1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individually.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
137 <para> These two flags control how generalisation is done.
138 See <xref linkend="monomorphism"/>.
145 <option>-XExtendedDefaultRules</option>:
146 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
149 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
150 Independent of the <option>-fglasgow-exts</option>
157 <option>-XOverlappingInstances</option>
158 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
161 <option>-XUndecidableInstances</option>
162 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
165 <option>-XIncoherentInstances</option>
166 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
169 <option>-fcontext-stack=N</option>
170 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
173 <para> See <xref linkend="instance-decls"/>. Only relevant
174 if you also use <option>-fglasgow-exts</option>.</para>
180 <option>-finline-phase</option>
181 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
184 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
185 you also use <option>-fglasgow-exts</option>.</para>
191 <option>-XArrows</option>
192 <indexterm><primary><option>-XArrows</option></primary></indexterm>
195 <para>See <xref linkend="arrow-notation"/>. Independent of
196 <option>-fglasgow-exts</option>.</para>
198 <para>New reserved words/symbols: <literal>rec</literal>,
199 <literal>proc</literal>, <literal>-<</literal>,
200 <literal>>-</literal>, <literal>-<<</literal>,
201 <literal>>>-</literal>.</para>
203 <para>Other syntax stolen: <literal>(|</literal>,
204 <literal>|)</literal>.</para>
210 <option>-XGenerics</option>
211 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
214 <para>See <xref linkend="generic-classes"/>. Independent of
215 <option>-fglasgow-exts</option>.</para>
220 <term><option>-XNoImplicitPrelude</option></term>
222 <para><indexterm><primary>-XNoImplicitPrelude
223 option</primary></indexterm> GHC normally imports
224 <filename>Prelude.hi</filename> files for you. If you'd
225 rather it didn't, then give it a
226 <option>-XNoImplicitPrelude</option> option. The idea is
227 that you can then import a Prelude of your own. (But don't
228 call it <literal>Prelude</literal>; the Haskell module
229 namespace is flat, and you must not conflict with any
230 Prelude module.)</para>
232 <para>Even though you have not imported the Prelude, most of
233 the built-in syntax still refers to the built-in Haskell
234 Prelude types and values, as specified by the Haskell
235 Report. For example, the type <literal>[Int]</literal>
236 still means <literal>Prelude.[] Int</literal>; tuples
237 continue to refer to the standard Prelude tuples; the
238 translation for list comprehensions continues to use
239 <literal>Prelude.map</literal> etc.</para>
241 <para>However, <option>-XNoImplicitPrelude</option> does
242 change the handling of certain built-in syntax: see <xref
243 linkend="rebindable-syntax"/>.</para>
248 <term><option>-XImplicitParams</option></term>
250 <para>Enables implicit parameters (see <xref
251 linkend="implicit-parameters"/>). Currently also implied by
252 <option>-fglasgow-exts</option>.</para>
255 <literal>?<replaceable>varid</replaceable></literal>,
256 <literal>%<replaceable>varid</replaceable></literal>.</para>
261 <term><option>-XOverloadedStrings</option></term>
263 <para>Enables overloaded string literals (see <xref
264 linkend="overloaded-strings"/>).</para>
269 <term><option>-XScopedTypeVariables</option></term>
271 <para>Enables lexically-scoped type variables (see <xref
272 linkend="scoped-type-variables"/>). Implied by
273 <option>-fglasgow-exts</option>.</para>
278 <term><option>-XTemplateHaskell</option></term>
280 <para>Enables Template Haskell (see <xref
281 linkend="template-haskell"/>). This flag must
282 be given explicitly; it is no longer implied by
283 <option>-fglasgow-exts</option>.</para>
285 <para>Syntax stolen: <literal>[|</literal>,
286 <literal>[e|</literal>, <literal>[p|</literal>,
287 <literal>[d|</literal>, <literal>[t|</literal>,
288 <literal>$(</literal>,
289 <literal>$<replaceable>varid</replaceable></literal>.</para>
294 <term><option>-XQuasiQuotes</option></term>
296 <para>Enables quasiquotation (see <xref
297 linkend="th-quasiquotation"/>).</para>
300 <literal>[:<replaceable>varid</replaceable>|</literal>.</para>
307 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
308 <sect1 id="primitives">
309 <title>Unboxed types and primitive operations</title>
311 <para>GHC is built on a raft of primitive data types and operations.
312 While you really can use this stuff to write fast code,
313 we generally find it a lot less painful, and more satisfying in the
314 long run, to use higher-level language features and libraries. With
315 any luck, the code you write will be optimised to the efficient
316 unboxed version in any case. And if it isn't, we'd like to know
319 <para>We do not currently have good, up-to-date documentation about the
320 primitives, perhaps because they are mainly intended for internal use.
321 There used to be a long section about them here in the User Guide, but it
322 became out of date, and wrong information is worse than none.</para>
324 <para>The Real Truth about what primitive types there are, and what operations
325 work over those types, is held in the file
326 <filename>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 XML
337 back end to the program that processes <filename>primops.txt</filename> so that
338 we could include the results here in the User Guide.</para>
340 <para>What follows here is a brief summary of some main points.</para>
342 <sect2 id="glasgow-unboxed">
347 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
350 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
351 that values of that type are represented by a pointer to a heap
352 object. The representation of a Haskell <literal>Int</literal>, for
353 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
354 type, however, is represented by the value itself, no pointers or heap
355 allocation are involved.
359 Unboxed types correspond to the “raw machine” types you
360 would use in C: <literal>Int#</literal> (long int),
361 <literal>Double#</literal> (double), <literal>Addr#</literal>
362 (void *), etc. The <emphasis>primitive operations</emphasis>
363 (PrimOps) on these types are what you might expect; e.g.,
364 <literal>(+#)</literal> is addition on
365 <literal>Int#</literal>s, and is the machine-addition that we all
366 know and love—usually one instruction.
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 manage 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 comprehension 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 occurring 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 example, 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 a <literal>let</literal> statement scope over other
1541 statements in the group, just as the bound name does.
1545 Moreover, a local fixity declaration *must* accompany a local binding of
1546 that name: it is not possible to revise the fixity of name bound
1549 let infixr 9 $ in ...
1552 Because local fixity declarations are technically Haskell 98, no flag is
1553 necessary to enable them.
1560 <!-- TYPE SYSTEM EXTENSIONS -->
1561 <sect1 id="data-type-extensions">
1562 <title>Extensions to data types and type synonyms</title>
1564 <sect2 id="nullary-types">
1565 <title>Data types with no constructors</title>
1567 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1568 a data type with no constructors. For example:</para>
1572 data T a -- T :: * -> *
1575 <para>Syntactically, the declaration lacks the "= constrs" part. The
1576 type can be parameterised over types of any kind, but if the kind is
1577 not <literal>*</literal> then an explicit kind annotation must be used
1578 (see <xref linkend="kinding"/>).</para>
1580 <para>Such data types have only one value, namely bottom.
1581 Nevertheless, they can be useful when defining "phantom types".</para>
1584 <sect2 id="infix-tycons">
1585 <title>Infix type constructors, classes, and type variables</title>
1588 GHC allows type constructors, classes, and type variables to be operators, and
1589 to be written infix, very much like expressions. More specifically:
1592 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1593 The lexical syntax is the same as that for data constructors.
1596 Data type and type-synonym declarations can be written infix, parenthesised
1597 if you want further arguments. E.g.
1599 data a :*: b = Foo a b
1600 type a :+: b = Either a b
1601 class a :=: b where ...
1603 data (a :**: b) x = Baz a b x
1604 type (a :++: b) y = Either (a,b) y
1608 Types, and class constraints, can be written infix. For example
1611 f :: (a :=: b) => a -> b
1615 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1616 The lexical syntax is the same as that for variable operators, excluding "(.)",
1617 "(!)", and "(*)". In a binding position, the operator must be
1618 parenthesised. For example:
1620 type T (+) = Int + Int
1624 liftA2 :: Arrow (~>)
1625 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1631 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1632 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1635 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1636 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1637 sets the fixity for a data constructor and the corresponding type constructor. For example:
1641 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1642 and similarly for <literal>:*:</literal>.
1643 <literal>Int `a` Bool</literal>.
1646 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1653 <sect2 id="type-synonyms">
1654 <title>Liberalised type synonyms</title>
1657 Type synonyms are like macros at the type level, and
1658 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1659 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1661 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1662 in a type synonym, thus:
1664 type Discard a = forall b. Show b => a -> b -> (a, String)
1669 g :: Discard Int -> (Int,String) -- A rank-2 type
1676 You can write an unboxed tuple in a type synonym:
1678 type Pr = (# Int, Int #)
1686 You can apply a type synonym to a forall type:
1688 type Foo a = a -> a -> Bool
1690 f :: Foo (forall b. b->b)
1692 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1694 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1699 You can apply a type synonym to a partially applied type synonym:
1701 type Generic i o = forall x. i x -> o x
1704 foo :: Generic Id []
1706 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1708 foo :: forall x. x -> [x]
1716 GHC currently does kind checking before expanding synonyms (though even that
1720 After expanding type synonyms, GHC does validity checking on types, looking for
1721 the following mal-formedness which isn't detected simply by kind checking:
1724 Type constructor applied to a type involving for-alls.
1727 Unboxed tuple on left of an arrow.
1730 Partially-applied type synonym.
1734 this will be rejected:
1736 type Pr = (# Int, Int #)
1741 because GHC does not allow unboxed tuples on the left of a function arrow.
1746 <sect2 id="existential-quantification">
1747 <title>Existentially quantified data constructors
1751 The idea of using existential quantification in data type declarations
1752 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1753 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1754 London, 1991). It was later formalised by Laufer and Odersky
1755 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1756 TOPLAS, 16(5), pp1411-1430, 1994).
1757 It's been in Lennart
1758 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1759 proved very useful. Here's the idea. Consider the declaration:
1765 data Foo = forall a. MkFoo a (a -> Bool)
1772 The data type <literal>Foo</literal> has two constructors with types:
1778 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1785 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1786 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1787 For example, the following expression is fine:
1793 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1799 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1800 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1801 isUpper</function> packages a character with a compatible function. These
1802 two things are each of type <literal>Foo</literal> and can be put in a list.
1806 What can we do with a value of type <literal>Foo</literal>?. In particular,
1807 what happens when we pattern-match on <function>MkFoo</function>?
1813 f (MkFoo val fn) = ???
1819 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1820 are compatible, the only (useful) thing we can do with them is to
1821 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1828 f (MkFoo val fn) = fn val
1834 What this allows us to do is to package heterogeneous values
1835 together with a bunch of functions that manipulate them, and then treat
1836 that collection of packages in a uniform manner. You can express
1837 quite a bit of object-oriented-like programming this way.
1840 <sect3 id="existential">
1841 <title>Why existential?
1845 What has this to do with <emphasis>existential</emphasis> quantification?
1846 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1852 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1858 But Haskell programmers can safely think of the ordinary
1859 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1860 adding a new existential quantification construct.
1865 <sect3 id="existential-with-context">
1866 <title>Existentials and type classes</title>
1869 An easy extension is to allow
1870 arbitrary contexts before the constructor. For example:
1876 data Baz = forall a. Eq a => Baz1 a a
1877 | forall b. Show b => Baz2 b (b -> b)
1883 The two constructors have the types you'd expect:
1889 Baz1 :: forall a. Eq a => a -> a -> Baz
1890 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1896 But when pattern matching on <function>Baz1</function> the matched values can be compared
1897 for equality, and when pattern matching on <function>Baz2</function> the first matched
1898 value can be converted to a string (as well as applying the function to it).
1899 So this program is legal:
1906 f (Baz1 p q) | p == q = "Yes"
1908 f (Baz2 v fn) = show (fn v)
1914 Operationally, in a dictionary-passing implementation, the
1915 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1916 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1917 extract it on pattern matching.
1922 <sect3 id="existential-records">
1923 <title>Record Constructors</title>
1926 GHC allows existentials to be used with records syntax as well. For example:
1929 data Counter a = forall self. NewCounter
1931 , _inc :: self -> self
1932 , _display :: self -> IO ()
1936 Here <literal>tag</literal> is a public field, with a well-typed selector
1937 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1938 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1939 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1940 compile-time error. In other words, <emphasis>GHC defines a record selector function
1941 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1942 (This example used an underscore in the fields for which record selectors
1943 will not be defined, but that is only programming style; GHC ignores them.)
1947 To make use of these hidden fields, we need to create some helper functions:
1950 inc :: Counter a -> Counter a
1951 inc (NewCounter x i d t) = NewCounter
1952 { _this = i x, _inc = i, _display = d, tag = t }
1954 display :: Counter a -> IO ()
1955 display NewCounter{ _this = x, _display = d } = d x
1958 Now we can define counters with different underlying implementations:
1961 counterA :: Counter String
1962 counterA = NewCounter
1963 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1965 counterB :: Counter String
1966 counterB = NewCounter
1967 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1970 display (inc counterA) -- prints "1"
1971 display (inc (inc counterB)) -- prints "##"
1974 At the moment, record update syntax is only supported for Haskell 98 data types,
1975 so the following function does <emphasis>not</emphasis> work:
1978 -- This is invalid; use explicit NewCounter instead for now
1979 setTag :: Counter a -> a -> Counter a
1980 setTag obj t = obj{ tag = t }
1989 <title>Restrictions</title>
1992 There are several restrictions on the ways in which existentially-quantified
1993 constructors can be use.
2002 When pattern matching, each pattern match introduces a new,
2003 distinct, type for each existential type variable. These types cannot
2004 be unified with any other type, nor can they escape from the scope of
2005 the pattern match. For example, these fragments are incorrect:
2013 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2014 is the result of <function>f1</function>. One way to see why this is wrong is to
2015 ask what type <function>f1</function> has:
2019 f1 :: Foo -> a -- Weird!
2023 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2028 f1 :: forall a. Foo -> a -- Wrong!
2032 The original program is just plain wrong. Here's another sort of error
2036 f2 (Baz1 a b) (Baz1 p q) = a==q
2040 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2041 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2042 from the two <function>Baz1</function> constructors.
2050 You can't pattern-match on an existentially quantified
2051 constructor in a <literal>let</literal> or <literal>where</literal> group of
2052 bindings. So this is illegal:
2056 f3 x = a==b where { Baz1 a b = x }
2059 Instead, use a <literal>case</literal> expression:
2062 f3 x = case x of Baz1 a b -> a==b
2065 In general, you can only pattern-match
2066 on an existentially-quantified constructor in a <literal>case</literal> expression or
2067 in the patterns of a function definition.
2069 The reason for this restriction is really an implementation one.
2070 Type-checking binding groups is already a nightmare without
2071 existentials complicating the picture. Also an existential pattern
2072 binding at the top level of a module doesn't make sense, because it's
2073 not clear how to prevent the existentially-quantified type "escaping".
2074 So for now, there's a simple-to-state restriction. We'll see how
2082 You can't use existential quantification for <literal>newtype</literal>
2083 declarations. So this is illegal:
2087 newtype T = forall a. Ord a => MkT a
2091 Reason: a value of type <literal>T</literal> must be represented as a
2092 pair of a dictionary for <literal>Ord t</literal> and a value of type
2093 <literal>t</literal>. That contradicts the idea that
2094 <literal>newtype</literal> should have no concrete representation.
2095 You can get just the same efficiency and effect by using
2096 <literal>data</literal> instead of <literal>newtype</literal>. If
2097 there is no overloading involved, then there is more of a case for
2098 allowing an existentially-quantified <literal>newtype</literal>,
2099 because the <literal>data</literal> version does carry an
2100 implementation cost, but single-field existentially quantified
2101 constructors aren't much use. So the simple restriction (no
2102 existential stuff on <literal>newtype</literal>) stands, unless there
2103 are convincing reasons to change it.
2111 You can't use <literal>deriving</literal> to define instances of a
2112 data type with existentially quantified data constructors.
2114 Reason: in most cases it would not make sense. For example:;
2117 data T = forall a. MkT [a] deriving( Eq )
2120 To derive <literal>Eq</literal> in the standard way we would need to have equality
2121 between the single component of two <function>MkT</function> constructors:
2125 (MkT a) == (MkT b) = ???
2128 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2129 It's just about possible to imagine examples in which the derived instance
2130 would make sense, but it seems altogether simpler simply to prohibit such
2131 declarations. Define your own instances!
2142 <!-- ====================== Generalised algebraic data types ======================= -->
2144 <sect2 id="gadt-style">
2145 <title>Declaring data types with explicit constructor signatures</title>
2147 <para>GHC allows you to declare an algebraic data type by
2148 giving the type signatures of constructors explicitly. For example:
2152 Just :: a -> Maybe a
2154 The form is called a "GADT-style declaration"
2155 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2156 can only be declared using this form.</para>
2157 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2158 For example, these two declarations are equivalent:
2160 data Foo = forall a. MkFoo a (a -> Bool)
2161 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2164 <para>Any data type that can be declared in standard Haskell-98 syntax
2165 can also be declared using GADT-style syntax.
2166 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2167 they treat class constraints on the data constructors differently.
2168 Specifically, if the constructor is given a type-class context, that
2169 context is made available by pattern matching. For example:
2172 MkSet :: Eq a => [a] -> Set a
2174 makeSet :: Eq a => [a] -> Set a
2175 makeSet xs = MkSet (nub xs)
2177 insert :: a -> Set a -> Set a
2178 insert a (MkSet as) | a `elem` as = MkSet as
2179 | otherwise = MkSet (a:as)
2181 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2182 gives rise to a <literal>(Eq a)</literal>
2183 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2184 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2185 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2186 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2187 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2188 In the example, the equality dictionary is used to satisfy the equality constraint
2189 generated by the call to <literal>elem</literal>, so that the type of
2190 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2193 For example, one possible application is to reify dictionaries:
2195 data NumInst a where
2196 MkNumInst :: Num a => NumInst a
2198 intInst :: NumInst Int
2201 plus :: NumInst a -> a -> a -> a
2202 plus MkNumInst p q = p + q
2204 Here, a value of type <literal>NumInst a</literal> is equivalent
2205 to an explicit <literal>(Num a)</literal> dictionary.
2208 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2209 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2213 = Num a => MkNumInst (NumInst a)
2215 Notice that, unlike the situation when declaring an existential, there is
2216 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2217 data type's universally quantified type variable <literal>a</literal>.
2218 A constructor may have both universal and existential type variables: for example,
2219 the following two declarations are equivalent:
2222 = forall b. (Num a, Eq b) => MkT1 a b
2224 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2227 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2228 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2229 In Haskell 98 the definition
2231 data Eq a => Set' a = MkSet' [a]
2233 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2234 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2235 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2236 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2237 GHC's behaviour is much more useful, as well as much more intuitive.
2241 The rest of this section gives further details about GADT-style data
2246 The result type of each data constructor must begin with the type constructor being defined.
2247 If the result type of all constructors
2248 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2249 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2250 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2254 The type signature of
2255 each constructor is independent, and is implicitly universally quantified as usual.
2256 Different constructors may have different universally-quantified type variables
2257 and different type-class constraints.
2258 For example, this is fine:
2261 T1 :: Eq b => b -> T b
2262 T2 :: (Show c, Ix c) => c -> [c] -> T c
2267 Unlike a Haskell-98-style
2268 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2269 have no scope. Indeed, one can write a kind signature instead:
2271 data Set :: * -> * where ...
2273 or even a mixture of the two:
2275 data Foo a :: (* -> *) -> * where ...
2277 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2280 data Foo a (b :: * -> *) where ...
2286 You can use strictness annotations, in the obvious places
2287 in the constructor type:
2290 Lit :: !Int -> Term Int
2291 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2292 Pair :: Term a -> Term b -> Term (a,b)
2297 You can use a <literal>deriving</literal> clause on a GADT-style data type
2298 declaration. For example, these two declarations are equivalent
2300 data Maybe1 a where {
2301 Nothing1 :: Maybe1 a ;
2302 Just1 :: a -> Maybe1 a
2303 } deriving( Eq, Ord )
2305 data Maybe2 a = Nothing2 | Just2 a
2311 You can use record syntax on a GADT-style data type declaration:
2315 Adult { name :: String, children :: [Person] } :: Person
2316 Child { name :: String } :: Person
2318 As usual, for every constructor that has a field <literal>f</literal>, the type of
2319 field <literal>f</literal> must be the same (modulo alpha conversion).
2322 At the moment, record updates are not yet possible with GADT-style declarations,
2323 so support is limited to record construction, selection and pattern matching.
2326 aPerson = Adult { name = "Fred", children = [] }
2328 shortName :: Person -> Bool
2329 hasChildren (Adult { children = kids }) = not (null kids)
2330 hasChildren (Child {}) = False
2335 As in the case of existentials declared using the Haskell-98-like record syntax
2336 (<xref linkend="existential-records"/>),
2337 record-selector functions are generated only for those fields that have well-typed
2339 Here is the example of that section, in GADT-style syntax:
2341 data Counter a where
2342 NewCounter { _this :: self
2343 , _inc :: self -> self
2344 , _display :: self -> IO ()
2349 As before, only one selector function is generated here, that for <literal>tag</literal>.
2350 Nevertheless, you can still use all the field names in pattern matching and record construction.
2352 </itemizedlist></para>
2356 <title>Generalised Algebraic Data Types (GADTs)</title>
2358 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2359 by allowing constructors to have richer return types. Here is an example:
2362 Lit :: Int -> Term Int
2363 Succ :: Term Int -> Term Int
2364 IsZero :: Term Int -> Term Bool
2365 If :: Term Bool -> Term a -> Term a -> Term a
2366 Pair :: Term a -> Term b -> Term (a,b)
2368 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2369 case with ordinary data types. This generality allows us to
2370 write a well-typed <literal>eval</literal> function
2371 for these <literal>Terms</literal>:
2375 eval (Succ t) = 1 + eval t
2376 eval (IsZero t) = eval t == 0
2377 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2378 eval (Pair e1 e2) = (eval e1, eval e2)
2380 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2381 For example, in the right hand side of the equation
2386 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2387 A precise specification of the type rules is beyond what this user manual aspires to,
2388 but the design closely follows that described in
2390 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2391 unification-based type inference for GADTs</ulink>,
2393 The general principle is this: <emphasis>type refinement is only carried out
2394 based on user-supplied type annotations</emphasis>.
2395 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2396 and lots of obscure error messages will
2397 occur. However, the refinement is quite general. For example, if we had:
2399 eval :: Term a -> a -> a
2400 eval (Lit i) j = i+j
2402 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2403 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2404 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2407 These and many other examples are given in papers by Hongwei Xi, and
2408 Tim Sheard. There is a longer introduction
2409 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2411 <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
2412 may use different notation to that implemented in GHC.
2415 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2416 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2419 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2420 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2421 The result type of each constructor must begin with the type constructor being defined,
2422 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2423 For example, in the <literal>Term</literal> data
2424 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2425 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
2430 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2431 an ordinary data type.
2435 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2439 Lit { val :: Int } :: Term Int
2440 Succ { num :: Term Int } :: Term Int
2441 Pred { num :: Term Int } :: Term Int
2442 IsZero { arg :: Term Int } :: Term Bool
2443 Pair { arg1 :: Term a
2446 If { cnd :: Term Bool
2451 However, for GADTs there is the following additional constraint:
2452 every constructor that has a field <literal>f</literal> must have
2453 the same result type (modulo alpha conversion)
2454 Hence, in the above example, we cannot merge the <literal>num</literal>
2455 and <literal>arg</literal> fields above into a
2456 single name. Although their field types are both <literal>Term Int</literal>,
2457 their selector functions actually have different types:
2460 num :: Term Int -> Term Int
2461 arg :: Term Bool -> Term Int
2471 <!-- ====================== End of Generalised algebraic data types ======================= -->
2473 <sect1 id="deriving">
2474 <title>Extensions to the "deriving" mechanism</title>
2476 <sect2 id="deriving-inferred">
2477 <title>Inferred context for deriving clauses</title>
2480 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2483 data T0 f a = MkT0 a deriving( Eq )
2484 data T1 f a = MkT1 (f a) deriving( Eq )
2485 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2487 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2489 instance Eq a => Eq (T0 f a) where ...
2490 instance Eq (f a) => Eq (T1 f a) where ...
2491 instance Eq (f (f a)) => Eq (T2 f a) where ...
2493 The first of these is obviously fine. The second is still fine, although less obviously.
2494 The third is not Haskell 98, and risks losing termination of instances.
2497 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2498 each constraint in the inferred instance context must consist only of type variables,
2499 with no repetitions.
2502 This rule is applied regardless of flags. If you want a more exotic context, you can write
2503 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2507 <sect2 id="stand-alone-deriving">
2508 <title>Stand-alone deriving declarations</title>
2511 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2513 data Foo a = Bar a | Baz String
2515 deriving instance Eq a => Eq (Foo a)
2517 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2518 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2519 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2520 exactly as you would in an ordinary instance declaration.
2521 (In contrast the context is inferred in a <literal>deriving</literal> clause
2522 attached to a data type declaration.) These <literal>deriving instance</literal>
2523 rules obey the same rules concerning form and termination as ordinary instance declarations,
2524 controlled by the same flags; see <xref linkend="instance-decls"/>. </para>
2526 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2527 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2530 newtype Foo a = MkFoo (State Int a)
2532 deriving instance MonadState Int Foo
2534 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2535 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2541 <sect2 id="deriving-typeable">
2542 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2545 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2546 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2547 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2548 classes <literal>Eq</literal>, <literal>Ord</literal>,
2549 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2552 GHC extends this list with two more classes that may be automatically derived
2553 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2554 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2555 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2556 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2558 <para>An instance of <literal>Typeable</literal> can only be derived if the
2559 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2560 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2562 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2563 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2565 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2566 are used, and only <literal>Typeable1</literal> up to
2567 <literal>Typeable7</literal> are provided in the library.)
2568 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2569 class, whose kind suits that of the data type constructor, and
2570 then writing the data type instance by hand.
2574 <sect2 id="newtype-deriving">
2575 <title>Generalised derived instances for newtypes</title>
2578 When you define an abstract type using <literal>newtype</literal>, you may want
2579 the new type to inherit some instances from its representation. In
2580 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2581 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2582 other classes you have to write an explicit instance declaration. For
2583 example, if you define
2586 newtype Dollars = Dollars Int
2589 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2590 explicitly define an instance of <literal>Num</literal>:
2593 instance Num Dollars where
2594 Dollars a + Dollars b = Dollars (a+b)
2597 All the instance does is apply and remove the <literal>newtype</literal>
2598 constructor. It is particularly galling that, since the constructor
2599 doesn't appear at run-time, this instance declaration defines a
2600 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2601 dictionary, only slower!
2605 <sect3> <title> Generalising the deriving clause </title>
2607 GHC now permits such instances to be derived instead,
2608 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2611 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2614 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2615 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2616 derives an instance declaration of the form
2619 instance Num Int => Num Dollars
2622 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2626 We can also derive instances of constructor classes in a similar
2627 way. For example, suppose we have implemented state and failure monad
2628 transformers, such that
2631 instance Monad m => Monad (State s m)
2632 instance Monad m => Monad (Failure m)
2634 In Haskell 98, we can define a parsing monad by
2636 type Parser tok m a = State [tok] (Failure m) a
2639 which is automatically a monad thanks to the instance declarations
2640 above. With the extension, we can make the parser type abstract,
2641 without needing to write an instance of class <literal>Monad</literal>, via
2644 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2647 In this case the derived instance declaration is of the form
2649 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2652 Notice that, since <literal>Monad</literal> is a constructor class, the
2653 instance is a <emphasis>partial application</emphasis> of the new type, not the
2654 entire left hand side. We can imagine that the type declaration is
2655 "eta-converted" to generate the context of the instance
2660 We can even derive instances of multi-parameter classes, provided the
2661 newtype is the last class parameter. In this case, a ``partial
2662 application'' of the class appears in the <literal>deriving</literal>
2663 clause. For example, given the class
2666 class StateMonad s m | m -> s where ...
2667 instance Monad m => StateMonad s (State s m) where ...
2669 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2671 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2672 deriving (Monad, StateMonad [tok])
2675 The derived instance is obtained by completing the application of the
2676 class to the new type:
2679 instance StateMonad [tok] (State [tok] (Failure m)) =>
2680 StateMonad [tok] (Parser tok m)
2685 As a result of this extension, all derived instances in newtype
2686 declarations are treated uniformly (and implemented just by reusing
2687 the dictionary for the representation type), <emphasis>except</emphasis>
2688 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2689 the newtype and its representation.
2693 <sect3> <title> A more precise specification </title>
2695 Derived instance declarations are constructed as follows. Consider the
2696 declaration (after expansion of any type synonyms)
2699 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2705 The <literal>ci</literal> are partial applications of
2706 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2707 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2710 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2713 The type <literal>t</literal> is an arbitrary type.
2716 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2717 nor in the <literal>ci</literal>, and
2720 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2721 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2722 should not "look through" the type or its constructor. You can still
2723 derive these classes for a newtype, but it happens in the usual way, not
2724 via this new mechanism.
2727 Then, for each <literal>ci</literal>, the derived instance
2730 instance ci t => ci (T v1...vk)
2732 As an example which does <emphasis>not</emphasis> work, consider
2734 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2736 Here we cannot derive the instance
2738 instance Monad (State s m) => Monad (NonMonad m)
2741 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2742 and so cannot be "eta-converted" away. It is a good thing that this
2743 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2744 not, in fact, a monad --- for the same reason. Try defining
2745 <literal>>>=</literal> with the correct type: you won't be able to.
2749 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2750 important, since we can only derive instances for the last one. If the
2751 <literal>StateMonad</literal> class above were instead defined as
2754 class StateMonad m s | m -> s where ...
2757 then we would not have been able to derive an instance for the
2758 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2759 classes usually have one "main" parameter for which deriving new
2760 instances is most interesting.
2762 <para>Lastly, all of this applies only for classes other than
2763 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2764 and <literal>Data</literal>, for which the built-in derivation applies (section
2765 4.3.3. of the Haskell Report).
2766 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2767 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2768 the standard method is used or the one described here.)
2775 <!-- TYPE SYSTEM EXTENSIONS -->
2776 <sect1 id="type-class-extensions">
2777 <title>Class and instances declarations</title>
2779 <sect2 id="multi-param-type-classes">
2780 <title>Class declarations</title>
2783 This section, and the next one, documents GHC's type-class extensions.
2784 There's lots of background in the paper <ulink
2785 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2786 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2787 Jones, Erik Meijer).
2790 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2794 <title>Multi-parameter type classes</title>
2796 Multi-parameter type classes are permitted. For example:
2800 class Collection c a where
2801 union :: c a -> c a -> c a
2809 <title>The superclasses of a class declaration</title>
2812 There are no restrictions on the context in a class declaration
2813 (which introduces superclasses), except that the class hierarchy must
2814 be acyclic. So these class declarations are OK:
2818 class Functor (m k) => FiniteMap m k where
2821 class (Monad m, Monad (t m)) => Transform t m where
2822 lift :: m a -> (t m) a
2828 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2829 of "acyclic" involves only the superclass relationships. For example,
2835 op :: D b => a -> b -> b
2838 class C a => D a where { ... }
2842 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2843 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2844 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2851 <sect3 id="class-method-types">
2852 <title>Class method types</title>
2855 Haskell 98 prohibits class method types to mention constraints on the
2856 class type variable, thus:
2859 fromList :: [a] -> s a
2860 elem :: Eq a => a -> s a -> Bool
2862 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2863 contains the constraint <literal>Eq a</literal>, constrains only the
2864 class type variable (in this case <literal>a</literal>).
2865 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2872 <sect2 id="functional-dependencies">
2873 <title>Functional dependencies
2876 <para> Functional dependencies are implemented as described by Mark Jones
2877 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2878 In Proceedings of the 9th European Symposium on Programming,
2879 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2883 Functional dependencies are introduced by a vertical bar in the syntax of a
2884 class declaration; e.g.
2886 class (Monad m) => MonadState s m | m -> s where ...
2888 class Foo a b c | a b -> c where ...
2890 There should be more documentation, but there isn't (yet). Yell if you need it.
2893 <sect3><title>Rules for functional dependencies </title>
2895 In a class declaration, all of the class type variables must be reachable (in the sense
2896 mentioned in <xref linkend="type-restrictions"/>)
2897 from the free variables of each method type.
2901 class Coll s a where
2903 insert :: s -> a -> s
2906 is not OK, because the type of <literal>empty</literal> doesn't mention
2907 <literal>a</literal>. Functional dependencies can make the type variable
2910 class Coll s a | s -> a where
2912 insert :: s -> a -> s
2915 Alternatively <literal>Coll</literal> might be rewritten
2918 class Coll s a where
2920 insert :: s a -> a -> s a
2924 which makes the connection between the type of a collection of
2925 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2926 Occasionally this really doesn't work, in which case you can split the
2934 class CollE s => Coll s a where
2935 insert :: s -> a -> s
2942 <title>Background on functional dependencies</title>
2944 <para>The following description of the motivation and use of functional dependencies is taken
2945 from the Hugs user manual, reproduced here (with minor changes) by kind
2946 permission of Mark Jones.
2949 Consider the following class, intended as part of a
2950 library for collection types:
2952 class Collects e ce where
2954 insert :: e -> ce -> ce
2955 member :: e -> ce -> Bool
2957 The type variable e used here represents the element type, while ce is the type
2958 of the container itself. Within this framework, we might want to define
2959 instances of this class for lists or characteristic functions (both of which
2960 can be used to represent collections of any equality type), bit sets (which can
2961 be used to represent collections of characters), or hash tables (which can be
2962 used to represent any collection whose elements have a hash function). Omitting
2963 standard implementation details, this would lead to the following declarations:
2965 instance Eq e => Collects e [e] where ...
2966 instance Eq e => Collects e (e -> Bool) where ...
2967 instance Collects Char BitSet where ...
2968 instance (Hashable e, Collects a ce)
2969 => Collects e (Array Int ce) where ...
2971 All this looks quite promising; we have a class and a range of interesting
2972 implementations. Unfortunately, there are some serious problems with the class
2973 declaration. First, the empty function has an ambiguous type:
2975 empty :: Collects e ce => ce
2977 By "ambiguous" we mean that there is a type variable e that appears on the left
2978 of the <literal>=></literal> symbol, but not on the right. The problem with
2979 this is that, according to the theoretical foundations of Haskell overloading,
2980 we cannot guarantee a well-defined semantics for any term with an ambiguous
2984 We can sidestep this specific problem by removing the empty member from the
2985 class declaration. However, although the remaining members, insert and member,
2986 do not have ambiguous types, we still run into problems when we try to use
2987 them. For example, consider the following two functions:
2989 f x y = insert x . insert y
2992 for which GHC infers the following types:
2994 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2995 g :: (Collects Bool c, Collects Char c) => c -> c
2997 Notice that the type for f allows the two parameters x and y to be assigned
2998 different types, even though it attempts to insert each of the two values, one
2999 after the other, into the same collection. If we're trying to model collections
3000 that contain only one type of value, then this is clearly an inaccurate
3001 type. Worse still, the definition for g is accepted, without causing a type
3002 error. As a result, the error in this code will not be flagged at the point
3003 where it appears. Instead, it will show up only when we try to use g, which
3004 might even be in a different module.
3007 <sect4><title>An attempt to use constructor classes</title>
3010 Faced with the problems described above, some Haskell programmers might be
3011 tempted to use something like the following version of the class declaration:
3013 class Collects e c where
3015 insert :: e -> c e -> c e
3016 member :: e -> c e -> Bool
3018 The key difference here is that we abstract over the type constructor c that is
3019 used to form the collection type c e, and not over that collection type itself,
3020 represented by ce in the original class declaration. This avoids the immediate
3021 problems that we mentioned above: empty has type <literal>Collects e c => c
3022 e</literal>, which is not ambiguous.
3025 The function f from the previous section has a more accurate type:
3027 f :: (Collects e c) => e -> e -> c e -> c e
3029 The function g from the previous section is now rejected with a type error as
3030 we would hope because the type of f does not allow the two arguments to have
3032 This, then, is an example of a multiple parameter class that does actually work
3033 quite well in practice, without ambiguity problems.
3034 There is, however, a catch. This version of the Collects class is nowhere near
3035 as general as the original class seemed to be: only one of the four instances
3036 for <literal>Collects</literal>
3037 given above can be used with this version of Collects because only one of
3038 them---the instance for lists---has a collection type that can be written in
3039 the form c e, for some type constructor c, and element type e.
3043 <sect4><title>Adding functional dependencies</title>
3046 To get a more useful version of the Collects class, Hugs provides a mechanism
3047 that allows programmers to specify dependencies between the parameters of a
3048 multiple parameter class (For readers with an interest in theoretical
3049 foundations and previous work: The use of dependency information can be seen
3050 both as a generalization of the proposal for `parametric type classes' that was
3051 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3052 later framework for "improvement" of qualified types. The
3053 underlying ideas are also discussed in a more theoretical and abstract setting
3054 in a manuscript [implparam], where they are identified as one point in a
3055 general design space for systems of implicit parameterization.).
3057 To start with an abstract example, consider a declaration such as:
3059 class C a b where ...
3061 which tells us simply that C can be thought of as a binary relation on types
3062 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3063 included in the definition of classes to add information about dependencies
3064 between parameters, as in the following examples:
3066 class D a b | a -> b where ...
3067 class E a b | a -> b, b -> a where ...
3069 The notation <literal>a -> b</literal> used here between the | and where
3070 symbols --- not to be
3071 confused with a function type --- indicates that the a parameter uniquely
3072 determines the b parameter, and might be read as "a determines b." Thus D is
3073 not just a relation, but actually a (partial) function. Similarly, from the two
3074 dependencies that are included in the definition of E, we can see that E
3075 represents a (partial) one-one mapping between types.
3078 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3079 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3080 m>=0, meaning that the y parameters are uniquely determined by the x
3081 parameters. Spaces can be used as separators if more than one variable appears
3082 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3083 annotated with multiple dependencies using commas as separators, as in the
3084 definition of E above. Some dependencies that we can write in this notation are
3085 redundant, and will be rejected because they don't serve any useful
3086 purpose, and may instead indicate an error in the program. Examples of
3087 dependencies like this include <literal>a -> a </literal>,
3088 <literal>a -> a a </literal>,
3089 <literal>a -> </literal>, etc. There can also be
3090 some redundancy if multiple dependencies are given, as in
3091 <literal>a->b</literal>,
3092 <literal>b->c </literal>, <literal>a->c </literal>, and
3093 in which some subset implies the remaining dependencies. Examples like this are
3094 not treated as errors. Note that dependencies appear only in class
3095 declarations, and not in any other part of the language. In particular, the
3096 syntax for instance declarations, class constraints, and types is completely
3100 By including dependencies in a class declaration, we provide a mechanism for
3101 the programmer to specify each multiple parameter class more precisely. The
3102 compiler, on the other hand, is responsible for ensuring that the set of
3103 instances that are in scope at any given point in the program is consistent
3104 with any declared dependencies. For example, the following pair of instance
3105 declarations cannot appear together in the same scope because they violate the
3106 dependency for D, even though either one on its own would be acceptable:
3108 instance D Bool Int where ...
3109 instance D Bool Char where ...
3111 Note also that the following declaration is not allowed, even by itself:
3113 instance D [a] b where ...
3115 The problem here is that this instance would allow one particular choice of [a]
3116 to be associated with more than one choice for b, which contradicts the
3117 dependency specified in the definition of D. More generally, this means that,
3118 in any instance of the form:
3120 instance D t s where ...
3122 for some particular types t and s, the only variables that can appear in s are
3123 the ones that appear in t, and hence, if the type t is known, then s will be
3124 uniquely determined.
3127 The benefit of including dependency information is that it allows us to define
3128 more general multiple parameter classes, without ambiguity problems, and with
3129 the benefit of more accurate types. To illustrate this, we return to the
3130 collection class example, and annotate the original definition of <literal>Collects</literal>
3131 with a simple dependency:
3133 class Collects e ce | ce -> e where
3135 insert :: e -> ce -> ce
3136 member :: e -> ce -> Bool
3138 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3139 determined by the type of the collection ce. Note that both parameters of
3140 Collects are of kind *; there are no constructor classes here. Note too that
3141 all of the instances of Collects that we gave earlier can be used
3142 together with this new definition.
3145 What about the ambiguity problems that we encountered with the original
3146 definition? The empty function still has type Collects e ce => ce, but it is no
3147 longer necessary to regard that as an ambiguous type: Although the variable e
3148 does not appear on the right of the => symbol, the dependency for class
3149 Collects tells us that it is uniquely determined by ce, which does appear on
3150 the right of the => symbol. Hence the context in which empty is used can still
3151 give enough information to determine types for both ce and e, without
3152 ambiguity. More generally, we need only regard a type as ambiguous if it
3153 contains a variable on the left of the => that is not uniquely determined
3154 (either directly or indirectly) by the variables on the right.
3157 Dependencies also help to produce more accurate types for user defined
3158 functions, and hence to provide earlier detection of errors, and less cluttered
3159 types for programmers to work with. Recall the previous definition for a
3162 f x y = insert x y = insert x . insert y
3164 for which we originally obtained a type:
3166 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3168 Given the dependency information that we have for Collects, however, we can
3169 deduce that a and b must be equal because they both appear as the second
3170 parameter in a Collects constraint with the same first parameter c. Hence we
3171 can infer a shorter and more accurate type for f:
3173 f :: (Collects a c) => a -> a -> c -> c
3175 In a similar way, the earlier definition of g will now be flagged as a type error.
3178 Although we have given only a few examples here, it should be clear that the
3179 addition of dependency information can help to make multiple parameter classes
3180 more useful in practice, avoiding ambiguity problems, and allowing more general
3181 sets of instance declarations.
3187 <sect2 id="instance-decls">
3188 <title>Instance declarations</title>
3190 <sect3 id="instance-rules">
3191 <title>Relaxed rules for instance declarations</title>
3193 <para>An instance declaration has the form
3195 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 ...
3197 The part before the "<literal>=></literal>" is the
3198 <emphasis>context</emphasis>, while the part after the
3199 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3203 In Haskell 98 the head of an instance declaration
3204 must be of the form <literal>C (T a1 ... an)</literal>, where
3205 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3206 and the <literal>a1 ... an</literal> are distinct type variables.
3207 Furthermore, the assertions in the context of the instance declaration
3208 must be of the form <literal>C a</literal> where <literal>a</literal>
3209 is a type variable that occurs in the head.
3212 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3213 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3214 the context and head of the instance declaration can each consist of arbitrary
3215 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3219 The Paterson Conditions: for each assertion in the context
3221 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3222 <listitem><para>The assertion has fewer constructors and variables (taken together
3223 and counting repetitions) than the head</para></listitem>
3227 <listitem><para>The Coverage Condition. For each functional dependency,
3228 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3229 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3230 every type variable in
3231 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3232 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3233 substitution mapping each type variable in the class declaration to the
3234 corresponding type in the instance declaration.
3237 These restrictions ensure that context reduction terminates: each reduction
3238 step makes the problem smaller by at least one
3239 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3240 if you give the <option>-fallow-undecidable-instances</option>
3241 flag (<xref linkend="undecidable-instances"/>).
3242 You can find lots of background material about the reason for these
3243 restrictions in the paper <ulink
3244 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3245 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3248 For example, these are OK:
3250 instance C Int [a] -- Multiple parameters
3251 instance Eq (S [a]) -- Structured type in head
3253 -- Repeated type variable in head
3254 instance C4 a a => C4 [a] [a]
3255 instance Stateful (ST s) (MutVar s)
3257 -- Head can consist of type variables only
3259 instance (Eq a, Show b) => C2 a b
3261 -- Non-type variables in context
3262 instance Show (s a) => Show (Sized s a)
3263 instance C2 Int a => C3 Bool [a]
3264 instance C2 Int a => C3 [a] b
3268 -- Context assertion no smaller than head
3269 instance C a => C a where ...
3270 -- (C b b) has more more occurrences of b than the head
3271 instance C b b => Foo [b] where ...
3276 The same restrictions apply to instances generated by
3277 <literal>deriving</literal> clauses. Thus the following is accepted:
3279 data MinHeap h a = H a (h a)
3282 because the derived instance
3284 instance (Show a, Show (h a)) => Show (MinHeap h a)
3286 conforms to the above rules.
3290 A useful idiom permitted by the above rules is as follows.
3291 If one allows overlapping instance declarations then it's quite
3292 convenient to have a "default instance" declaration that applies if
3293 something more specific does not:
3301 <sect3 id="undecidable-instances">
3302 <title>Undecidable instances</title>
3305 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3306 For example, sometimes you might want to use the following to get the
3307 effect of a "class synonym":
3309 class (C1 a, C2 a, C3 a) => C a where { }
3311 instance (C1 a, C2 a, C3 a) => C a where { }
3313 This allows you to write shorter signatures:
3319 f :: (C1 a, C2 a, C3 a) => ...
3321 The restrictions on functional dependencies (<xref
3322 linkend="functional-dependencies"/>) are particularly troublesome.
3323 It is tempting to introduce type variables in the context that do not appear in
3324 the head, something that is excluded by the normal rules. For example:
3326 class HasConverter a b | a -> b where
3329 data Foo a = MkFoo a
3331 instance (HasConverter a b,Show b) => Show (Foo a) where
3332 show (MkFoo value) = show (convert value)
3334 This is dangerous territory, however. Here, for example, is a program that would make the
3339 instance F [a] [[a]]
3340 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3342 Similarly, it can be tempting to lift the coverage condition:
3344 class Mul a b c | a b -> c where
3345 (.*.) :: a -> b -> c
3347 instance Mul Int Int Int where (.*.) = (*)
3348 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3349 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3351 The third instance declaration does not obey the coverage condition;
3352 and indeed the (somewhat strange) definition:
3354 f = \ b x y -> if b then x .*. [y] else y
3356 makes instance inference go into a loop, because it requires the constraint
3357 <literal>(Mul a [b] b)</literal>.
3360 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3361 the experimental flag <option>-XUndecidableInstances</option>
3362 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3363 both the Paterson Conditions and the Coverage Condition
3364 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3365 fixed-depth recursion stack. If you exceed the stack depth you get a
3366 sort of backtrace, and the opportunity to increase the stack depth
3367 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3373 <sect3 id="instance-overlap">
3374 <title>Overlapping instances</title>
3376 In general, <emphasis>GHC requires that that it be unambiguous which instance
3378 should be used to resolve a type-class constraint</emphasis>. This behaviour
3379 can be modified by two flags: <option>-XOverlappingInstances</option>
3380 <indexterm><primary>-XOverlappingInstances
3381 </primary></indexterm>
3382 and <option>-XIncoherentInstances</option>
3383 <indexterm><primary>-XIncoherentInstances
3384 </primary></indexterm>, as this section discusses. Both these
3385 flags are dynamic flags, and can be set on a per-module basis, using
3386 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3388 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3389 it tries to match every instance declaration against the
3391 by instantiating the head of the instance declaration. For example, consider
3394 instance context1 => C Int a where ... -- (A)
3395 instance context2 => C a Bool where ... -- (B)
3396 instance context3 => C Int [a] where ... -- (C)
3397 instance context4 => C Int [Int] where ... -- (D)
3399 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3400 but (C) and (D) do not. When matching, GHC takes
3401 no account of the context of the instance declaration
3402 (<literal>context1</literal> etc).
3403 GHC's default behaviour is that <emphasis>exactly one instance must match the
3404 constraint it is trying to resolve</emphasis>.
3405 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3406 including both declarations (A) and (B), say); an error is only reported if a
3407 particular constraint matches more than one.
3411 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3412 more than one instance to match, provided there is a most specific one. For
3413 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3414 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3415 most-specific match, the program is rejected.
3418 However, GHC is conservative about committing to an overlapping instance. For example:
3423 Suppose that from the RHS of <literal>f</literal> we get the constraint
3424 <literal>C Int [b]</literal>. But
3425 GHC does not commit to instance (C), because in a particular
3426 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3427 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3428 So GHC rejects the program.
3429 (If you add the flag <option>-XIncoherentInstances</option>,
3430 GHC will instead pick (C), without complaining about
3431 the problem of subsequent instantiations.)
3434 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3435 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3436 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3437 it instead. In this case, GHC will refrain from
3438 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3439 as before) but, rather than rejecting the program, it will infer the type
3441 f :: C Int b => [b] -> [b]
3443 That postpones the question of which instance to pick to the
3444 call site for <literal>f</literal>
3445 by which time more is known about the type <literal>b</literal>.
3448 The willingness to be overlapped or incoherent is a property of
3449 the <emphasis>instance declaration</emphasis> itself, controlled by the
3450 presence or otherwise of the <option>-XOverlappingInstances</option>
3451 and <option>-XIncoherentInstances</option> flags when that module is
3452 being defined. Neither flag is required in a module that imports and uses the
3453 instance declaration. Specifically, during the lookup process:
3456 An instance declaration is ignored during the lookup process if (a) a more specific
3457 match is found, and (b) the instance declaration was compiled with
3458 <option>-XOverlappingInstances</option>. The flag setting for the
3459 more-specific instance does not matter.
3462 Suppose an instance declaration does not match the constraint being looked up, but
3463 does unify with it, so that it might match when the constraint is further
3464 instantiated. Usually GHC will regard this as a reason for not committing to
3465 some other constraint. But if the instance declaration was compiled with
3466 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3467 check for that declaration.
3470 These rules make it possible for a library author to design a library that relies on
3471 overlapping instances without the library client having to know.
3474 If an instance declaration is compiled without
3475 <option>-XOverlappingInstances</option>,
3476 then that instance can never be overlapped. This could perhaps be
3477 inconvenient. Perhaps the rule should instead say that the
3478 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3479 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3480 at a usage site should be permitted regardless of how the instance declarations
3481 are compiled, if the <option>-XOverlappingInstances</option> flag is
3482 used at the usage site. (Mind you, the exact usage site can occasionally be
3483 hard to pin down.) We are interested to receive feedback on these points.
3485 <para>The <option>-XIncoherentInstances</option> flag implies the
3486 <option>-XOverlappingInstances</option> flag, but not vice versa.
3491 <title>Type synonyms in the instance head</title>
3494 <emphasis>Unlike Haskell 98, instance heads may use type
3495 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3496 As always, using a type synonym is just shorthand for
3497 writing the RHS of the type synonym definition. For example:
3501 type Point = (Int,Int)
3502 instance C Point where ...
3503 instance C [Point] where ...
3507 is legal. However, if you added
3511 instance C (Int,Int) where ...
3515 as well, then the compiler will complain about the overlapping
3516 (actually, identical) instance declarations. As always, type synonyms
3517 must be fully applied. You cannot, for example, write:
3522 instance Monad P where ...
3526 This design decision is independent of all the others, and easily
3527 reversed, but it makes sense to me.
3535 <sect2 id="overloaded-strings">
3536 <title>Overloaded string literals
3540 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3541 string literal has type <literal>String</literal>, but with overloaded string
3542 literals enabled (with <literal>-XOverloadedStrings</literal>)
3543 a string literal has type <literal>(IsString a) => a</literal>.
3546 This means that the usual string syntax can be used, e.g., for packed strings
3547 and other variations of string like types. String literals behave very much
3548 like integer literals, i.e., they can be used in both expressions and patterns.
3549 If used in a pattern the literal with be replaced by an equality test, in the same
3550 way as an integer literal is.
3553 The class <literal>IsString</literal> is defined as:
3555 class IsString a where
3556 fromString :: String -> a
3558 The only predefined instance is the obvious one to make strings work as usual:
3560 instance IsString [Char] where
3563 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3564 it explicitly (for example, to give an instance declaration for it), you can import it
3565 from module <literal>GHC.Exts</literal>.
3568 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3572 Each type in a default declaration must be an
3573 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3577 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3578 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3579 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3580 <emphasis>or</emphasis> <literal>IsString</literal>.
3589 import GHC.Exts( IsString(..) )
3591 newtype MyString = MyString String deriving (Eq, Show)
3592 instance IsString MyString where
3593 fromString = MyString
3595 greet :: MyString -> MyString
3596 greet "hello" = "world"
3600 print $ greet "hello"
3601 print $ greet "fool"
3605 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3606 to work since it gets translated into an equality comparison.
3612 <sect1 id="other-type-extensions">
3613 <title>Other type system extensions</title>
3615 <sect2 id="type-restrictions">
3616 <title>Type signatures</title>
3618 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3620 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3621 the form <emphasis>(class type-variable)</emphasis> or
3622 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3623 these type signatures are perfectly OK
3626 g :: Ord (T a ()) => ...
3630 GHC imposes the following restrictions on the constraints in a type signature.
3634 forall tv1..tvn (c1, ...,cn) => type
3637 (Here, we write the "foralls" explicitly, although the Haskell source
3638 language omits them; in Haskell 98, all the free type variables of an
3639 explicit source-language type signature are universally quantified,
3640 except for the class type variables in a class declaration. However,
3641 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3650 <emphasis>Each universally quantified type variable
3651 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3653 A type variable <literal>a</literal> is "reachable" if it appears
3654 in the same constraint as either a type variable free in
3655 <literal>type</literal>, or another reachable type variable.
3656 A value with a type that does not obey
3657 this reachability restriction cannot be used without introducing
3658 ambiguity; that is why the type is rejected.
3659 Here, for example, is an illegal type:
3663 forall a. Eq a => Int
3667 When a value with this type was used, the constraint <literal>Eq tv</literal>
3668 would be introduced where <literal>tv</literal> is a fresh type variable, and
3669 (in the dictionary-translation implementation) the value would be
3670 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3671 can never know which instance of <literal>Eq</literal> to use because we never
3672 get any more information about <literal>tv</literal>.
3676 that the reachability condition is weaker than saying that <literal>a</literal> is
3677 functionally dependent on a type variable free in
3678 <literal>type</literal> (see <xref
3679 linkend="functional-dependencies"/>). The reason for this is there
3680 might be a "hidden" dependency, in a superclass perhaps. So
3681 "reachable" is a conservative approximation to "functionally dependent".
3682 For example, consider:
3684 class C a b | a -> b where ...
3685 class C a b => D a b where ...
3686 f :: forall a b. D a b => a -> a
3688 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3689 but that is not immediately apparent from <literal>f</literal>'s type.
3695 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3696 universally quantified type variables <literal>tvi</literal></emphasis>.
3698 For example, this type is OK because <literal>C a b</literal> mentions the
3699 universally quantified type variable <literal>b</literal>:
3703 forall a. C a b => burble
3707 The next type is illegal because the constraint <literal>Eq b</literal> does not
3708 mention <literal>a</literal>:
3712 forall a. Eq b => burble
3716 The reason for this restriction is milder than the other one. The
3717 excluded types are never useful or necessary (because the offending
3718 context doesn't need to be witnessed at this point; it can be floated
3719 out). Furthermore, floating them out increases sharing. Lastly,
3720 excluding them is a conservative choice; it leaves a patch of
3721 territory free in case we need it later.
3735 <sect2 id="implicit-parameters">
3736 <title>Implicit parameters</title>
3738 <para> Implicit parameters are implemented as described in
3739 "Implicit parameters: dynamic scoping with static types",
3740 J Lewis, MB Shields, E Meijer, J Launchbury,
3741 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3745 <para>(Most of the following, still rather incomplete, documentation is
3746 due to Jeff Lewis.)</para>
3748 <para>Implicit parameter support is enabled with the option
3749 <option>-XImplicitParams</option>.</para>
3752 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3753 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3754 context. In Haskell, all variables are statically bound. Dynamic
3755 binding of variables is a notion that goes back to Lisp, but was later
3756 discarded in more modern incarnations, such as Scheme. Dynamic binding
3757 can be very confusing in an untyped language, and unfortunately, typed
3758 languages, in particular Hindley-Milner typed languages like Haskell,
3759 only support static scoping of variables.
3762 However, by a simple extension to the type class system of Haskell, we
3763 can support dynamic binding. Basically, we express the use of a
3764 dynamically bound variable as a constraint on the type. These
3765 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3766 function uses a dynamically-bound variable <literal>?x</literal>
3767 of type <literal>t'</literal>". For
3768 example, the following expresses the type of a sort function,
3769 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3771 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3773 The dynamic binding constraints are just a new form of predicate in the type class system.
3776 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3777 where <literal>x</literal> is
3778 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3779 Use of this construct also introduces a new
3780 dynamic-binding constraint in the type of the expression.
3781 For example, the following definition
3782 shows how we can define an implicitly parameterized sort function in
3783 terms of an explicitly parameterized <literal>sortBy</literal> function:
3785 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3787 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3793 <title>Implicit-parameter type constraints</title>
3795 Dynamic binding constraints behave just like other type class
3796 constraints in that they are automatically propagated. Thus, when a
3797 function is used, its implicit parameters are inherited by the
3798 function that called it. For example, our <literal>sort</literal> function might be used
3799 to pick out the least value in a list:
3801 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3802 least xs = head (sort xs)
3804 Without lifting a finger, the <literal>?cmp</literal> parameter is
3805 propagated to become a parameter of <literal>least</literal> as well. With explicit
3806 parameters, the default is that parameters must always be explicit
3807 propagated. With implicit parameters, the default is to always
3811 An implicit-parameter type constraint differs from other type class constraints in the
3812 following way: All uses of a particular implicit parameter must have
3813 the same type. This means that the type of <literal>(?x, ?x)</literal>
3814 is <literal>(?x::a) => (a,a)</literal>, and not
3815 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3819 <para> You can't have an implicit parameter in the context of a class or instance
3820 declaration. For example, both these declarations are illegal:
3822 class (?x::Int) => C a where ...
3823 instance (?x::a) => Foo [a] where ...
3825 Reason: exactly which implicit parameter you pick up depends on exactly where
3826 you invoke a function. But the ``invocation'' of instance declarations is done
3827 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3828 Easiest thing is to outlaw the offending types.</para>
3830 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3832 f :: (?x :: [a]) => Int -> Int
3835 g :: (Read a, Show a) => String -> String
3838 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3839 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3840 quite unambiguous, and fixes the type <literal>a</literal>.
3845 <title>Implicit-parameter bindings</title>
3848 An implicit parameter is <emphasis>bound</emphasis> using the standard
3849 <literal>let</literal> or <literal>where</literal> binding forms.
3850 For example, we define the <literal>min</literal> function by binding
3851 <literal>cmp</literal>.
3854 min = let ?cmp = (<=) in least
3858 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3859 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3860 (including in a list comprehension, or do-notation, or pattern guards),
3861 or a <literal>where</literal> clause.
3862 Note the following points:
3865 An implicit-parameter binding group must be a
3866 collection of simple bindings to implicit-style variables (no
3867 function-style bindings, and no type signatures); these bindings are
3868 neither polymorphic or recursive.
3871 You may not mix implicit-parameter bindings with ordinary bindings in a
3872 single <literal>let</literal>
3873 expression; use two nested <literal>let</literal>s instead.
3874 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3878 You may put multiple implicit-parameter bindings in a
3879 single binding group; but they are <emphasis>not</emphasis> treated
3880 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3881 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3882 parameter. The bindings are not nested, and may be re-ordered without changing
3883 the meaning of the program.
3884 For example, consider:
3886 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3888 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3889 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3891 f :: (?x::Int) => Int -> Int
3899 <sect3><title>Implicit parameters and polymorphic recursion</title>
3902 Consider these two definitions:
3905 len1 xs = let ?acc = 0 in len_acc1 xs
3908 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3913 len2 xs = let ?acc = 0 in len_acc2 xs
3915 len_acc2 :: (?acc :: Int) => [a] -> Int
3917 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3919 The only difference between the two groups is that in the second group
3920 <literal>len_acc</literal> is given a type signature.
3921 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3922 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3923 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3924 has a type signature, the recursive call is made to the
3925 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3926 as an implicit parameter. So we get the following results in GHCi:
3933 Adding a type signature dramatically changes the result! This is a rather
3934 counter-intuitive phenomenon, worth watching out for.
3938 <sect3><title>Implicit parameters and monomorphism</title>
3940 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3941 Haskell Report) to implicit parameters. For example, consider:
3949 Since the binding for <literal>y</literal> falls under the Monomorphism
3950 Restriction it is not generalised, so the type of <literal>y</literal> is
3951 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3952 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3953 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3954 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3955 <literal>y</literal> in the body of the <literal>let</literal> will see the
3956 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3957 <literal>14</literal>.
3962 <!-- ======================= COMMENTED OUT ========================
3964 We intend to remove linear implicit parameters, so I'm at least removing
3965 them from the 6.6 user manual
3967 <sect2 id="linear-implicit-parameters">
3968 <title>Linear implicit parameters</title>
3970 Linear implicit parameters are an idea developed by Koen Claessen,
3971 Mark Shields, and Simon PJ. They address the long-standing
3972 problem that monads seem over-kill for certain sorts of problem, notably:
3975 <listitem> <para> distributing a supply of unique names </para> </listitem>
3976 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3977 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3981 Linear implicit parameters are just like ordinary implicit parameters,
3982 except that they are "linear"; that is, they cannot be copied, and
3983 must be explicitly "split" instead. Linear implicit parameters are
3984 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3985 (The '/' in the '%' suggests the split!)
3990 import GHC.Exts( Splittable )
3992 data NameSupply = ...
3994 splitNS :: NameSupply -> (NameSupply, NameSupply)
3995 newName :: NameSupply -> Name
3997 instance Splittable NameSupply where
4001 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4002 f env (Lam x e) = Lam x' (f env e)
4005 env' = extend env x x'
4006 ...more equations for f...
4008 Notice that the implicit parameter %ns is consumed
4010 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4011 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4015 So the translation done by the type checker makes
4016 the parameter explicit:
4018 f :: NameSupply -> Env -> Expr -> Expr
4019 f ns env (Lam x e) = Lam x' (f ns1 env e)
4021 (ns1,ns2) = splitNS ns
4023 env = extend env x x'
4025 Notice the call to 'split' introduced by the type checker.
4026 How did it know to use 'splitNS'? Because what it really did
4027 was to introduce a call to the overloaded function 'split',
4028 defined by the class <literal>Splittable</literal>:
4030 class Splittable a where
4033 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4034 split for name supplies. But we can simply write
4040 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4042 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4043 <literal>GHC.Exts</literal>.
4048 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4049 are entirely distinct implicit parameters: you
4050 can use them together and they won't interfere with each other. </para>
4053 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4055 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4056 in the context of a class or instance declaration. </para></listitem>
4060 <sect3><title>Warnings</title>
4063 The monomorphism restriction is even more important than usual.
4064 Consider the example above:
4066 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4067 f env (Lam x e) = Lam x' (f env e)
4070 env' = extend env x x'
4072 If we replaced the two occurrences of x' by (newName %ns), which is
4073 usually a harmless thing to do, we get:
4075 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4076 f env (Lam x e) = Lam (newName %ns) (f env e)
4078 env' = extend env x (newName %ns)
4080 But now the name supply is consumed in <emphasis>three</emphasis> places
4081 (the two calls to newName,and the recursive call to f), so
4082 the result is utterly different. Urk! We don't even have
4086 Well, this is an experimental change. With implicit
4087 parameters we have already lost beta reduction anyway, and
4088 (as John Launchbury puts it) we can't sensibly reason about
4089 Haskell programs without knowing their typing.
4094 <sect3><title>Recursive functions</title>
4095 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4098 foo :: %x::T => Int -> [Int]
4100 foo n = %x : foo (n-1)
4102 where T is some type in class Splittable.</para>
4104 Do you get a list of all the same T's or all different T's
4105 (assuming that split gives two distinct T's back)?
4107 If you supply the type signature, taking advantage of polymorphic
4108 recursion, you get what you'd probably expect. Here's the
4109 translated term, where the implicit param is made explicit:
4112 foo x n = let (x1,x2) = split x
4113 in x1 : foo x2 (n-1)
4115 But if you don't supply a type signature, GHC uses the Hindley
4116 Milner trick of using a single monomorphic instance of the function
4117 for the recursive calls. That is what makes Hindley Milner type inference
4118 work. So the translation becomes
4122 foom n = x : foom (n-1)
4126 Result: 'x' is not split, and you get a list of identical T's. So the
4127 semantics of the program depends on whether or not foo has a type signature.
4130 You may say that this is a good reason to dislike linear implicit parameters
4131 and you'd be right. That is why they are an experimental feature.
4137 ================ END OF Linear Implicit Parameters commented out -->
4139 <sect2 id="kinding">
4140 <title>Explicitly-kinded quantification</title>
4143 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4144 to give the kind explicitly as (machine-checked) documentation,
4145 just as it is nice to give a type signature for a function. On some occasions,
4146 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4147 John Hughes had to define the data type:
4149 data Set cxt a = Set [a]
4150 | Unused (cxt a -> ())
4152 The only use for the <literal>Unused</literal> constructor was to force the correct
4153 kind for the type variable <literal>cxt</literal>.
4156 GHC now instead allows you to specify the kind of a type variable directly, wherever
4157 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4160 This flag enables kind signatures in the following places:
4162 <listitem><para><literal>data</literal> declarations:
4164 data Set (cxt :: * -> *) a = Set [a]
4165 </screen></para></listitem>
4166 <listitem><para><literal>type</literal> declarations:
4168 type T (f :: * -> *) = f Int
4169 </screen></para></listitem>
4170 <listitem><para><literal>class</literal> declarations:
4172 class (Eq a) => C (f :: * -> *) a where ...
4173 </screen></para></listitem>
4174 <listitem><para><literal>forall</literal>'s in type signatures:
4176 f :: forall (cxt :: * -> *). Set cxt Int
4177 </screen></para></listitem>
4182 The parentheses are required. Some of the spaces are required too, to
4183 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4184 will get a parse error, because "<literal>::*->*</literal>" is a
4185 single lexeme in Haskell.
4189 As part of the same extension, you can put kind annotations in types
4192 f :: (Int :: *) -> Int
4193 g :: forall a. a -> (a :: *)
4197 atype ::= '(' ctype '::' kind ')
4199 The parentheses are required.
4204 <sect2 id="universal-quantification">
4205 <title>Arbitrary-rank polymorphism
4209 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4210 allows us to say exactly what this means. For example:
4218 g :: forall b. (b -> b)
4220 The two are treated identically.
4224 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4225 explicit universal quantification in
4227 For example, all the following types are legal:
4229 f1 :: forall a b. a -> b -> a
4230 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4232 f2 :: (forall a. a->a) -> Int -> Int
4233 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4235 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4237 f4 :: Int -> (forall a. a -> a)
4239 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4240 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4241 The <literal>forall</literal> makes explicit the universal quantification that
4242 is implicitly added by Haskell.
4245 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4246 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4247 shows, the polymorphic type on the left of the function arrow can be overloaded.
4250 The function <literal>f3</literal> has a rank-3 type;
4251 it has rank-2 types on the left of a function arrow.
4254 GHC has three flags to control higher-rank types:
4257 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4260 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4263 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4264 That is, you can nest <literal>forall</literal>s
4265 arbitrarily deep in function arrows.
4266 In particular, a forall-type (also called a "type scheme"),
4267 including an operational type class context, is legal:
4269 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4270 of a function arrow </para> </listitem>
4271 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4272 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4273 field type signatures.</para> </listitem>
4274 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4275 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4279 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4280 a type variable any more!
4289 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4290 the types of the constructor arguments. Here are several examples:
4296 data T a = T1 (forall b. b -> b -> b) a
4298 data MonadT m = MkMonad { return :: forall a. a -> m a,
4299 bind :: forall a b. m a -> (a -> m b) -> m b
4302 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4308 The constructors have rank-2 types:
4314 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4315 MkMonad :: forall m. (forall a. a -> m a)
4316 -> (forall a b. m a -> (a -> m b) -> m b)
4318 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4324 Notice that you don't need to use a <literal>forall</literal> if there's an
4325 explicit context. For example in the first argument of the
4326 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4327 prefixed to the argument type. The implicit <literal>forall</literal>
4328 quantifies all type variables that are not already in scope, and are
4329 mentioned in the type quantified over.
4333 As for type signatures, implicit quantification happens for non-overloaded
4334 types too. So if you write this:
4337 data T a = MkT (Either a b) (b -> b)
4340 it's just as if you had written this:
4343 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4346 That is, since the type variable <literal>b</literal> isn't in scope, it's
4347 implicitly universally quantified. (Arguably, it would be better
4348 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4349 where that is what is wanted. Feedback welcomed.)
4353 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4354 the constructor to suitable values, just as usual. For example,
4365 a3 = MkSwizzle reverse
4368 a4 = let r x = Just x
4375 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4376 mkTs f x y = [T1 f x, T1 f y]
4382 The type of the argument can, as usual, be more general than the type
4383 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4384 does not need the <literal>Ord</literal> constraint.)
4388 When you use pattern matching, the bound variables may now have
4389 polymorphic types. For example:
4395 f :: T a -> a -> (a, Char)
4396 f (T1 w k) x = (w k x, w 'c' 'd')
4398 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4399 g (MkSwizzle s) xs f = s (map f (s xs))
4401 h :: MonadT m -> [m a] -> m [a]
4402 h m [] = return m []
4403 h m (x:xs) = bind m x $ \y ->
4404 bind m (h m xs) $ \ys ->
4411 In the function <function>h</function> we use the record selectors <literal>return</literal>
4412 and <literal>bind</literal> to extract the polymorphic bind and return functions
4413 from the <literal>MonadT</literal> data structure, rather than using pattern
4419 <title>Type inference</title>
4422 In general, type inference for arbitrary-rank types is undecidable.
4423 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4424 to get a decidable algorithm by requiring some help from the programmer.
4425 We do not yet have a formal specification of "some help" but the rule is this:
4428 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4429 provides an explicit polymorphic type for x, or GHC's type inference will assume
4430 that x's type has no foralls in it</emphasis>.
4433 What does it mean to "provide" an explicit type for x? You can do that by
4434 giving a type signature for x directly, using a pattern type signature
4435 (<xref linkend="scoped-type-variables"/>), thus:
4437 \ f :: (forall a. a->a) -> (f True, f 'c')
4439 Alternatively, you can give a type signature to the enclosing
4440 context, which GHC can "push down" to find the type for the variable:
4442 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4444 Here the type signature on the expression can be pushed inwards
4445 to give a type signature for f. Similarly, and more commonly,
4446 one can give a type signature for the function itself:
4448 h :: (forall a. a->a) -> (Bool,Char)
4449 h f = (f True, f 'c')
4451 You don't need to give a type signature if the lambda bound variable
4452 is a constructor argument. Here is an example we saw earlier:
4454 f :: T a -> a -> (a, Char)
4455 f (T1 w k) x = (w k x, w 'c' 'd')
4457 Here we do not need to give a type signature to <literal>w</literal>, because
4458 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4465 <sect3 id="implicit-quant">
4466 <title>Implicit quantification</title>
4469 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4470 user-written types, if and only if there is no explicit <literal>forall</literal>,
4471 GHC finds all the type variables mentioned in the type that are not already
4472 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4476 f :: forall a. a -> a
4483 h :: forall b. a -> b -> b
4489 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4492 f :: (a -> a) -> Int
4494 f :: forall a. (a -> a) -> Int
4496 f :: (forall a. a -> a) -> Int
4499 g :: (Ord a => a -> a) -> Int
4500 -- MEANS the illegal type
4501 g :: forall a. (Ord a => a -> a) -> Int
4503 g :: (forall a. Ord a => a -> a) -> Int
4505 The latter produces an illegal type, which you might think is silly,
4506 but at least the rule is simple. If you want the latter type, you
4507 can write your for-alls explicitly. Indeed, doing so is strongly advised
4514 <sect2 id="impredicative-polymorphism">
4515 <title>Impredicative polymorphism
4517 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4518 enabled with <option>-XImpredicativeTypes</option>.
4520 that you can call a polymorphic function at a polymorphic type, and
4521 parameterise data structures over polymorphic types. For example:
4523 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4524 f (Just g) = Just (g [3], g "hello")
4527 Notice here that the <literal>Maybe</literal> type is parameterised by the
4528 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4531 <para>The technical details of this extension are described in the paper
4532 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4533 type inference for higher-rank types and impredicativity</ulink>,
4534 which appeared at ICFP 2006.
4538 <sect2 id="scoped-type-variables">
4539 <title>Lexically scoped type variables
4543 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4544 which some type signatures are simply impossible to write. For example:
4546 f :: forall a. [a] -> [a]
4552 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4553 the entire definition of <literal>f</literal>.
4554 In particular, it is in scope at the type signature for <varname>ys</varname>.
4555 In Haskell 98 it is not possible to declare
4556 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4557 it becomes possible to do so.
4559 <para>Lexically-scoped type variables are enabled by
4560 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4562 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4563 variables work, compared to earlier releases. Read this section
4567 <title>Overview</title>
4569 <para>The design follows the following principles
4571 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4572 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4573 design.)</para></listitem>
4574 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4575 type variables. This means that every programmer-written type signature
4576 (including one that contains free scoped type variables) denotes a
4577 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4578 checker, and no inference is involved.</para></listitem>
4579 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4580 changing the program.</para></listitem>
4584 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4586 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4587 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4588 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4589 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4593 In Haskell, a programmer-written type signature is implicitly quantified over
4594 its free type variables (<ulink
4595 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4597 of the Haskell Report).
4598 Lexically scoped type variables affect this implicit quantification rules
4599 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4600 quantified. For example, if type variable <literal>a</literal> is in scope,
4603 (e :: a -> a) means (e :: a -> a)
4604 (e :: b -> b) means (e :: forall b. b->b)
4605 (e :: a -> b) means (e :: forall b. a->b)
4613 <sect3 id="decl-type-sigs">
4614 <title>Declaration type signatures</title>
4615 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4616 quantification (using <literal>forall</literal>) brings into scope the
4617 explicitly-quantified
4618 type variables, in the definition of the named function. For example:
4620 f :: forall a. [a] -> [a]
4621 f (x:xs) = xs ++ [ x :: a ]
4623 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4624 the definition of "<literal>f</literal>".
4626 <para>This only happens if:
4628 <listitem><para> The quantification in <literal>f</literal>'s type
4629 signature is explicit. For example:
4632 g (x:xs) = xs ++ [ x :: a ]
4634 This program will be rejected, because "<literal>a</literal>" does not scope
4635 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4636 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4637 quantification rules.
4639 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4640 not a pattern binding.
4643 f1 :: forall a. [a] -> [a]
4644 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4646 f2 :: forall a. [a] -> [a]
4647 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4649 f3 :: forall a. [a] -> [a]
4650 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4652 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4653 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4654 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4655 the type signature brings <literal>a</literal> into scope.
4661 <sect3 id="exp-type-sigs">
4662 <title>Expression type signatures</title>
4664 <para>An expression type signature that has <emphasis>explicit</emphasis>
4665 quantification (using <literal>forall</literal>) brings into scope the
4666 explicitly-quantified
4667 type variables, in the annotated expression. For example:
4669 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4671 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4672 type variable <literal>s</literal> into scope, in the annotated expression
4673 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4678 <sect3 id="pattern-type-sigs">
4679 <title>Pattern type signatures</title>
4681 A type signature may occur in any pattern; this is a <emphasis>pattern type
4682 signature</emphasis>.
4685 -- f and g assume that 'a' is already in scope
4686 f = \(x::Int, y::a) -> x
4688 h ((x,y) :: (Int,Bool)) = (y,x)
4690 In the case where all the type variables in the pattern type signature are
4691 already in scope (i.e. bound by the enclosing context), matters are simple: the
4692 signature simply constrains the type of the pattern in the obvious way.
4695 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4696 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4697 that are already in scope. For example:
4699 f :: forall a. [a] -> (Int, [a])
4702 (ys::[a], n) = (reverse xs, length xs) -- OK
4703 zs::[a] = xs ++ ys -- OK
4705 Just (v::b) = ... -- Not OK; b is not in scope
4707 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4708 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4712 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4713 type signature may mention a type variable that is not in scope; in this case,
4714 <emphasis>the signature brings that type variable into scope</emphasis>.
4715 This is particularly important for existential data constructors. For example:
4717 data T = forall a. MkT [a]
4720 k (MkT [t::a]) = MkT t3
4724 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4725 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4726 because it is bound by the pattern match. GHC's rule is that in this situation
4727 (and only then), a pattern type signature can mention a type variable that is
4728 not already in scope; the effect is to bring it into scope, standing for the
4729 existentially-bound type variable.
4732 When a pattern type signature binds a type variable in this way, GHC insists that the
4733 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4734 This means that any user-written type signature always stands for a completely known type.
4737 If all this seems a little odd, we think so too. But we must have
4738 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4739 could not name existentially-bound type variables in subsequent type signatures.
4742 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4743 signature is allowed to mention a lexical variable that is not already in
4745 For example, both <literal>f</literal> and <literal>g</literal> would be
4746 illegal if <literal>a</literal> was not already in scope.
4752 <!-- ==================== Commented out part about result type signatures
4754 <sect3 id="result-type-sigs">
4755 <title>Result type signatures</title>
4758 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4761 {- f assumes that 'a' is already in scope -}
4762 f x y :: [a] = [x,y,x]
4764 g = \ x :: [Int] -> [3,4]
4766 h :: forall a. [a] -> a
4770 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4771 the result of the function. Similarly, the body of the lambda in the RHS of
4772 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4773 alternative in <literal>h</literal> is <literal>a</literal>.
4775 <para> A result type signature never brings new type variables into scope.</para>
4777 There are a couple of syntactic wrinkles. First, notice that all three
4778 examples would parse quite differently with parentheses:
4780 {- f assumes that 'a' is already in scope -}
4781 f x (y :: [a]) = [x,y,x]
4783 g = \ (x :: [Int]) -> [3,4]
4785 h :: forall a. [a] -> a
4789 Now the signature is on the <emphasis>pattern</emphasis>; and
4790 <literal>h</literal> would certainly be ill-typed (since the pattern
4791 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4793 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4794 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4795 token or a parenthesised type of some sort). To see why,
4796 consider how one would parse this:
4805 <sect3 id="cls-inst-scoped-tyvars">
4806 <title>Class and instance declarations</title>
4809 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4810 scope over the methods defined in the <literal>where</literal> part. For example:
4828 <sect2 id="typing-binds">
4829 <title>Generalised typing of mutually recursive bindings</title>
4832 The Haskell Report specifies that a group of bindings (at top level, or in a
4833 <literal>let</literal> or <literal>where</literal>) should be sorted into
4834 strongly-connected components, and then type-checked in dependency order
4835 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4836 Report, Section 4.5.1</ulink>).
4837 As each group is type-checked, any binders of the group that
4839 an explicit type signature are put in the type environment with the specified
4841 and all others are monomorphic until the group is generalised
4842 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4845 <para>Following a suggestion of Mark Jones, in his paper
4846 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4848 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4850 <emphasis>the dependency analysis ignores references to variables that have an explicit
4851 type signature</emphasis>.
4852 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4853 typecheck. For example, consider:
4855 f :: Eq a => a -> Bool
4856 f x = (x == x) || g True || g "Yes"
4858 g y = (y <= y) || f True
4860 This is rejected by Haskell 98, but under Jones's scheme the definition for
4861 <literal>g</literal> is typechecked first, separately from that for
4862 <literal>f</literal>,
4863 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4864 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4865 type is generalised, to get
4867 g :: Ord a => a -> Bool
4869 Now, the definition for <literal>f</literal> is typechecked, with this type for
4870 <literal>g</literal> in the type environment.
4874 The same refined dependency analysis also allows the type signatures of
4875 mutually-recursive functions to have different contexts, something that is illegal in
4876 Haskell 98 (Section 4.5.2, last sentence). With
4877 <option>-XRelaxedPolyRec</option>
4878 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4879 type signatures; in practice this means that only variables bound by the same
4880 pattern binding must have the same context. For example, this is fine:
4882 f :: Eq a => a -> Bool
4883 f x = (x == x) || g True
4885 g :: Ord a => a -> Bool
4886 g y = (y <= y) || f True
4891 <sect2 id="type-families">
4892 <title>Type families
4896 GHC supports the definition of type families indexed by types. They may be
4897 seen as an extension of Haskell 98's class-based overloading of values to
4898 types. When type families are declared in classes, they are also known as
4902 There are two forms of type families: data families and type synonym families.
4903 Currently, only the former are fully implemented, while we are still working
4904 on the latter. As a result, the specification of the language extension is
4905 also still to some degree in flux. Hence, a more detailed description of
4906 the language extension and its use is currently available
4907 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4908 wiki page on type families</ulink>. The material will be moved to this user's
4909 guide when it has stabilised.
4912 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4919 <!-- ==================== End of type system extensions ================= -->
4921 <!-- ====================== TEMPLATE HASKELL ======================= -->
4923 <sect1 id="template-haskell">
4924 <title>Template Haskell</title>
4926 <para>Template Haskell allows you to do compile-time meta-programming in
4929 the main technical innovations is discussed in "<ulink
4930 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
4931 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4934 There is a Wiki page about
4935 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
4936 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4940 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4941 Haskell library reference material</ulink>
4942 (look for module <literal>Language.Haskell.TH</literal>).
4943 Many changes to the original design are described in
4944 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4945 Notes on Template Haskell version 2</ulink>.
4946 Not all of these changes are in GHC, however.
4949 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4950 as a worked example to help get you started.
4954 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4955 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4960 <title>Syntax</title>
4962 <para> Template Haskell has the following new syntactic
4963 constructions. You need to use the flag
4964 <option>-XTemplateHaskell</option>
4965 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4966 </indexterm>to switch these syntactic extensions on
4967 (<option>-XTemplateHaskell</option> is no longer implied by
4968 <option>-fglasgow-exts</option>).</para>
4972 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4973 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4974 There must be no space between the "$" and the identifier or parenthesis. This use
4975 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4976 of "." as an infix operator. If you want the infix operator, put spaces around it.
4978 <para> A splice can occur in place of
4980 <listitem><para> an expression; the spliced expression must
4981 have type <literal>Q Exp</literal></para></listitem>
4982 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4985 Inside a splice you can can only call functions defined in imported modules,
4986 not functions defined elsewhere in the same module.</listitem>
4990 A expression quotation is written in Oxford brackets, thus:
4992 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4993 the quotation has type <literal>Q Exp</literal>.</para></listitem>
4994 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4995 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4996 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4997 the quotation has type <literal>Q Typ</literal>.</para></listitem>
4998 </itemizedlist></para></listitem>
5001 A quasi-quotation can appear in either a pattern context or an
5002 expression context and is also written in Oxford brackets:
5004 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5005 where the "..." is an arbitrary string; a full description of the
5006 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5007 </itemizedlist></para></listitem>
5010 A name can be quoted with either one or two prefix single quotes:
5012 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5013 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5014 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5016 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5017 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5020 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5021 may also be given as an argument to the <literal>reify</literal> function.
5027 (Compared to the original paper, there are many differences of detail.
5028 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5029 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5030 Type splices are not implemented, and neither are pattern splices or quotations.
5034 <sect2> <title> Using Template Haskell </title>
5038 The data types and monadic constructor functions for Template Haskell are in the library
5039 <literal>Language.Haskell.THSyntax</literal>.
5043 You can only run a function at compile time if it is imported from another module. That is,
5044 you can't define a function in a module, and call it from within a splice in the same module.
5045 (It would make sense to do so, but it's hard to implement.)
5049 You can only run a function at compile time if it is imported
5050 from another module <emphasis>that is not part of a mutually-recursive group of modules
5051 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5052 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5053 splice is to be run.</para>
5055 For example, when compiling module A,
5056 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5057 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5061 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5064 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5065 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5066 compiles and runs a program, and then looks at the result. So it's important that
5067 the program it compiles produces results whose representations are identical to
5068 those of the compiler itself.
5072 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5073 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5078 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5079 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5080 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5087 -- Import our template "pr"
5088 import Printf ( pr )
5090 -- The splice operator $ takes the Haskell source code
5091 -- generated at compile time by "pr" and splices it into
5092 -- the argument of "putStrLn".
5093 main = putStrLn ( $(pr "Hello") )
5099 -- Skeletal printf from the paper.
5100 -- It needs to be in a separate module to the one where
5101 -- you intend to use it.
5103 -- Import some Template Haskell syntax
5104 import Language.Haskell.TH
5106 -- Describe a format string
5107 data Format = D | S | L String
5109 -- Parse a format string. This is left largely to you
5110 -- as we are here interested in building our first ever
5111 -- Template Haskell program and not in building printf.
5112 parse :: String -> [Format]
5115 -- Generate Haskell source code from a parsed representation
5116 -- of the format string. This code will be spliced into
5117 -- the module which calls "pr", at compile time.
5118 gen :: [Format] -> Q Exp
5119 gen [D] = [| \n -> show n |]
5120 gen [S] = [| \s -> s |]
5121 gen [L s] = stringE s
5123 -- Here we generate the Haskell code for the splice
5124 -- from an input format string.
5125 pr :: String -> Q Exp
5126 pr s = gen (parse s)
5129 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5132 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5135 <para>Run "main.exe" and here is your output:</para>
5145 <title>Using Template Haskell with Profiling</title>
5146 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5148 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5149 interpreter to run the splice expressions. The bytecode interpreter
5150 runs the compiled expression on top of the same runtime on which GHC
5151 itself is running; this means that the compiled code referred to by
5152 the interpreted expression must be compatible with this runtime, and
5153 in particular this means that object code that is compiled for
5154 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5155 expression, because profiled object code is only compatible with the
5156 profiling version of the runtime.</para>
5158 <para>This causes difficulties if you have a multi-module program
5159 containing Template Haskell code and you need to compile it for
5160 profiling, because GHC cannot load the profiled object code and use it
5161 when executing the splices. Fortunately GHC provides a workaround.
5162 The basic idea is to compile the program twice:</para>
5166 <para>Compile the program or library first the normal way, without
5167 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5170 <para>Then compile it again with <option>-prof</option>, and
5171 additionally use <option>-osuf
5172 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5173 to name the object files differently (you can choose any suffix
5174 that isn't the normal object suffix here). GHC will automatically
5175 load the object files built in the first step when executing splice
5176 expressions. If you omit the <option>-osuf</option> flag when
5177 building with <option>-prof</option> and Template Haskell is used,
5178 GHC will emit an error message. </para>
5183 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5184 <para>Quasi-quotation allows patterns and expressions to be written using
5185 programmer-defined concrete syntax; the motivation behind the extension and
5186 several examples are documented in
5187 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5188 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5189 2007). The example below shows how to write a quasiquoter for a simple
5190 expression language.</para>
5193 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5194 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5195 functions for quoting expressions and patterns, respectively. The first argument
5196 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5197 context of the quasi-quotation statement determines which of the two parsers is
5198 called: if the quasi-quotation occurs in an expression context, the expression
5199 parser is called, and if it occurs in a pattern context, the pattern parser is
5203 Note that in the example we make use of an antiquoted
5204 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5205 (this syntax for anti-quotation was defined by the parser's
5206 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5207 integer value argument of the constructor <literal>IntExpr</literal> when
5208 pattern matching. Please see the referenced paper for further details regarding
5209 anti-quotation as well as the description of a technique that uses SYB to
5210 leverage a single parser of type <literal>String -> a</literal> to generate both
5211 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5212 pattern parser that returns a value of type <literal>Q Pat</literal>.
5215 <para>In general, a quasi-quote has the form
5216 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5217 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5218 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5219 can be arbitrary, and may contain newlines.
5222 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5223 the example, <literal>expr</literal> cannot be defined
5224 in <literal>Main.hs</literal> where it is used, but must be imported.
5235 main = do { print $ eval [$expr|1 + 2|]
5237 { [$expr|'int:n|] -> print n
5246 import qualified Language.Haskell.TH as TH
5247 import Language.Haskell.TH.Quasi
5249 data Expr = IntExpr Integer
5250 | AntiIntExpr String
5251 | BinopExpr BinOp Expr Expr
5253 deriving(Show, Typeable, Data)
5259 deriving(Show, Typeable, Data)
5261 eval :: Expr -> Integer
5262 eval (IntExpr n) = n
5263 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5270 expr = QuasiQuoter parseExprExp parseExprPat
5272 -- Parse an Expr, returning its representation as
5273 -- either a Q Exp or a Q Pat. See the referenced paper
5274 -- for how to use SYB to do this by writing a single
5275 -- parser of type String -> Expr instead of two
5276 -- separate parsers.
5278 parseExprExp :: String -> Q Exp
5281 parseExprPat :: String -> Q Pat
5285 <para>Now run the compiler:
5288 $ ghc --make -XQuasiQuotes Main.hs -o main
5291 <para>Run "main" and here is your output:</para>
5303 <!-- ===================== Arrow notation =================== -->
5305 <sect1 id="arrow-notation">
5306 <title>Arrow notation
5309 <para>Arrows are a generalization of monads introduced by John Hughes.
5310 For more details, see
5315 “Generalising Monads to Arrows”,
5316 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5317 pp67–111, May 2000.
5323 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5324 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5330 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5331 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5337 and the arrows web page at
5338 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5339 With the <option>-XArrows</option> flag, GHC supports the arrow
5340 notation described in the second of these papers.
5341 What follows is a brief introduction to the notation;
5342 it won't make much sense unless you've read Hughes's paper.
5343 This notation is translated to ordinary Haskell,
5344 using combinators from the
5345 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5349 <para>The extension adds a new kind of expression for defining arrows:
5351 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5352 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5354 where <literal>proc</literal> is a new keyword.
5355 The variables of the pattern are bound in the body of the
5356 <literal>proc</literal>-expression,
5357 which is a new sort of thing called a <firstterm>command</firstterm>.
5358 The syntax of commands is as follows:
5360 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5361 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5362 | <replaceable>cmd</replaceable><superscript>0</superscript>
5364 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5365 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5366 infix operators as for expressions, and
5368 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5369 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5370 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5371 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5372 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5373 | <replaceable>fcmd</replaceable>
5375 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5376 | ( <replaceable>cmd</replaceable> )
5377 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5379 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5380 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5381 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5382 | <replaceable>cmd</replaceable>
5384 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5385 except that the bodies are commands instead of expressions.
5389 Commands produce values, but (like monadic computations)
5390 may yield more than one value,
5391 or none, and may do other things as well.
5392 For the most part, familiarity with monadic notation is a good guide to
5394 However the values of expressions, even monadic ones,
5395 are determined by the values of the variables they contain;
5396 this is not necessarily the case for commands.
5400 A simple example of the new notation is the expression
5402 proc x -> f -< x+1
5404 We call this a <firstterm>procedure</firstterm> or
5405 <firstterm>arrow abstraction</firstterm>.
5406 As with a lambda expression, the variable <literal>x</literal>
5407 is a new variable bound within the <literal>proc</literal>-expression.
5408 It refers to the input to the arrow.
5409 In the above example, <literal>-<</literal> is not an identifier but an
5410 new reserved symbol used for building commands from an expression of arrow
5411 type and an expression to be fed as input to that arrow.
5412 (The weird look will make more sense later.)
5413 It may be read as analogue of application for arrows.
5414 The above example is equivalent to the Haskell expression
5416 arr (\ x -> x+1) >>> f
5418 That would make no sense if the expression to the left of
5419 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5420 More generally, the expression to the left of <literal>-<</literal>
5421 may not involve any <firstterm>local variable</firstterm>,
5422 i.e. a variable bound in the current arrow abstraction.
5423 For such a situation there is a variant <literal>-<<</literal>, as in
5425 proc x -> f x -<< x+1
5427 which is equivalent to
5429 arr (\ x -> (f x, x+1)) >>> app
5431 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5433 Such an arrow is equivalent to a monad, so if you're using this form
5434 you may find a monadic formulation more convenient.
5438 <title>do-notation for commands</title>
5441 Another form of command is a form of <literal>do</literal>-notation.
5442 For example, you can write
5451 You can read this much like ordinary <literal>do</literal>-notation,
5452 but with commands in place of monadic expressions.
5453 The first line sends the value of <literal>x+1</literal> as an input to
5454 the arrow <literal>f</literal>, and matches its output against
5455 <literal>y</literal>.
5456 In the next line, the output is discarded.
5457 The arrow <function>returnA</function> is defined in the
5458 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5459 module as <literal>arr id</literal>.
5460 The above example is treated as an abbreviation for
5462 arr (\ x -> (x, x)) >>>
5463 first (arr (\ x -> x+1) >>> f) >>>
5464 arr (\ (y, x) -> (y, (x, y))) >>>
5465 first (arr (\ y -> 2*y) >>> g) >>>
5467 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5468 first (arr (\ (x, z) -> x*z) >>> h) >>>
5469 arr (\ (t, z) -> t+z) >>>
5472 Note that variables not used later in the composition are projected out.
5473 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5475 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5476 module, this reduces to
5478 arr (\ x -> (x+1, x)) >>>
5480 arr (\ (y, x) -> (2*y, (x, y))) >>>
5482 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5484 arr (\ (t, z) -> t+z)
5486 which is what you might have written by hand.
5487 With arrow notation, GHC keeps track of all those tuples of variables for you.
5491 Note that although the above translation suggests that
5492 <literal>let</literal>-bound variables like <literal>z</literal> must be
5493 monomorphic, the actual translation produces Core,
5494 so polymorphic variables are allowed.
5498 It's also possible to have mutually recursive bindings,
5499 using the new <literal>rec</literal> keyword, as in the following example:
5501 counter :: ArrowCircuit a => a Bool Int
5502 counter = proc reset -> do
5503 rec output <- returnA -< if reset then 0 else next
5504 next <- delay 0 -< output+1
5505 returnA -< output
5507 The translation of such forms uses the <function>loop</function> combinator,
5508 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5514 <title>Conditional commands</title>
5517 In the previous example, we used a conditional expression to construct the
5519 Sometimes we want to conditionally execute different commands, as in
5526 which is translated to
5528 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5529 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5531 Since the translation uses <function>|||</function>,
5532 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5536 There are also <literal>case</literal> commands, like
5542 y <- h -< (x1, x2)
5546 The syntax is the same as for <literal>case</literal> expressions,
5547 except that the bodies of the alternatives are commands rather than expressions.
5548 The translation is similar to that of <literal>if</literal> commands.
5554 <title>Defining your own control structures</title>
5557 As we're seen, arrow notation provides constructs,
5558 modelled on those for expressions,
5559 for sequencing, value recursion and conditionals.
5560 But suitable combinators,
5561 which you can define in ordinary Haskell,
5562 may also be used to build new commands out of existing ones.
5563 The basic idea is that a command defines an arrow from environments to values.
5564 These environments assign values to the free local variables of the command.
5565 Thus combinators that produce arrows from arrows
5566 may also be used to build commands from commands.
5567 For example, the <literal>ArrowChoice</literal> class includes a combinator
5569 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5571 so we can use it to build commands:
5573 expr' = proc x -> do
5576 symbol Plus -< ()
5577 y <- term -< ()
5580 symbol Minus -< ()
5581 y <- term -< ()
5584 (The <literal>do</literal> on the first line is needed to prevent the first
5585 <literal><+> ...</literal> from being interpreted as part of the
5586 expression on the previous line.)
5587 This is equivalent to
5589 expr' = (proc x -> returnA -< x)
5590 <+> (proc x -> do
5591 symbol Plus -< ()
5592 y <- term -< ()
5594 <+> (proc x -> do
5595 symbol Minus -< ()
5596 y <- term -< ()
5599 It is essential that this operator be polymorphic in <literal>e</literal>
5600 (representing the environment input to the command
5601 and thence to its subcommands)
5602 and satisfy the corresponding naturality property
5604 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5606 at least for strict <literal>k</literal>.
5607 (This should be automatic if you're not using <function>seq</function>.)
5608 This ensures that environments seen by the subcommands are environments
5609 of the whole command,
5610 and also allows the translation to safely trim these environments.
5611 The operator must also not use any variable defined within the current
5616 We could define our own operator
5618 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5619 untilA body cond = proc x ->
5620 if cond x then returnA -< ()
5623 untilA body cond -< x
5625 and use it in the same way.
5626 Of course this infix syntax only makes sense for binary operators;
5627 there is also a more general syntax involving special brackets:
5631 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5638 <title>Primitive constructs</title>
5641 Some operators will need to pass additional inputs to their subcommands.
5642 For example, in an arrow type supporting exceptions,
5643 the operator that attaches an exception handler will wish to pass the
5644 exception that occurred to the handler.
5645 Such an operator might have a type
5647 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5649 where <literal>Ex</literal> is the type of exceptions handled.
5650 You could then use this with arrow notation by writing a command
5652 body `handleA` \ ex -> handler
5654 so that if an exception is raised in the command <literal>body</literal>,
5655 the variable <literal>ex</literal> is bound to the value of the exception
5656 and the command <literal>handler</literal>,
5657 which typically refers to <literal>ex</literal>, is entered.
5658 Though the syntax here looks like a functional lambda,
5659 we are talking about commands, and something different is going on.
5660 The input to the arrow represented by a command consists of values for
5661 the free local variables in the command, plus a stack of anonymous values.
5662 In all the prior examples, this stack was empty.
5663 In the second argument to <function>handleA</function>,
5664 this stack consists of one value, the value of the exception.
5665 The command form of lambda merely gives this value a name.
5670 the values on the stack are paired to the right of the environment.
5671 So operators like <function>handleA</function> that pass
5672 extra inputs to their subcommands can be designed for use with the notation
5673 by pairing the values with the environment in this way.
5674 More precisely, the type of each argument of the operator (and its result)
5675 should have the form
5677 a (...(e,t1), ... tn) t
5679 where <replaceable>e</replaceable> is a polymorphic variable
5680 (representing the environment)
5681 and <replaceable>ti</replaceable> are the types of the values on the stack,
5682 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5683 The polymorphic variable <replaceable>e</replaceable> must not occur in
5684 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5685 <replaceable>t</replaceable>.
5686 However the arrows involved need not be the same.
5687 Here are some more examples of suitable operators:
5689 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5690 runReader :: ... => a e c -> a' (e,State) c
5691 runState :: ... => a e c -> a' (e,State) (c,State)
5693 We can supply the extra input required by commands built with the last two
5694 by applying them to ordinary expressions, as in
5698 (|runReader (do { ... })|) s
5700 which adds <literal>s</literal> to the stack of inputs to the command
5701 built using <function>runReader</function>.
5705 The command versions of lambda abstraction and application are analogous to
5706 the expression versions.
5707 In particular, the beta and eta rules describe equivalences of commands.
5708 These three features (operators, lambda abstraction and application)
5709 are the core of the notation; everything else can be built using them,
5710 though the results would be somewhat clumsy.
5711 For example, we could simulate <literal>do</literal>-notation by defining
5713 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5714 u `bind` f = returnA &&& u >>> f
5716 bind_ :: Arrow a => a e b -> a e c -> a e c
5717 u `bind_` f = u `bind` (arr fst >>> f)
5719 We could simulate <literal>if</literal> by defining
5721 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5722 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5729 <title>Differences with the paper</title>
5734 <para>Instead of a single form of arrow application (arrow tail) with two
5735 translations, the implementation provides two forms
5736 <quote><literal>-<</literal></quote> (first-order)
5737 and <quote><literal>-<<</literal></quote> (higher-order).
5742 <para>User-defined operators are flagged with banana brackets instead of
5743 a new <literal>form</literal> keyword.
5752 <title>Portability</title>
5755 Although only GHC implements arrow notation directly,
5756 there is also a preprocessor
5758 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5759 that translates arrow notation into Haskell 98
5760 for use with other Haskell systems.
5761 You would still want to check arrow programs with GHC;
5762 tracing type errors in the preprocessor output is not easy.
5763 Modules intended for both GHC and the preprocessor must observe some
5764 additional restrictions:
5769 The module must import
5770 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5776 The preprocessor cannot cope with other Haskell extensions.
5777 These would have to go in separate modules.
5783 Because the preprocessor targets Haskell (rather than Core),
5784 <literal>let</literal>-bound variables are monomorphic.
5795 <!-- ==================== BANG PATTERNS ================= -->
5797 <sect1 id="bang-patterns">
5798 <title>Bang patterns
5799 <indexterm><primary>Bang patterns</primary></indexterm>
5801 <para>GHC supports an extension of pattern matching called <emphasis>bang
5802 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5804 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5805 prime feature description</ulink> contains more discussion and examples
5806 than the material below.
5809 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5812 <sect2 id="bang-patterns-informal">
5813 <title>Informal description of bang patterns
5816 The main idea is to add a single new production to the syntax of patterns:
5820 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5821 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5826 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5827 whereas without the bang it would be lazy.
5828 Bang patterns can be nested of course:
5832 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5833 <literal>y</literal>.
5834 A bang only really has an effect if it precedes a variable or wild-card pattern:
5839 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5840 forces evaluation anyway does nothing.
5842 Bang patterns work in <literal>case</literal> expressions too, of course:
5844 g5 x = let y = f x in body
5845 g6 x = case f x of { y -> body }
5846 g7 x = case f x of { !y -> body }
5848 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5849 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5850 result, and then evaluates <literal>body</literal>.
5852 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5853 definitions too. For example:
5857 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5858 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5859 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5860 in a function argument <literal>![x,y]</literal> means the
5861 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5862 is part of the syntax of <literal>let</literal> bindings.
5867 <sect2 id="bang-patterns-sem">
5868 <title>Syntax and semantics
5872 We add a single new production to the syntax of patterns:
5876 There is one problem with syntactic ambiguity. Consider:
5880 Is this a definition of the infix function "<literal>(!)</literal>",
5881 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5882 ambiguity in favour of the latter. If you want to define
5883 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5888 The semantics of Haskell pattern matching is described in <ulink
5889 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5890 Section 3.17.2</ulink> of the Haskell Report. To this description add
5891 one extra item 10, saying:
5892 <itemizedlist><listitem><para>Matching
5893 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5894 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5895 <listitem><para>otherwise, <literal>pat</literal> is matched against
5896 <literal>v</literal></para></listitem>
5898 </para></listitem></itemizedlist>
5899 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5900 Section 3.17.3</ulink>, add a new case (t):
5902 case v of { !pat -> e; _ -> e' }
5903 = v `seq` case v of { pat -> e; _ -> e' }
5906 That leaves let expressions, whose translation is given in
5907 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5909 of the Haskell Report.
5910 In the translation box, first apply
5911 the following transformation: for each pattern <literal>pi</literal> that is of
5912 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5913 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5914 have a bang at the top, apply the rules in the existing box.
5916 <para>The effect of the let rule is to force complete matching of the pattern
5917 <literal>qi</literal> before evaluation of the body is begun. The bang is
5918 retained in the translated form in case <literal>qi</literal> is a variable,
5926 The let-binding can be recursive. However, it is much more common for
5927 the let-binding to be non-recursive, in which case the following law holds:
5928 <literal>(let !p = rhs in body)</literal>
5930 <literal>(case rhs of !p -> body)</literal>
5933 A pattern with a bang at the outermost level is not allowed at the top level of
5939 <!-- ==================== ASSERTIONS ================= -->
5941 <sect1 id="assertions">
5943 <indexterm><primary>Assertions</primary></indexterm>
5947 If you want to make use of assertions in your standard Haskell code, you
5948 could define a function like the following:
5954 assert :: Bool -> a -> a
5955 assert False x = error "assertion failed!"
5962 which works, but gives you back a less than useful error message --
5963 an assertion failed, but which and where?
5967 One way out is to define an extended <function>assert</function> function which also
5968 takes a descriptive string to include in the error message and
5969 perhaps combine this with the use of a pre-processor which inserts
5970 the source location where <function>assert</function> was used.
5974 Ghc offers a helping hand here, doing all of this for you. For every
5975 use of <function>assert</function> in the user's source:
5981 kelvinToC :: Double -> Double
5982 kelvinToC k = assert (k >= 0.0) (k+273.15)
5988 Ghc will rewrite this to also include the source location where the
5995 assert pred val ==> assertError "Main.hs|15" pred val
6001 The rewrite is only performed by the compiler when it spots
6002 applications of <function>Control.Exception.assert</function>, so you
6003 can still define and use your own versions of
6004 <function>assert</function>, should you so wish. If not, import
6005 <literal>Control.Exception</literal> to make use
6006 <function>assert</function> in your code.
6010 GHC ignores assertions when optimisation is turned on with the
6011 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6012 <literal>assert pred e</literal> will be rewritten to
6013 <literal>e</literal>. You can also disable assertions using the
6014 <option>-fignore-asserts</option>
6015 option<indexterm><primary><option>-fignore-asserts</option></primary>
6016 </indexterm>.</para>
6019 Assertion failures can be caught, see the documentation for the
6020 <literal>Control.Exception</literal> library for the details.
6026 <!-- =============================== PRAGMAS =========================== -->
6028 <sect1 id="pragmas">
6029 <title>Pragmas</title>
6031 <indexterm><primary>pragma</primary></indexterm>
6033 <para>GHC supports several pragmas, or instructions to the
6034 compiler placed in the source code. Pragmas don't normally affect
6035 the meaning of the program, but they might affect the efficiency
6036 of the generated code.</para>
6038 <para>Pragmas all take the form
6040 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6042 where <replaceable>word</replaceable> indicates the type of
6043 pragma, and is followed optionally by information specific to that
6044 type of pragma. Case is ignored in
6045 <replaceable>word</replaceable>. The various values for
6046 <replaceable>word</replaceable> that GHC understands are described
6047 in the following sections; any pragma encountered with an
6048 unrecognised <replaceable>word</replaceable> is (silently)
6049 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6050 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6052 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6053 pragma must precede the <literal>module</literal> keyword in the file.
6054 There can be as many file-header pragmas as you please, and they can be
6055 preceded or followed by comments.</para>
6057 <sect2 id="language-pragma">
6058 <title>LANGUAGE pragma</title>
6060 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6061 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6063 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6065 It is the intention that all Haskell compilers support the
6066 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6067 all extensions are supported by all compilers, of
6068 course. The <literal>LANGUAGE</literal> pragma should be used instead
6069 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6071 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6073 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6075 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6077 <para>Every language extension can also be turned into a command-line flag
6078 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6079 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6082 <para>A list of all supported language extensions can be obtained by invoking
6083 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6085 <para>Any extension from the <literal>Extension</literal> type defined in
6087 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6088 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6092 <sect2 id="options-pragma">
6093 <title>OPTIONS_GHC pragma</title>
6094 <indexterm><primary>OPTIONS_GHC</primary>
6096 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6099 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6100 additional options that are given to the compiler when compiling
6101 this source file. See <xref linkend="source-file-options"/> for
6104 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6105 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6108 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6110 <sect2 id="include-pragma">
6111 <title>INCLUDE pragma</title>
6113 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6114 of C header files that should be <literal>#include</literal>'d into
6115 the C source code generated by the compiler for the current module (if
6116 compiling via C). For example:</para>
6119 {-# INCLUDE "foo.h" #-}
6120 {-# INCLUDE <stdio.h> #-}</programlisting>
6122 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6124 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6125 to the <option>-#include</option> option (<xref
6126 linkend="options-C-compiler" />), because the
6127 <literal>INCLUDE</literal> pragma is understood by other
6128 compilers. Yet another alternative is to add the include file to each
6129 <literal>foreign import</literal> declaration in your code, but we
6130 don't recommend using this approach with GHC.</para>
6133 <sect2 id="deprecated-pragma">
6134 <title>DEPRECATED pragma</title>
6135 <indexterm><primary>DEPRECATED</primary>
6138 <para>The DEPRECATED pragma lets you specify that a particular
6139 function, class, or type, is deprecated. There are two
6144 <para>You can deprecate an entire module thus:</para>
6146 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6149 <para>When you compile any module that import
6150 <literal>Wibble</literal>, GHC will print the specified
6155 <para>You can deprecate a function, class, type, or data constructor, with the
6156 following top-level declaration:</para>
6158 {-# DEPRECATED f, C, T "Don't use these" #-}
6160 <para>When you compile any module that imports and uses any
6161 of the specified entities, GHC will print the specified
6163 <para> You can only deprecate entities declared at top level in the module
6164 being compiled, and you can only use unqualified names in the list of
6165 entities being deprecated. A capitalised name, such as <literal>T</literal>
6166 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6167 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6168 both are in scope. If both are in scope, there is currently no way to deprecate
6169 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
6172 Any use of the deprecated item, or of anything from a deprecated
6173 module, will be flagged with an appropriate message. However,
6174 deprecations are not reported for
6175 (a) uses of a deprecated function within its defining module, and
6176 (b) uses of a deprecated function in an export list.
6177 The latter reduces spurious complaints within a library
6178 in which one module gathers together and re-exports
6179 the exports of several others.
6181 <para>You can suppress the warnings with the flag
6182 <option>-fno-warn-deprecations</option>.</para>
6185 <sect2 id="inline-noinline-pragma">
6186 <title>INLINE and NOINLINE pragmas</title>
6188 <para>These pragmas control the inlining of function
6191 <sect3 id="inline-pragma">
6192 <title>INLINE pragma</title>
6193 <indexterm><primary>INLINE</primary></indexterm>
6195 <para>GHC (with <option>-O</option>, as always) tries to
6196 inline (or “unfold”) functions/values that are
6197 “small enough,” thus avoiding the call overhead
6198 and possibly exposing other more-wonderful optimisations.
6199 Normally, if GHC decides a function is “too
6200 expensive” to inline, it will not do so, nor will it
6201 export that unfolding for other modules to use.</para>
6203 <para>The sledgehammer you can bring to bear is the
6204 <literal>INLINE</literal><indexterm><primary>INLINE
6205 pragma</primary></indexterm> pragma, used thusly:</para>
6208 key_function :: Int -> String -> (Bool, Double)
6210 #ifdef __GLASGOW_HASKELL__
6211 {-# INLINE key_function #-}
6215 <para>(You don't need to do the C pre-processor carry-on
6216 unless you're going to stick the code through HBC—it
6217 doesn't like <literal>INLINE</literal> pragmas.)</para>
6219 <para>The major effect of an <literal>INLINE</literal> pragma
6220 is to declare a function's “cost” to be very low.
6221 The normal unfolding machinery will then be very keen to
6222 inline it. However, an <literal>INLINE</literal> pragma for a
6223 function "<literal>f</literal>" has a number of other effects:
6226 No functions are inlined into <literal>f</literal>. Otherwise
6227 GHC might inline a big function into <literal>f</literal>'s right hand side,
6228 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6231 The float-in, float-out, and common-sub-expression transformations are not
6232 applied to the body of <literal>f</literal>.
6235 An INLINE function is not worker/wrappered by strictness analysis.
6236 It's going to be inlined wholesale instead.
6239 All of these effects are aimed at ensuring that what gets inlined is
6240 exactly what you asked for, no more and no less.
6242 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6243 function can be put anywhere its type signature could be
6246 <para><literal>INLINE</literal> pragmas are a particularly
6248 <literal>then</literal>/<literal>return</literal> (or
6249 <literal>bind</literal>/<literal>unit</literal>) functions in
6250 a monad. For example, in GHC's own
6251 <literal>UniqueSupply</literal> monad code, we have:</para>
6254 #ifdef __GLASGOW_HASKELL__
6255 {-# INLINE thenUs #-}
6256 {-# INLINE returnUs #-}
6260 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6261 linkend="noinline-pragma"/>).</para>
6264 <sect3 id="noinline-pragma">
6265 <title>NOINLINE pragma</title>
6267 <indexterm><primary>NOINLINE</primary></indexterm>
6268 <indexterm><primary>NOTINLINE</primary></indexterm>
6270 <para>The <literal>NOINLINE</literal> pragma does exactly what
6271 you'd expect: it stops the named function from being inlined
6272 by the compiler. You shouldn't ever need to do this, unless
6273 you're very cautious about code size.</para>
6275 <para><literal>NOTINLINE</literal> is a synonym for
6276 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6277 specified by Haskell 98 as the standard way to disable
6278 inlining, so it should be used if you want your code to be
6282 <sect3 id="phase-control">
6283 <title>Phase control</title>
6285 <para> Sometimes you want to control exactly when in GHC's
6286 pipeline the INLINE pragma is switched on. Inlining happens
6287 only during runs of the <emphasis>simplifier</emphasis>. Each
6288 run of the simplifier has a different <emphasis>phase
6289 number</emphasis>; the phase number decreases towards zero.
6290 If you use <option>-dverbose-core2core</option> you'll see the
6291 sequence of phase numbers for successive runs of the
6292 simplifier. In an INLINE pragma you can optionally specify a
6296 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6297 <literal>f</literal>
6298 until phase <literal>k</literal>, but from phase
6299 <literal>k</literal> onwards be very keen to inline it.
6302 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6303 <literal>f</literal>
6304 until phase <literal>k</literal>, but from phase
6305 <literal>k</literal> onwards do not inline it.
6308 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6309 <literal>f</literal>
6310 until phase <literal>k</literal>, but from phase
6311 <literal>k</literal> onwards be willing to inline it (as if
6312 there was no pragma).
6315 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6316 <literal>f</literal>
6317 until phase <literal>k</literal>, but from phase
6318 <literal>k</literal> onwards do not inline it.
6321 The same information is summarised here:
6323 -- Before phase 2 Phase 2 and later
6324 {-# INLINE [2] f #-} -- No Yes
6325 {-# INLINE [~2] f #-} -- Yes No
6326 {-# NOINLINE [2] f #-} -- No Maybe
6327 {-# NOINLINE [~2] f #-} -- Maybe No
6329 {-# INLINE f #-} -- Yes Yes
6330 {-# NOINLINE f #-} -- No No
6332 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6333 function body is small, or it is applied to interesting-looking arguments etc).
6334 Another way to understand the semantics is this:
6336 <listitem><para>For both INLINE and NOINLINE, the phase number says
6337 when inlining is allowed at all.</para></listitem>
6338 <listitem><para>The INLINE pragma has the additional effect of making the
6339 function body look small, so that when inlining is allowed it is very likely to
6344 <para>The same phase-numbering control is available for RULES
6345 (<xref linkend="rewrite-rules"/>).</para>
6349 <sect2 id="line-pragma">
6350 <title>LINE pragma</title>
6352 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6353 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6354 <para>This pragma is similar to C's <literal>#line</literal>
6355 pragma, and is mainly for use in automatically generated Haskell
6356 code. It lets you specify the line number and filename of the
6357 original code; for example</para>
6359 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6361 <para>if you'd generated the current file from something called
6362 <filename>Foo.vhs</filename> and this line corresponds to line
6363 42 in the original. GHC will adjust its error messages to refer
6364 to the line/file named in the <literal>LINE</literal>
6369 <title>RULES pragma</title>
6371 <para>The RULES pragma lets you specify rewrite rules. It is
6372 described in <xref linkend="rewrite-rules"/>.</para>
6375 <sect2 id="specialize-pragma">
6376 <title>SPECIALIZE pragma</title>
6378 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6379 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6380 <indexterm><primary>overloading, death to</primary></indexterm>
6382 <para>(UK spelling also accepted.) For key overloaded
6383 functions, you can create extra versions (NB: more code space)
6384 specialised to particular types. Thus, if you have an
6385 overloaded function:</para>
6388 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6391 <para>If it is heavily used on lists with
6392 <literal>Widget</literal> keys, you could specialise it as
6396 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6399 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6400 be put anywhere its type signature could be put.</para>
6402 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6403 (a) a specialised version of the function and (b) a rewrite rule
6404 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6405 un-specialised function into a call to the specialised one.</para>
6407 <para>The type in a SPECIALIZE pragma can be any type that is less
6408 polymorphic than the type of the original function. In concrete terms,
6409 if the original function is <literal>f</literal> then the pragma
6411 {-# SPECIALIZE f :: <type> #-}
6413 is valid if and only if the definition
6415 f_spec :: <type>
6418 is valid. Here are some examples (where we only give the type signature
6419 for the original function, not its code):
6421 f :: Eq a => a -> b -> b
6422 {-# SPECIALISE f :: Int -> b -> b #-}
6424 g :: (Eq a, Ix b) => a -> b -> b
6425 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6427 h :: Eq a => a -> a -> a
6428 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6430 The last of these examples will generate a
6431 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6432 well. If you use this kind of specialisation, let us know how well it works.
6435 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6436 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6437 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6438 The <literal>INLINE</literal> pragma affects the specialised version of the
6439 function (only), and applies even if the function is recursive. The motivating
6442 -- A GADT for arrays with type-indexed representation
6444 ArrInt :: !Int -> ByteArray# -> Arr Int
6445 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6447 (!:) :: Arr e -> Int -> e
6448 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6449 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6450 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6451 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6453 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6454 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6455 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6456 the specialised function will be inlined. It has two calls to
6457 <literal>(!:)</literal>,
6458 both at type <literal>Int</literal>. Both these calls fire the first
6459 specialisation, whose body is also inlined. The result is a type-based
6460 unrolling of the indexing function.</para>
6461 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6462 on an ordinarily-recursive function.</para>
6464 <para>Note: In earlier versions of GHC, it was possible to provide your own
6465 specialised function for a given type:
6468 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6471 This feature has been removed, as it is now subsumed by the
6472 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6476 <sect2 id="specialize-instance-pragma">
6477 <title>SPECIALIZE instance pragma
6481 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6482 <indexterm><primary>overloading, death to</primary></indexterm>
6483 Same idea, except for instance declarations. For example:
6486 instance (Eq a) => Eq (Foo a) where {
6487 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6491 The pragma must occur inside the <literal>where</literal> part
6492 of the instance declaration.
6495 Compatible with HBC, by the way, except perhaps in the placement
6501 <sect2 id="unpack-pragma">
6502 <title>UNPACK pragma</title>
6504 <indexterm><primary>UNPACK</primary></indexterm>
6506 <para>The <literal>UNPACK</literal> indicates to the compiler
6507 that it should unpack the contents of a constructor field into
6508 the constructor itself, removing a level of indirection. For
6512 data T = T {-# UNPACK #-} !Float
6513 {-# UNPACK #-} !Float
6516 <para>will create a constructor <literal>T</literal> containing
6517 two unboxed floats. This may not always be an optimisation: if
6518 the <function>T</function> constructor is scrutinised and the
6519 floats passed to a non-strict function for example, they will
6520 have to be reboxed (this is done automatically by the
6523 <para>Unpacking constructor fields should only be used in
6524 conjunction with <option>-O</option>, in order to expose
6525 unfoldings to the compiler so the reboxing can be removed as
6526 often as possible. For example:</para>
6530 f (T f1 f2) = f1 + f2
6533 <para>The compiler will avoid reboxing <function>f1</function>
6534 and <function>f2</function> by inlining <function>+</function>
6535 on floats, but only when <option>-O</option> is on.</para>
6537 <para>Any single-constructor data is eligible for unpacking; for
6541 data T = T {-# UNPACK #-} !(Int,Int)
6544 <para>will store the two <literal>Int</literal>s directly in the
6545 <function>T</function> constructor, by flattening the pair.
6546 Multi-level unpacking is also supported:
6549 data T = T {-# UNPACK #-} !S
6550 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6553 will store two unboxed <literal>Int#</literal>s
6554 directly in the <function>T</function> constructor. The
6555 unpacker can see through newtypes, too.</para>
6557 <para>If a field cannot be unpacked, you will not get a warning,
6558 so it might be an idea to check the generated code with
6559 <option>-ddump-simpl</option>.</para>
6561 <para>See also the <option>-funbox-strict-fields</option> flag,
6562 which essentially has the effect of adding
6563 <literal>{-# UNPACK #-}</literal> to every strict
6564 constructor field.</para>
6567 <sect2 id="source-pragma">
6568 <title>SOURCE pragma</title>
6570 <indexterm><primary>SOURCE</primary></indexterm>
6571 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6572 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6578 <!-- ======================= REWRITE RULES ======================== -->
6580 <sect1 id="rewrite-rules">
6581 <title>Rewrite rules
6583 <indexterm><primary>RULES pragma</primary></indexterm>
6584 <indexterm><primary>pragma, RULES</primary></indexterm>
6585 <indexterm><primary>rewrite rules</primary></indexterm></title>
6588 The programmer can specify rewrite rules as part of the source program
6589 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6590 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6591 and (b) the <option>-fno-rewrite-rules</option> flag
6592 (<xref linkend="options-f"/>) is not specified, and (c) the
6593 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6602 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6608 <title>Syntax</title>
6611 From a syntactic point of view:
6617 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6618 may be generated by the layout rule).
6624 The layout rule applies in a pragma.
6625 Currently no new indentation level
6626 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6627 you must lay out the starting in the same column as the enclosing definitions.
6630 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6631 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6634 Furthermore, the closing <literal>#-}</literal>
6635 should start in a column to the right of the opening <literal>{-#</literal>.
6641 Each rule has a name, enclosed in double quotes. The name itself has
6642 no significance at all. It is only used when reporting how many times the rule fired.
6648 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6649 immediately after the name of the rule. Thus:
6652 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6655 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6656 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6665 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6666 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6667 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6668 by spaces, just like in a type <literal>forall</literal>.
6674 A pattern variable may optionally have a type signature.
6675 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6676 For example, here is the <literal>foldr/build</literal> rule:
6679 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6680 foldr k z (build g) = g k z
6683 Since <function>g</function> has a polymorphic type, it must have a type signature.
6690 The left hand side of a rule must consist of a top-level variable applied
6691 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6694 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6695 "wrong2" forall f. f True = True
6698 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6705 A rule does not need to be in the same module as (any of) the
6706 variables it mentions, though of course they need to be in scope.
6712 Rules are automatically exported from a module, just as instance declarations are.
6723 <title>Semantics</title>
6726 From a semantic point of view:
6732 Rules are only applied if you use the <option>-O</option> flag.
6738 Rules are regarded as left-to-right rewrite rules.
6739 When GHC finds an expression that is a substitution instance of the LHS
6740 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6741 By "a substitution instance" we mean that the LHS can be made equal to the
6742 expression by substituting for the pattern variables.
6749 The LHS and RHS of a rule are typechecked, and must have the
6757 GHC makes absolutely no attempt to verify that the LHS and RHS
6758 of a rule have the same meaning. That is undecidable in general, and
6759 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6766 GHC makes no attempt to make sure that the rules are confluent or
6767 terminating. For example:
6770 "loop" forall x,y. f x y = f y x
6773 This rule will cause the compiler to go into an infinite loop.
6780 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6786 GHC currently uses a very simple, syntactic, matching algorithm
6787 for matching a rule LHS with an expression. It seeks a substitution
6788 which makes the LHS and expression syntactically equal modulo alpha
6789 conversion. The pattern (rule), but not the expression, is eta-expanded if
6790 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6791 But not beta conversion (that's called higher-order matching).
6795 Matching is carried out on GHC's intermediate language, which includes
6796 type abstractions and applications. So a rule only matches if the
6797 types match too. See <xref linkend="rule-spec"/> below.
6803 GHC keeps trying to apply the rules as it optimises the program.
6804 For example, consider:
6813 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6814 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6815 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6816 not be substituted, and the rule would not fire.
6823 In the earlier phases of compilation, GHC inlines <emphasis>nothing
6824 that appears on the LHS of a rule</emphasis>, because once you have substituted
6825 for something you can't match against it (given the simple minded
6826 matching). So if you write the rule
6829 "map/map" forall f,g. map f . map g = map (f.g)
6832 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
6833 It will only match something written with explicit use of ".".
6834 Well, not quite. It <emphasis>will</emphasis> match the expression
6840 where <function>wibble</function> is defined:
6843 wibble f g = map f . map g
6846 because <function>wibble</function> will be inlined (it's small).
6848 Later on in compilation, GHC starts inlining even things on the
6849 LHS of rules, but still leaves the rules enabled. This inlining
6850 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
6857 All rules are implicitly exported from the module, and are therefore
6858 in force in any module that imports the module that defined the rule, directly
6859 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6860 in force when compiling A.) The situation is very similar to that for instance
6872 <title>List fusion</title>
6875 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6876 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6877 intermediate list should be eliminated entirely.
6881 The following are good producers:
6893 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6899 Explicit lists (e.g. <literal>[True, False]</literal>)
6905 The cons constructor (e.g <literal>3:4:[]</literal>)
6911 <function>++</function>
6917 <function>map</function>
6923 <function>take</function>, <function>filter</function>
6929 <function>iterate</function>, <function>repeat</function>
6935 <function>zip</function>, <function>zipWith</function>
6944 The following are good consumers:
6956 <function>array</function> (on its second argument)
6962 <function>++</function> (on its first argument)
6968 <function>foldr</function>
6974 <function>map</function>
6980 <function>take</function>, <function>filter</function>
6986 <function>concat</function>
6992 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6998 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6999 will fuse with one but not the other)
7005 <function>partition</function>
7011 <function>head</function>
7017 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7023 <function>sequence_</function>
7029 <function>msum</function>
7035 <function>sortBy</function>
7044 So, for example, the following should generate no intermediate lists:
7047 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7053 This list could readily be extended; if there are Prelude functions that you use
7054 a lot which are not included, please tell us.
7058 If you want to write your own good consumers or producers, look at the
7059 Prelude definitions of the above functions to see how to do so.
7064 <sect2 id="rule-spec">
7065 <title>Specialisation
7069 Rewrite rules can be used to get the same effect as a feature
7070 present in earlier versions of GHC.
7071 For example, suppose that:
7074 genericLookup :: Ord a => Table a b -> a -> b
7075 intLookup :: Table Int b -> Int -> b
7078 where <function>intLookup</function> is an implementation of
7079 <function>genericLookup</function> that works very fast for
7080 keys of type <literal>Int</literal>. You might wish
7081 to tell GHC to use <function>intLookup</function> instead of
7082 <function>genericLookup</function> whenever the latter was called with
7083 type <literal>Table Int b -> Int -> b</literal>.
7084 It used to be possible to write
7087 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7090 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7093 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7096 This slightly odd-looking rule instructs GHC to replace
7097 <function>genericLookup</function> by <function>intLookup</function>
7098 <emphasis>whenever the types match</emphasis>.
7099 What is more, this rule does not need to be in the same
7100 file as <function>genericLookup</function>, unlike the
7101 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7102 have an original definition available to specialise).
7105 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7106 <function>intLookup</function> really behaves as a specialised version
7107 of <function>genericLookup</function>!!!</para>
7109 <para>An example in which using <literal>RULES</literal> for
7110 specialisation will Win Big:
7113 toDouble :: Real a => a -> Double
7114 toDouble = fromRational . toRational
7116 {-# RULES "toDouble/Int" toDouble = i2d #-}
7117 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7120 The <function>i2d</function> function is virtually one machine
7121 instruction; the default conversion—via an intermediate
7122 <literal>Rational</literal>—is obscenely expensive by
7129 <title>Controlling what's going on</title>
7137 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7143 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7144 If you add <option>-dppr-debug</option> you get a more detailed listing.
7150 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7153 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7154 {-# INLINE build #-}
7158 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7159 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7160 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7161 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7168 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7169 see how to write rules that will do fusion and yet give an efficient
7170 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7180 <sect2 id="core-pragma">
7181 <title>CORE pragma</title>
7183 <indexterm><primary>CORE pragma</primary></indexterm>
7184 <indexterm><primary>pragma, CORE</primary></indexterm>
7185 <indexterm><primary>core, annotation</primary></indexterm>
7188 The external core format supports <quote>Note</quote> annotations;
7189 the <literal>CORE</literal> pragma gives a way to specify what these
7190 should be in your Haskell source code. Syntactically, core
7191 annotations are attached to expressions and take a Haskell string
7192 literal as an argument. The following function definition shows an
7196 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7199 Semantically, this is equivalent to:
7207 However, when external core is generated (via
7208 <option>-fext-core</option>), there will be Notes attached to the
7209 expressions <function>show</function> and <varname>x</varname>.
7210 The core function declaration for <function>f</function> is:
7214 f :: %forall a . GHCziShow.ZCTShow a ->
7215 a -> GHCziBase.ZMZN GHCziBase.Char =
7216 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7218 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7220 (tpl1::GHCziBase.Int ->
7222 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7224 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7225 (tpl3::GHCziBase.ZMZN a ->
7226 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7234 Here, we can see that the function <function>show</function> (which
7235 has been expanded out to a case expression over the Show dictionary)
7236 has a <literal>%note</literal> attached to it, as does the
7237 expression <varname>eta</varname> (which used to be called
7238 <varname>x</varname>).
7245 <sect1 id="special-ids">
7246 <title>Special built-in functions</title>
7247 <para>GHC has a few built-in functions with special behaviour. These
7248 are now described in the module <ulink
7249 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7250 in the library documentation.</para>
7254 <sect1 id="generic-classes">
7255 <title>Generic classes</title>
7258 The ideas behind this extension are described in detail in "Derivable type classes",
7259 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7260 An example will give the idea:
7268 fromBin :: [Int] -> (a, [Int])
7270 toBin {| Unit |} Unit = []
7271 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7272 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7273 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7275 fromBin {| Unit |} bs = (Unit, bs)
7276 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7277 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7278 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7279 (y,bs'') = fromBin bs'
7282 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7283 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7284 which are defined thus in the library module <literal>Generics</literal>:
7288 data a :+: b = Inl a | Inr b
7289 data a :*: b = a :*: b
7292 Now you can make a data type into an instance of Bin like this:
7294 instance (Bin a, Bin b) => Bin (a,b)
7295 instance Bin a => Bin [a]
7297 That is, just leave off the "where" clause. Of course, you can put in the
7298 where clause and over-ride whichever methods you please.
7302 <title> Using generics </title>
7303 <para>To use generics you need to</para>
7306 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7307 <option>-XGenerics</option> (to generate extra per-data-type code),
7308 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7312 <para>Import the module <literal>Generics</literal> from the
7313 <literal>lang</literal> package. This import brings into
7314 scope the data types <literal>Unit</literal>,
7315 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7316 don't need this import if you don't mention these types
7317 explicitly; for example, if you are simply giving instance
7318 declarations.)</para>
7323 <sect2> <title> Changes wrt the paper </title>
7325 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7326 can be written infix (indeed, you can now use
7327 any operator starting in a colon as an infix type constructor). Also note that
7328 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7329 Finally, note that the syntax of the type patterns in the class declaration
7330 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7331 alone would ambiguous when they appear on right hand sides (an extension we
7332 anticipate wanting).
7336 <sect2> <title>Terminology and restrictions</title>
7338 Terminology. A "generic default method" in a class declaration
7339 is one that is defined using type patterns as above.
7340 A "polymorphic default method" is a default method defined as in Haskell 98.
7341 A "generic class declaration" is a class declaration with at least one
7342 generic default method.
7350 Alas, we do not yet implement the stuff about constructor names and
7357 A generic class can have only one parameter; you can't have a generic
7358 multi-parameter class.
7364 A default method must be defined entirely using type patterns, or entirely
7365 without. So this is illegal:
7368 op :: a -> (a, Bool)
7369 op {| Unit |} Unit = (Unit, True)
7372 However it is perfectly OK for some methods of a generic class to have
7373 generic default methods and others to have polymorphic default methods.
7379 The type variable(s) in the type pattern for a generic method declaration
7380 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:
7384 op {| p :*: q |} (x :*: y) = op (x :: p)
7392 The type patterns in a generic default method must take one of the forms:
7398 where "a" and "b" are type variables. Furthermore, all the type patterns for
7399 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7400 must use the same type variables. So this is illegal:
7404 op {| a :+: b |} (Inl x) = True
7405 op {| p :+: q |} (Inr y) = False
7407 The type patterns must be identical, even in equations for different methods of the class.
7408 So this too is illegal:
7412 op1 {| a :*: b |} (x :*: y) = True
7415 op2 {| p :*: q |} (x :*: y) = False
7417 (The reason for this restriction is that we gather all the equations for a particular type constructor
7418 into a single generic instance declaration.)
7424 A generic method declaration must give a case for each of the three type constructors.
7430 The type for a generic method can be built only from:
7432 <listitem> <para> Function arrows </para> </listitem>
7433 <listitem> <para> Type variables </para> </listitem>
7434 <listitem> <para> Tuples </para> </listitem>
7435 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7437 Here are some example type signatures for generic methods:
7440 op2 :: Bool -> (a,Bool)
7441 op3 :: [Int] -> a -> a
7444 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7448 This restriction is an implementation restriction: we just haven't got around to
7449 implementing the necessary bidirectional maps over arbitrary type constructors.
7450 It would be relatively easy to add specific type constructors, such as Maybe and list,
7451 to the ones that are allowed.</para>
7456 In an instance declaration for a generic class, the idea is that the compiler
7457 will fill in the methods for you, based on the generic templates. However it can only
7462 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7467 No constructor of the instance type has unboxed fields.
7471 (Of course, these things can only arise if you are already using GHC extensions.)
7472 However, you can still give an instance declarations for types which break these rules,
7473 provided you give explicit code to override any generic default methods.
7481 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7482 what the compiler does with generic declarations.
7487 <sect2> <title> Another example </title>
7489 Just to finish with, here's another example I rather like:
7493 nCons {| Unit |} _ = 1
7494 nCons {| a :*: b |} _ = 1
7495 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7498 tag {| Unit |} _ = 1
7499 tag {| a :*: b |} _ = 1
7500 tag {| a :+: b |} (Inl x) = tag x
7501 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7507 <sect1 id="monomorphism">
7508 <title>Control over monomorphism</title>
7510 <para>GHC supports two flags that control the way in which generalisation is
7511 carried out at let and where bindings.
7515 <title>Switching off the dreaded Monomorphism Restriction</title>
7516 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7518 <para>Haskell's monomorphism restriction (see
7519 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7521 of the Haskell Report)
7522 can be completely switched off by
7523 <option>-XNoMonomorphismRestriction</option>.
7528 <title>Monomorphic pattern bindings</title>
7529 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7530 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7532 <para> As an experimental change, we are exploring the possibility of
7533 making pattern bindings monomorphic; that is, not generalised at all.
7534 A pattern binding is a binding whose LHS has no function arguments,
7535 and is not a simple variable. For example:
7537 f x = x -- Not a pattern binding
7538 f = \x -> x -- Not a pattern binding
7539 f :: Int -> Int = \x -> x -- Not a pattern binding
7541 (g,h) = e -- A pattern binding
7542 (f) = e -- A pattern binding
7543 [x] = e -- A pattern binding
7545 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7546 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7555 ;;; Local Variables: ***
7557 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7558 ;;; ispell-local-dictionary: "british" ***
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