-in functions with special behaviour. These
7238 are now described in the module <ulink
7239 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7240 in the library documentation.</para>
7244 <sect1 id="generic-classes">
7245 <title>Generic classes</title>
7248 The ideas behind this extension are described in detail in "Derivable type classes",
7249 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7250 An example will give the idea:
7258 fromBin :: [Int] -> (a, [Int])
7260 toBin {| Unit |} Unit = []
7261 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7262 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7263 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7265 fromBin {| Unit |} bs = (Unit, bs)
7266 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7267 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7268 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7269 (y,bs'') = fromBin bs'
7272 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7273 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7274 which are defined thus in the library module <literal>Generics</literal>:
7278 data a :+: b = Inl a | Inr b
7279 data a :*: b = a :*: b
7282 Now you can make a data type into an instance of Bin like this:
7284 instance (Bin a, Bin b) => Bin (a,b)
7285 instance Bin a => Bin [a]
7287 That is, just leave off the "where" clause. Of course, you can put in the
7288 where clause and over-ride whichever methods you please.
7292 <title> Using generics </title>
7293 <para>To use generics you need to</para>
7296 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7297 <option>-XGenerics</option> (to generate extra per-data-type code),
7298 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7302 <para>Import the module <literal>Generics</literal> from the
7303 <literal>lang</literal> package. This import brings into
7304 scope the data types <literal>Unit</literal>,
7305 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7306 don't need this import if you don't mention these types
7307 explicitly; for example, if you are simply giving instance
7308 declarations.)</para>
7313 <sect2> <title> Changes wrt the paper </title>
7315 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7316 can be written infix (indeed, you can now use
7317 any operator starting in a colon as an infix type constructor). Also note that
7318 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7319 Finally, note that the syntax of the type patterns in the class declaration
7320 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7321 alone would ambiguous when they appear on right hand sides (an extension we
7322 anticipate wanting).
7326 <sect2> <title>Terminology and restrictions</title>
7328 Terminology. A "generic default method" in a class declaration
7329 is one that is defined using type patterns as above.
7330 A "polymorphic default method" is a default method defined as in Haskell 98.
7331 A "generic class declaration" is a class declaration with at least one
7332 generic default method.
7340 Alas, we do not yet implement the stuff about constructor names and
7347 A generic class can have only one parameter; you can't have a generic
7348 multi-parameter class.
7354 A default method must be defined entirely using type patterns, or entirely
7355 without. So this is illegal:
7358 op :: a -> (a, Bool)
7359 op {| Unit |} Unit = (Unit, True)
7362 However it is perfectly OK for some methods of a generic class to have
7363 generic default methods and others to have polymorphic default methods.
7369 The type variable(s) in the type pattern for a generic method declaration
7370 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:
7374 op {| p :*: q |} (x :*: y) = op (x :: p)
7382 The type patterns in a generic default method must take one of the forms:
7388 where "a" and "b" are type variables. Furthermore, all the type patterns for
7389 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7390 must use the same type variables. So this is illegal:
7394 op {| a :+: b |} (Inl x) = True
7395 op {| p :+: q |} (Inr y) = False
7397 The type patterns must be identical, even in equations for different methods of the class.
7398 So this too is illegal:
7402 op1 {| a :*: b |} (x :*: y) = True
7405 op2 {| p :*: q |} (x :*: y) = False
7407 (The reason for this restriction is that we gather all the equations for a particular type constructor
7408 into a single generic instance declaration.)
7414 A generic method declaration must give a case for each of the three type constructors.
7420 The type for a generic method can be built only from:
7422 <listitem> <para> Function arrows </para> </listitem>
7423 <listitem> <para> Type variables </para> </listitem>
7424 <listitem> <para> Tuples </para> </listitem>
7425 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7427 Here are some example type signatures for generic methods:
7430 op2 :: Bool -> (a,Bool)
7431 op3 :: [Int] -> a -> a
7434 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7438 This restriction is an implementation restriction: we just haven't got around to
7439 implementing the necessary bidirectional maps over arbitrary type constructors.
7440 It would be relatively easy to add specific type constructors, such as Maybe and list,
7441 to the ones that are allowed.</para>
7446 In an instance declaration for a generic class, the idea is that the compiler
7447 will fill in the methods for you, based on the generic templates. However it can only
7452 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7457 No constructor of the instance type has unboxed fields.
7461 (Of course, these things can only arise if you are already using GHC extensions.)
7462 However, you can still give an instance declarations for types which break these rules,
7463 provided you give explicit code to override any generic default methods.
7471 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7472 what the compiler does with generic declarations.
7477 <sect2> <title> Another example </title>
7479 Just to finish with, here's another example I rather like:
7483 nCons {| Unit |} _ = 1
7484 nCons {| a :*: b |} _ = 1
7485 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7488 tag {| Unit |} _ = 1
7489 tag {| a :*: b |} _ = 1
7490 tag {| a :+: b |} (Inl x) = tag x
7491 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7497 <sect1 id="monomorphism">
7498 <title>Control over monomorphism</title>
7500 <para>GHC supports two flags that control the way in which generalisation is
7501 carried out at let and where bindings.
7505 <title>Switching off the dreaded Monomorphism Restriction</title>
7506 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7508 <para>Haskell's monomorphism restriction (see
7509 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7511 of the Haskell Report)
7512 can be completely switched off by
7513 <option>-XNoMonomorphismRestriction</option>.
7518 <title>Monomorphic pattern bindings</title>
7519 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7520 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7522 <para> As an experimental change, we are exploring the possibility of
7523 making pattern bindings monomorphic; that is, not generalised at all.
7524 A pattern binding is a binding whose LHS has no function arguments,
7525 and is not a simple variable. For example:
7527 f x = x -- Not a pattern binding
7528 f = \x -> x -- Not a pattern binding
7529 f :: Int -> Int = \x -> x -- Not a pattern binding
7531 (g,h) = e -- A pattern binding
7532 (f) = e -- A pattern binding
7533 [x] = e -- A pattern binding
7535 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7536 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7545 ;;; Local Variables: ***
7547 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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