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>-XMagicHash</option>:
137 <para> Allow "#" as a <link linkend="magic-hash">postfix modifier on identifiers</link>.
144 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
147 <para> These two flags control how generalisation is done.
148 See <xref linkend="monomorphism"/>.
155 <option>-XExtendedDefaultRules</option>:
156 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
159 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
160 Independent of the <option>-fglasgow-exts</option>
167 <option>-XRank2Types</option>
168 <indexterm><primary><option>-XRank2Types</option></primary></indexterm>
171 <option>-XRankNTypes</option>
172 <indexterm><primary><option>-XRankNTypes</option></primary></indexterm>
175 <option>-XPolymorphicComponents</option>
176 <indexterm><primary><option>-XPolymorphicComponents</option></primary></indexterm>
179 <para> These flags control higher-rank polymorphism.
180 See <xref linkend="universal-quantification"/>.</para>
181 <para>New reserved words: <literal>forall</literal>.</para>
187 <option>-XLiberalTypeSynonyms</option>
188 <indexterm><primary><option>-XLiberalTypeSynonyms</option></primary></indexterm>
191 <para> Allow more liberal type synonyms.
192 See <xref linkend="type-synonyms"/>.</para>
193 <para>New reserved words: <literal>forall</literal>.</para>
199 <option>-XOverlappingInstances</option>
200 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
203 <option>-XUndecidableInstances</option>
204 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
207 <option>-XIncoherentInstances</option>
208 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
211 <option>-fcontext-stack=N</option>
212 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
215 <para> See <xref linkend="instance-decls"/>. </para>
221 <option>-finline-phase</option>
222 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
225 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
226 you also use <option>-fglasgow-exts</option>.</para>
232 <option>-XArrows</option>
233 <indexterm><primary><option>-XArrows</option></primary></indexterm>
236 <para>See <xref linkend="arrow-notation"/>. Independent of
237 <option>-fglasgow-exts</option>.</para>
239 <para>New reserved words/symbols: <literal>rec</literal>,
240 <literal>proc</literal>, <literal>-<</literal>,
241 <literal>>-</literal>, <literal>-<<</literal>,
242 <literal>>>-</literal>.</para>
244 <para>Other syntax stolen: <literal>(|</literal>,
245 <literal>|)</literal>.</para>
251 <option>-XGenerics</option>
252 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
255 <para>See <xref linkend="generic-classes"/>. Independent of
256 <option>-fglasgow-exts</option>.</para>
261 <term><option>-XNoImplicitPrelude</option></term>
263 <para><indexterm><primary>-XNoImplicitPrelude
264 option</primary></indexterm> GHC normally imports
265 <filename>Prelude.hi</filename> files for you. If you'd
266 rather it didn't, then give it a
267 <option>-XNoImplicitPrelude</option> option. The idea is
268 that you can then import a Prelude of your own. (But don't
269 call it <literal>Prelude</literal>; the Haskell module
270 namespace is flat, and you must not conflict with any
271 Prelude module.)</para>
273 <para>Even though you have not imported the Prelude, most of
274 the built-in syntax still refers to the built-in Haskell
275 Prelude types and values, as specified by the Haskell
276 Report. For example, the type <literal>[Int]</literal>
277 still means <literal>Prelude.[] Int</literal>; tuples
278 continue to refer to the standard Prelude tuples; the
279 translation for list comprehensions continues to use
280 <literal>Prelude.map</literal> etc.</para>
282 <para>However, <option>-XNoImplicitPrelude</option> does
283 change the handling of certain built-in syntax: see <xref
284 linkend="rebindable-syntax"/>.</para>
289 <term><option>-XImplicitParams</option></term>
291 <para>Enables implicit parameters (see <xref
292 linkend="implicit-parameters"/>). Currently also implied by
293 <option>-fglasgow-exts</option>.</para>
296 <literal>?<replaceable>varid</replaceable></literal>,
297 <literal>%<replaceable>varid</replaceable></literal>.</para>
302 <term><option>-XOverloadedStrings</option></term>
304 <para>Enables overloaded string literals (see <xref
305 linkend="overloaded-strings"/>).</para>
310 <term><option>-XScopedTypeVariables</option></term>
312 <para>Enables lexically-scoped type variables (see <xref
313 linkend="scoped-type-variables"/>). Implied by
314 <option>-fglasgow-exts</option>.</para>
319 <term><option>-XTemplateHaskell</option></term>
321 <para>Enables Template Haskell (see <xref
322 linkend="template-haskell"/>). This flag must
323 be given explicitly; it is no longer implied by
324 <option>-fglasgow-exts</option>.</para>
326 <para>Syntax stolen: <literal>[|</literal>,
327 <literal>[e|</literal>, <literal>[p|</literal>,
328 <literal>[d|</literal>, <literal>[t|</literal>,
329 <literal>$(</literal>,
330 <literal>$<replaceable>varid</replaceable></literal>.</para>
335 <term><option>-XQuasiQuotes</option></term>
337 <para>Enables quasiquotation (see <xref
338 linkend="th-quasiquotation"/>).</para>
341 <literal>[:<replaceable>varid</replaceable>|</literal>.</para>
348 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
349 <sect1 id="primitives">
350 <title>Unboxed types and primitive operations</title>
352 <para>GHC is built on a raft of primitive data types and operations;
353 "primitive" in the sense that they cannot be defined in Haskell itself.
354 While you really can use this stuff to write fast code,
355 we generally find it a lot less painful, and more satisfying in the
356 long run, to use higher-level language features and libraries. With
357 any luck, the code you write will be optimised to the efficient
358 unboxed version in any case. And if it isn't, we'd like to know
361 <para>All these primitive data types and operations are exported by the
362 library <literal>GHC.Prim</literal>, for which there is
363 <ulink url="../libraries/base/GHC.Prim.html">detailed online documentation</ulink>.
364 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
367 If you want to mention any of the primitive data types or operations in your
368 program, you must first import <literal>GHC.Prim</literal> to bring them
369 into scope. Many of them have names ending in "#", and to mention such
370 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
373 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
374 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
375 we briefly summarise here. </para>
377 <sect2 id="glasgow-unboxed">
382 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
385 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
386 that values of that type are represented by a pointer to a heap
387 object. The representation of a Haskell <literal>Int</literal>, for
388 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
389 type, however, is represented by the value itself, no pointers or heap
390 allocation are involved.
394 Unboxed types correspond to the “raw machine” types you
395 would use in C: <literal>Int#</literal> (long int),
396 <literal>Double#</literal> (double), <literal>Addr#</literal>
397 (void *), etc. The <emphasis>primitive operations</emphasis>
398 (PrimOps) on these types are what you might expect; e.g.,
399 <literal>(+#)</literal> is addition on
400 <literal>Int#</literal>s, and is the machine-addition that we all
401 know and love—usually one instruction.
405 Primitive (unboxed) types cannot be defined in Haskell, and are
406 therefore built into the language and compiler. Primitive types are
407 always unlifted; that is, a value of a primitive type cannot be
408 bottom. We use the convention (but it is only a convention)
409 that primitive types, values, and
410 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
411 For some primitive types we have special syntax for literals, also
412 described in the <link linkend="magic-hash">same section</link>.
416 Primitive values are often represented by a simple bit-pattern, such
417 as <literal>Int#</literal>, <literal>Float#</literal>,
418 <literal>Double#</literal>. But this is not necessarily the case:
419 a primitive value might be represented by a pointer to a
420 heap-allocated object. Examples include
421 <literal>Array#</literal>, the type of primitive arrays. A
422 primitive array is heap-allocated because it is too big a value to fit
423 in a register, and would be too expensive to copy around; in a sense,
424 it is accidental that it is represented by a pointer. If a pointer
425 represents a primitive value, then it really does point to that value:
426 no unevaluated thunks, no indirections…nothing can be at the
427 other end of the pointer than the primitive value.
428 A numerically-intensive program using unboxed types can
429 go a <emphasis>lot</emphasis> faster than its “standard”
430 counterpart—we saw a threefold speedup on one example.
434 There are some restrictions on the use of primitive types:
436 <listitem><para>The main restriction
437 is that you can't pass a primitive value to a polymorphic
438 function or store one in a polymorphic data type. This rules out
439 things like <literal>[Int#]</literal> (i.e. lists of primitive
440 integers). The reason for this restriction is that polymorphic
441 arguments and constructor fields are assumed to be pointers: if an
442 unboxed integer is stored in one of these, the garbage collector would
443 attempt to follow it, leading to unpredictable space leaks. Or a
444 <function>seq</function> operation on the polymorphic component may
445 attempt to dereference the pointer, with disastrous results. Even
446 worse, the unboxed value might be larger than a pointer
447 (<literal>Double#</literal> for instance).
450 <listitem><para> You cannot define a newtype whose representation type
451 (the argument type of the data constructor) is an unboxed type. Thus,
457 <listitem><para> You cannot bind a variable with an unboxed type
458 in a <emphasis>top-level</emphasis> binding.
460 <listitem><para> You cannot bind a variable with an unboxed type
461 in a <emphasis>recursive</emphasis> binding.
463 <listitem><para> You may bind unboxed variables in a (non-recursive,
464 non-top-level) pattern binding, but any such variable causes the entire
466 to become strict. For example:
468 data Foo = Foo Int Int#
470 f x = let (Foo a b, w) = ..rhs.. in ..body..
472 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
474 is strict, and the program behaves as if you had written
476 data Foo = Foo Int Int#
478 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
487 <sect2 id="unboxed-tuples">
488 <title>Unboxed Tuples
492 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
493 they're available by default with <option>-fglasgow-exts</option>. An
494 unboxed tuple looks like this:
506 where <literal>e_1..e_n</literal> are expressions of any
507 type (primitive or non-primitive). The type of an unboxed tuple looks
512 Unboxed tuples are used for functions that need to return multiple
513 values, but they avoid the heap allocation normally associated with
514 using fully-fledged tuples. When an unboxed tuple is returned, the
515 components are put directly into registers or on the stack; the
516 unboxed tuple itself does not have a composite representation. Many
517 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
519 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
520 tuples to avoid unnecessary allocation during sequences of operations.
524 There are some pretty stringent restrictions on the use of unboxed tuples:
529 Values of unboxed tuple types are subject to the same restrictions as
530 other unboxed types; i.e. they may not be stored in polymorphic data
531 structures or passed to polymorphic functions.
538 No variable can have an unboxed tuple type, nor may a constructor or function
539 argument have an unboxed tuple type. The following are all illegal:
543 data Foo = Foo (# Int, Int #)
545 f :: (# Int, Int #) -> (# Int, Int #)
548 g :: (# Int, Int #) -> Int
551 h x = let y = (# x,x #) in ...
558 The typical use of unboxed tuples is simply to return multiple values,
559 binding those multiple results with a <literal>case</literal> expression, thus:
561 f x y = (# x+1, y-1 #)
562 g x = case f x x of { (# a, b #) -> a + b }
564 You can have an unboxed tuple in a pattern binding, thus
566 f x = let (# p,q #) = h x in ..body..
568 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
569 the resulting binding is lazy like any other Haskell pattern binding. The
570 above example desugars like this:
572 f x = let t = case h x o f{ (# p,q #) -> (p,q)
577 Indeed, the bindings can even be recursive.
584 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
586 <sect1 id="syntax-extns">
587 <title>Syntactic extensions</title>
589 <sect2 id="magic-hash">
590 <title>The magic hash</title>
591 <para>The language extension <option>-XMagicHash</option> allows "#" as a
592 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
593 a valid type constructor or data constructor.</para>
595 <para>The hash sign does not change sematics at all. We tend to use variable
596 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
597 but there is no requirement to do so; they are just plain ordinary variables.
598 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
599 For example, to bring <literal>Int#</literal> into scope you must
600 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
601 the <option>-XMagicHash</option> extension
602 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
603 that is now in scope.</para>
604 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
606 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
607 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
608 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
609 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
610 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
611 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
612 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
613 is a <literal>Word#</literal>. </para> </listitem>
614 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
615 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
620 <!-- ====================== HIERARCHICAL MODULES ======================= -->
623 <sect2 id="hierarchical-modules">
624 <title>Hierarchical Modules</title>
626 <para>GHC supports a small extension to the syntax of module
627 names: a module name is allowed to contain a dot
628 <literal>‘.’</literal>. This is also known as the
629 “hierarchical module namespace” extension, because
630 it extends the normally flat Haskell module namespace into a
631 more flexible hierarchy of modules.</para>
633 <para>This extension has very little impact on the language
634 itself; modules names are <emphasis>always</emphasis> fully
635 qualified, so you can just think of the fully qualified module
636 name as <quote>the module name</quote>. In particular, this
637 means that the full module name must be given after the
638 <literal>module</literal> keyword at the beginning of the
639 module; for example, the module <literal>A.B.C</literal> must
642 <programlisting>module A.B.C</programlisting>
645 <para>It is a common strategy to use the <literal>as</literal>
646 keyword to save some typing when using qualified names with
647 hierarchical modules. For example:</para>
650 import qualified Control.Monad.ST.Strict as ST
653 <para>For details on how GHC searches for source and interface
654 files in the presence of hierarchical modules, see <xref
655 linkend="search-path"/>.</para>
657 <para>GHC comes with a large collection of libraries arranged
658 hierarchically; see the accompanying <ulink
659 url="../libraries/index.html">library
660 documentation</ulink>. More libraries to install are available
662 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
665 <!-- ====================== PATTERN GUARDS ======================= -->
667 <sect2 id="pattern-guards">
668 <title>Pattern guards</title>
671 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
672 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.)
676 Suppose we have an abstract data type of finite maps, with a
680 lookup :: FiniteMap -> Int -> Maybe Int
683 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
684 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
688 clunky env var1 var2 | ok1 && ok2 = val1 + val2
689 | otherwise = var1 + var2
700 The auxiliary functions are
704 maybeToBool :: Maybe a -> Bool
705 maybeToBool (Just x) = True
706 maybeToBool Nothing = False
708 expectJust :: Maybe a -> a
709 expectJust (Just x) = x
710 expectJust Nothing = error "Unexpected Nothing"
714 What is <function>clunky</function> doing? The guard <literal>ok1 &&
715 ok2</literal> checks that both lookups succeed, using
716 <function>maybeToBool</function> to convert the <function>Maybe</function>
717 types to booleans. The (lazily evaluated) <function>expectJust</function>
718 calls extract the values from the results of the lookups, and binds the
719 returned values to <varname>val1</varname> and <varname>val2</varname>
720 respectively. If either lookup fails, then clunky takes the
721 <literal>otherwise</literal> case and returns the sum of its arguments.
725 This is certainly legal Haskell, but it is a tremendously verbose and
726 un-obvious way to achieve the desired effect. Arguably, a more direct way
727 to write clunky would be to use case expressions:
731 clunky env var1 var2 = case lookup env var1 of
733 Just val1 -> case lookup env var2 of
735 Just val2 -> val1 + val2
741 This is a bit shorter, but hardly better. Of course, we can rewrite any set
742 of pattern-matching, guarded equations as case expressions; that is
743 precisely what the compiler does when compiling equations! The reason that
744 Haskell provides guarded equations is because they allow us to write down
745 the cases we want to consider, one at a time, independently of each other.
746 This structure is hidden in the case version. Two of the right-hand sides
747 are really the same (<function>fail</function>), and the whole expression
748 tends to become more and more indented.
752 Here is how I would write clunky:
757 | Just val1 <- lookup env var1
758 , Just val2 <- lookup env var2
760 ...other equations for clunky...
764 The semantics should be clear enough. The qualifiers are matched in order.
765 For a <literal><-</literal> qualifier, which I call a pattern guard, the
766 right hand side is evaluated and matched against the pattern on the left.
767 If the match fails then the whole guard fails and the next equation is
768 tried. If it succeeds, then the appropriate binding takes place, and the
769 next qualifier is matched, in the augmented environment. Unlike list
770 comprehensions, however, the type of the expression to the right of the
771 <literal><-</literal> is the same as the type of the pattern to its
772 left. The bindings introduced by pattern guards scope over all the
773 remaining guard qualifiers, and over the right hand side of the equation.
777 Just as with list comprehensions, boolean expressions can be freely mixed
778 with among the pattern guards. For example:
789 Haskell's current guards therefore emerge as a special case, in which the
790 qualifier list has just one element, a boolean expression.
794 <!-- ===================== View patterns =================== -->
796 <sect2 id="view-patterns">
801 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
802 More information and examples of view patterns can be found on the
803 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
808 View patterns are somewhat like pattern guards that can be nested inside
809 of other patterns. They are a convenient way of pattern-matching
810 against values of abstract types. For example, in a programming language
811 implementation, we might represent the syntax of the types of the
820 view :: Type -> TypeView
822 -- additional operations for constructing Typ's ...
825 The representation of Typ is held abstract, permitting implementations
826 to use a fancy representation (e.g., hash-consing to manage sharing).
828 Without view patterns, using this signature a little inconvenient:
830 size :: Typ -> Integer
831 size t = case view t of
833 Arrow t1 t2 -> size t1 + size t2
836 It is necessary to iterate the case, rather than using an equational
837 function definition. And the situation is even worse when the matching
838 against <literal>t</literal> is buried deep inside another pattern.
842 View patterns permit calling the view function inside the pattern and
843 matching against the result:
845 size (view -> Unit) = 1
846 size (view -> Arrow t1 t2) = size t1 + size t2
849 That is, we add a new form of pattern, written
850 <replaceable>expression</replaceable> <literal>-></literal>
851 <replaceable>pattern</replaceable> that means "apply the expression to
852 whatever we're trying to match against, and then match the result of
853 that application against the pattern". The expression can be any Haskell
854 expression of function type, and view patterns can be used wherever
859 The semantics of a pattern <literal>(</literal>
860 <replaceable>exp</replaceable> <literal>-></literal>
861 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
867 <para>The variables bound by the view pattern are the variables bound by
868 <replaceable>pat</replaceable>.
872 Any variables in <replaceable>exp</replaceable> are bound occurrences,
873 but variables bound "to the left" in a pattern are in scope. This
874 feature permits, for example, one argument to a function to be used in
875 the view of another argument. For example, the function
876 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
877 written using view patterns as follows:
880 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
881 ...other equations for clunky...
886 More precisely, the scoping rules are:
890 In a single pattern, variables bound by patterns to the left of a view
891 pattern expression are in scope. For example:
893 example :: Maybe ((String -> Integer,Integer), String) -> Bool
894 example Just ((f,_), f -> 4) = True
897 Additionally, in function definitions, variables bound by matching earlier curried
898 arguments may be used in view pattern expressions in later arguments:
900 example :: (String -> Integer) -> String -> Bool
901 example f (f -> 4) = True
903 That is, the scoping is the same as it would be if the curried arguments
904 were collected into a tuple.
910 In mutually recursive bindings, such as <literal>let</literal>,
911 <literal>where</literal>, or the top level, view patterns in one
912 declaration may not mention variables bound by other declarations. That
913 is, each declaration must be self-contained. For example, the following
914 program is not allowed:
921 restriction in the future; the only cost is that type checking patterns
922 would get a little more complicated.)
932 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
933 <replaceable>T1</replaceable> <literal>-></literal>
934 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
935 a <replaceable>T2</replaceable>, then the whole view pattern matches a
936 <replaceable>T1</replaceable>.
939 <listitem><para> Matching: To the equations in Section 3.17.3 of the
940 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
941 Report</ulink>, add the following:
943 case v of { (e -> p) -> e1 ; _ -> e2 }
945 case (e v) of { p -> e1 ; _ -> e2 }
947 That is, to match a variable <replaceable>v</replaceable> against a pattern
948 <literal>(</literal> <replaceable>exp</replaceable>
949 <literal>-></literal> <replaceable>pat</replaceable>
950 <literal>)</literal>, evaluate <literal>(</literal>
951 <replaceable>exp</replaceable> <replaceable> v</replaceable>
952 <literal>)</literal> and match the result against
953 <replaceable>pat</replaceable>.
956 <listitem><para> Efficiency: When the same view function is applied in
957 multiple branches of a function definition or a case expression (e.g.,
958 in <literal>size</literal> above), GHC makes an attempt to collect these
959 applications into a single nested case expression, so that the view
960 function is only applied once. Pattern compilation in GHC follows the
961 matrix algorithm described in Chapter 4 of <ulink
962 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
963 Implementation of Functional Programming Languages</ulink>. When the
964 top rows of the first column of a matrix are all view patterns with the
965 "same" expression, these patterns are transformed into a single nested
966 case. This includes, for example, adjacent view patterns that line up
969 f ((view -> A, p1), p2) = e1
970 f ((view -> B, p3), p4) = e2
974 <para> The current notion of when two view pattern expressions are "the
975 same" is very restricted: it is not even full syntactic equality.
976 However, it does include variables, literals, applications, and tuples;
977 e.g., two instances of <literal>view ("hi", "there")</literal> will be
978 collected. However, the current implementation does not compare up to
979 alpha-equivalence, so two instances of <literal>(x, view x ->
980 y)</literal> will not be coalesced.
990 <!-- ===================== Recursive do-notation =================== -->
992 <sect2 id="mdo-notation">
993 <title>The recursive do-notation
996 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
997 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
998 by Levent Erkok, John Launchbury,
999 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
1000 This paper is essential reading for anyone making non-trivial use of mdo-notation,
1001 and we do not repeat it here.
1004 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
1005 that is, the variables bound in a do-expression are visible only in the textually following
1006 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
1007 group. It turns out that several applications can benefit from recursive bindings in
1008 the do-notation, and this extension provides the necessary syntactic support.
1011 Here is a simple (yet contrived) example:
1014 import Control.Monad.Fix
1016 justOnes = mdo xs <- Just (1:xs)
1020 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
1024 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
1027 class Monad m => MonadFix m where
1028 mfix :: (a -> m a) -> m a
1031 The function <literal>mfix</literal>
1032 dictates how the required recursion operation should be performed. For example,
1033 <literal>justOnes</literal> desugars as follows:
1035 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
1037 For full details of the way in which mdo is typechecked and desugared, see
1038 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
1039 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
1042 If recursive bindings are required for a monad,
1043 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
1044 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1045 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
1046 for Haskell's internal state monad (strict and lazy, respectively).
1049 Here are some important points in using the recursive-do notation:
1052 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
1053 than <literal>do</literal>).
1057 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
1058 <literal>-fglasgow-exts</literal>.
1062 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
1063 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
1064 be distinct (Section 3.3 of the paper).
1068 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
1069 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
1070 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
1071 and improve termination (Section 3.2 of the paper).
1077 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb/">http://www.cse.ogi.edu/PacSoft/projects/rmb/</ulink>
1078 contains up to date information on recursive monadic bindings.
1082 Historical note: The old implementation of the mdo-notation (and most
1083 of the existing documents) used the name
1084 <literal>MonadRec</literal> for the class and the corresponding library.
1085 This name is not supported by GHC.
1091 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1093 <sect2 id="parallel-list-comprehensions">
1094 <title>Parallel List Comprehensions</title>
1095 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1097 <indexterm><primary>parallel list comprehensions</primary>
1100 <para>Parallel list comprehensions are a natural extension to list
1101 comprehensions. List comprehensions can be thought of as a nice
1102 syntax for writing maps and filters. Parallel comprehensions
1103 extend this to include the zipWith family.</para>
1105 <para>A parallel list comprehension has multiple independent
1106 branches of qualifier lists, each separated by a `|' symbol. For
1107 example, the following zips together two lists:</para>
1110 [ (x, y) | x <- xs | y <- ys ]
1113 <para>The behavior of parallel list comprehensions follows that of
1114 zip, in that the resulting list will have the same length as the
1115 shortest branch.</para>
1117 <para>We can define parallel list comprehensions by translation to
1118 regular comprehensions. Here's the basic idea:</para>
1120 <para>Given a parallel comprehension of the form: </para>
1123 [ e | p1 <- e11, p2 <- e12, ...
1124 | q1 <- e21, q2 <- e22, ...
1129 <para>This will be translated to: </para>
1132 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1133 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1138 <para>where `zipN' is the appropriate zip for the given number of
1143 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1145 <sect2 id="generalised-list-comprehensions">
1146 <title>Generalised (SQL-Like) List Comprehensions</title>
1147 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1149 <indexterm><primary>extended list comprehensions</primary>
1151 <indexterm><primary>group</primary></indexterm>
1152 <indexterm><primary>sql</primary></indexterm>
1155 <para>Generalised list comprehensions are a further enhancement to the
1156 list comprehension syntatic sugar to allow operations such as sorting
1157 and grouping which are familiar from SQL. They are fully described in the
1158 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1159 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1160 except that the syntax we use differs slightly from the paper.</para>
1161 <para>Here is an example:
1163 employees = [ ("Simon", "MS", 80)
1164 , ("Erik", "MS", 100)
1165 , ("Phil", "Ed", 40)
1166 , ("Gordon", "Ed", 45)
1167 , ("Paul", "Yale", 60)]
1169 output = [ (the dept, sum salary)
1170 | (name, dept, salary) <- employees
1171 , then group by dept
1172 , then sortWith by (sum salary)
1175 In this example, the list <literal>output</literal> would take on
1179 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1182 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1183 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1184 function that is exported by <literal>GHC.Exts</literal>.)</para>
1186 <para>There are five new forms of comprehension qualifier,
1187 all introduced by the (existing) keyword <literal>then</literal>:
1195 This statement requires that <literal>f</literal> have the type <literal>
1196 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1197 motivating example, as this form is used to apply <literal>take 5</literal>.
1208 This form is similar to the previous one, but allows you to create a function
1209 which will be passed as the first argument to f. As a consequence f must have
1210 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1211 from the type, this function lets f "project out" some information
1212 from the elements of the list it is transforming.</para>
1214 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1215 is supplied with a function that lets it find out the <literal>sum salary</literal>
1216 for any item in the list comprehension it transforms.</para>
1224 then group by e using f
1227 <para>This is the most general of the grouping-type statements. In this form,
1228 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1229 As with the <literal>then f by e</literal> case above, the first argument
1230 is a function supplied to f by the compiler which lets it compute e on every
1231 element of the list being transformed. However, unlike the non-grouping case,
1232 f additionally partitions the list into a number of sublists: this means that
1233 at every point after this statement, binders occurring before it in the comprehension
1234 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1235 this, let's look at an example:</para>
1238 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1239 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1240 groupRuns f = groupBy (\x y -> f x == f y)
1242 output = [ (the x, y)
1243 | x <- ([1..3] ++ [1..2])
1245 , then group by x using groupRuns ]
1248 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1251 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1254 <para>Note that we have used the <literal>the</literal> function to change the type
1255 of x from a list to its original numeric type. The variable y, in contrast, is left
1256 unchanged from the list form introduced by the grouping.</para>
1266 <para>This form of grouping is essentially the same as the one described above. However,
1267 since no function to use for the grouping has been supplied it will fall back on the
1268 <literal>groupWith</literal> function defined in
1269 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1270 is the form of the group statement that we made use of in the opening example.</para>
1281 <para>With this form of the group statement, f is required to simply have the type
1282 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1283 comprehension so far directly. An example of this form is as follows:</para>
1289 , then group using inits]
1292 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1295 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1303 <!-- ===================== REBINDABLE SYNTAX =================== -->
1305 <sect2 id="rebindable-syntax">
1306 <title>Rebindable syntax</title>
1308 <para>GHC allows most kinds of built-in syntax to be rebound by
1309 the user, to facilitate replacing the <literal>Prelude</literal>
1310 with a home-grown version, for example.</para>
1312 <para>You may want to define your own numeric class
1313 hierarchy. It completely defeats that purpose if the
1314 literal "1" means "<literal>Prelude.fromInteger
1315 1</literal>", which is what the Haskell Report specifies.
1316 So the <option>-XNoImplicitPrelude</option> flag causes
1317 the following pieces of built-in syntax to refer to
1318 <emphasis>whatever is in scope</emphasis>, not the Prelude
1323 <para>An integer literal <literal>368</literal> means
1324 "<literal>fromInteger (368::Integer)</literal>", rather than
1325 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1328 <listitem><para>Fractional literals are handed in just the same way,
1329 except that the translation is
1330 <literal>fromRational (3.68::Rational)</literal>.
1333 <listitem><para>The equality test in an overloaded numeric pattern
1334 uses whatever <literal>(==)</literal> is in scope.
1337 <listitem><para>The subtraction operation, and the
1338 greater-than-or-equal test, in <literal>n+k</literal> patterns
1339 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1343 <para>Negation (e.g. "<literal>- (f x)</literal>")
1344 means "<literal>negate (f x)</literal>", both in numeric
1345 patterns, and expressions.
1349 <para>"Do" notation is translated using whatever
1350 functions <literal>(>>=)</literal>,
1351 <literal>(>>)</literal>, and <literal>fail</literal>,
1352 are in scope (not the Prelude
1353 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1354 comprehensions, are unaffected. </para></listitem>
1358 notation (see <xref linkend="arrow-notation"/>)
1359 uses whatever <literal>arr</literal>,
1360 <literal>(>>>)</literal>, <literal>first</literal>,
1361 <literal>app</literal>, <literal>(|||)</literal> and
1362 <literal>loop</literal> functions are in scope. But unlike the
1363 other constructs, the types of these functions must match the
1364 Prelude types very closely. Details are in flux; if you want
1368 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1369 even if that is a little unexpected. For example, the
1370 static semantics of the literal <literal>368</literal>
1371 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1372 <literal>fromInteger</literal> to have any of the types:
1374 fromInteger :: Integer -> Integer
1375 fromInteger :: forall a. Foo a => Integer -> a
1376 fromInteger :: Num a => a -> Integer
1377 fromInteger :: Integer -> Bool -> Bool
1381 <para>Be warned: this is an experimental facility, with
1382 fewer checks than usual. Use <literal>-dcore-lint</literal>
1383 to typecheck the desugared program. If Core Lint is happy
1384 you should be all right.</para>
1388 <sect2 id="postfix-operators">
1389 <title>Postfix operators</title>
1392 GHC allows a small extension to the syntax of left operator sections, which
1393 allows you to define postfix operators. The extension is this: the left section
1397 is equivalent (from the point of view of both type checking and execution) to the expression
1401 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1402 The strict Haskell 98 interpretation is that the section is equivalent to
1406 That is, the operator must be a function of two arguments. GHC allows it to
1407 take only one argument, and that in turn allows you to write the function
1410 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1411 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1412 change their behaviour, of course.)
1414 <para>The extension does not extend to the left-hand side of function
1415 definitions; you must define such a function in prefix form.</para>
1419 <sect2 id="disambiguate-fields">
1420 <title>Record field disambiguation</title>
1422 In record construction and record pattern matching
1423 it is entirely unambiguous which field is referred to, even if there are two different
1424 data types in scope with a common field name. For example:
1427 data S = MkS { x :: Int, y :: Bool }
1432 data T = MkT { x :: Int }
1434 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1436 ok2 n = MkT { x = n+1 } -- Unambiguous
1438 bad1 k = k { x = 3 } -- Ambiguous
1439 bad2 k = x k -- Ambiguous
1441 Even though there are two <literal>x</literal>'s in scope,
1442 it is clear that the <literal>x</literal> in the pattern in the
1443 definition of <literal>ok1</literal> can only mean the field
1444 <literal>x</literal> from type <literal>S</literal>. Similarly for
1445 the function <literal>ok2</literal>. However, in the record update
1446 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1447 it is not clear which of the two types is intended.
1450 Haskell 98 regards all four as ambiguous, but with the
1451 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1452 the former two. The rules are precisely the same as those for instance
1453 declarations in Haskell 98, where the method names on the left-hand side
1454 of the method bindings in an instance declaration refer unambiguously
1455 to the method of that class (provided they are in scope at all), even
1456 if there are other variables in scope with the same name.
1457 This reduces the clutter of qualified names when you import two
1458 records from different modules that use the same field name.
1462 <!-- ===================== Record puns =================== -->
1464 <sect2 id="record-puns">
1469 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1473 When using records, it is common to write a pattern that binds a
1474 variable with the same name as a record field, such as:
1477 data C = C {a :: Int}
1483 Record punning permits the variable name to be elided, so one can simply
1490 to mean the same pattern as above. That is, in a record pattern, the
1491 pattern <literal>a</literal> expands into the pattern <literal>a =
1492 a</literal> for the same name <literal>a</literal>.
1496 Note that puns and other patterns can be mixed in the same record:
1498 data C = C {a :: Int, b :: Int}
1499 f (C {a, b = 4}) = a
1501 and that puns can be used wherever record patterns occur (e.g. in
1502 <literal>let</literal> bindings or at the top-level).
1506 Record punning can also be used in an expression, writing, for example,
1512 let a = 1 in C {a = a}
1515 Note that this expansion is purely syntactic, so the record pun
1516 expression refers to the nearest enclosing variable that is spelled the
1517 same as the field name.
1522 <!-- ===================== Record wildcards =================== -->
1524 <sect2 id="record-wildcards">
1525 <title>Record wildcards
1529 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1533 For records with many fields, it can be tiresome to write out each field
1534 individually in a record pattern, as in
1536 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1537 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1542 Record wildcard syntax permits a (<literal>..</literal>) in a record
1543 pattern, where each elided field <literal>f</literal> is replaced by the
1544 pattern <literal>f = f</literal>. For example, the above pattern can be
1547 f (C {a = 1, ..}) = b + c + d
1552 Note that wildcards can be mixed with other patterns, including puns
1553 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1554 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1555 wherever record patterns occur, including in <literal>let</literal>
1556 bindings and at the top-level. For example, the top-level binding
1560 defines <literal>b</literal>, <literal>c</literal>, and
1561 <literal>d</literal>.
1565 Record wildcards can also be used in expressions, writing, for example,
1568 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1574 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1577 Note that this expansion is purely syntactic, so the record wildcard
1578 expression refers to the nearest enclosing variables that are spelled
1579 the same as the omitted field names.
1584 <!-- ===================== Local fixity declarations =================== -->
1586 <sect2 id="local-fixity-declarations">
1587 <title>Local Fixity Declarations
1590 <para>A careful reading of the Haskell 98 Report reveals that fixity
1591 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1592 <literal>infixr</literal>) are permitted to appear inside local bindings
1593 such those introduced by <literal>let</literal> and
1594 <literal>where</literal>. However, the Haskell Report does not specify
1595 the semantics of such bindings very precisely.
1598 <para>In GHC, a fixity declaration may accompany a local binding:
1605 and the fixity declaration applies wherever the binding is in scope.
1606 For example, in a <literal>let</literal>, it applies in the right-hand
1607 sides of other <literal>let</literal>-bindings and the body of the
1608 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1609 expressions (<xref linkend="mdo-notation"/>), the local fixity
1610 declarations of a <literal>let</literal> statement scope over other
1611 statements in the group, just as the bound name does.
1615 Moreover, a local fixity declaration *must* accompany a local binding of
1616 that name: it is not possible to revise the fixity of name bound
1619 let infixr 9 $ in ...
1622 Because local fixity declarations are technically Haskell 98, no flag is
1623 necessary to enable them.
1627 <sect2 id="package-imports">
1628 <title>Package-qualified imports</title>
1630 <para>With the <option>-XPackageImports</option> flag, GHC allows
1631 import declarations to be qualified by the package name that the
1632 module is intended to be imported from. For example:</para>
1635 import "network" Network.Socket
1638 <para>would import the module <literal>Network.Socket</literal> from
1639 the package <literal>network</literal> (any version). This may
1640 be used to disambiguate an import when the same module is
1641 available from multiple packages, or is present in both the
1642 current package being built and an external package.</para>
1644 <para>Note: you probably don't need to use this feature, it was
1645 added mainly so that we can build backwards-compatible versions of
1646 packages when APIs change. It can lead to fragile dependencies in
1647 the common case: modules occasionally move from one package to
1648 another, rendering any package-qualified imports broken.</para>
1653 <!-- TYPE SYSTEM EXTENSIONS -->
1654 <sect1 id="data-type-extensions">
1655 <title>Extensions to data types and type synonyms</title>
1657 <sect2 id="nullary-types">
1658 <title>Data types with no constructors</title>
1660 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1661 a data type with no constructors. For example:</para>
1665 data T a -- T :: * -> *
1668 <para>Syntactically, the declaration lacks the "= constrs" part. The
1669 type can be parameterised over types of any kind, but if the kind is
1670 not <literal>*</literal> then an explicit kind annotation must be used
1671 (see <xref linkend="kinding"/>).</para>
1673 <para>Such data types have only one value, namely bottom.
1674 Nevertheless, they can be useful when defining "phantom types".</para>
1677 <sect2 id="infix-tycons">
1678 <title>Infix type constructors, classes, and type variables</title>
1681 GHC allows type constructors, classes, and type variables to be operators, and
1682 to be written infix, very much like expressions. More specifically:
1685 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1686 The lexical syntax is the same as that for data constructors.
1689 Data type and type-synonym declarations can be written infix, parenthesised
1690 if you want further arguments. E.g.
1692 data a :*: b = Foo a b
1693 type a :+: b = Either a b
1694 class a :=: b where ...
1696 data (a :**: b) x = Baz a b x
1697 type (a :++: b) y = Either (a,b) y
1701 Types, and class constraints, can be written infix. For example
1704 f :: (a :=: b) => a -> b
1708 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1709 The lexical syntax is the same as that for variable operators, excluding "(.)",
1710 "(!)", and "(*)". In a binding position, the operator must be
1711 parenthesised. For example:
1713 type T (+) = Int + Int
1717 liftA2 :: Arrow (~>)
1718 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1724 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1725 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1728 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1729 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1730 sets the fixity for a data constructor and the corresponding type constructor. For example:
1734 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1735 and similarly for <literal>:*:</literal>.
1736 <literal>Int `a` Bool</literal>.
1739 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1746 <sect2 id="type-synonyms">
1747 <title>Liberalised type synonyms</title>
1750 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1751 on individual synonym declarations.
1752 With the <option>-XLiberalTypeSynonyms</option> extension,
1753 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1754 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1757 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1758 in a type synonym, thus:
1760 type Discard a = forall b. Show b => a -> b -> (a, String)
1765 g :: Discard Int -> (Int,String) -- A rank-2 type
1772 If you also use <option>-XUnboxedTuples</option>,
1773 you can write an unboxed tuple in a type synonym:
1775 type Pr = (# Int, Int #)
1783 You can apply a type synonym to a forall type:
1785 type Foo a = a -> a -> Bool
1787 f :: Foo (forall b. b->b)
1789 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1791 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1796 You can apply a type synonym to a partially applied type synonym:
1798 type Generic i o = forall x. i x -> o x
1801 foo :: Generic Id []
1803 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1805 foo :: forall x. x -> [x]
1813 GHC currently does kind checking before expanding synonyms (though even that
1817 After expanding type synonyms, GHC does validity checking on types, looking for
1818 the following mal-formedness which isn't detected simply by kind checking:
1821 Type constructor applied to a type involving for-alls.
1824 Unboxed tuple on left of an arrow.
1827 Partially-applied type synonym.
1831 this will be rejected:
1833 type Pr = (# Int, Int #)
1838 because GHC does not allow unboxed tuples on the left of a function arrow.
1843 <sect2 id="existential-quantification">
1844 <title>Existentially quantified data constructors
1848 The idea of using existential quantification in data type declarations
1849 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1850 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1851 London, 1991). It was later formalised by Laufer and Odersky
1852 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1853 TOPLAS, 16(5), pp1411-1430, 1994).
1854 It's been in Lennart
1855 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1856 proved very useful. Here's the idea. Consider the declaration:
1862 data Foo = forall a. MkFoo a (a -> Bool)
1869 The data type <literal>Foo</literal> has two constructors with types:
1875 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1882 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1883 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1884 For example, the following expression is fine:
1890 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1896 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1897 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1898 isUpper</function> packages a character with a compatible function. These
1899 two things are each of type <literal>Foo</literal> and can be put in a list.
1903 What can we do with a value of type <literal>Foo</literal>?. In particular,
1904 what happens when we pattern-match on <function>MkFoo</function>?
1910 f (MkFoo val fn) = ???
1916 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1917 are compatible, the only (useful) thing we can do with them is to
1918 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1925 f (MkFoo val fn) = fn val
1931 What this allows us to do is to package heterogeneous values
1932 together with a bunch of functions that manipulate them, and then treat
1933 that collection of packages in a uniform manner. You can express
1934 quite a bit of object-oriented-like programming this way.
1937 <sect3 id="existential">
1938 <title>Why existential?
1942 What has this to do with <emphasis>existential</emphasis> quantification?
1943 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1949 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1955 But Haskell programmers can safely think of the ordinary
1956 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1957 adding a new existential quantification construct.
1962 <sect3 id="existential-with-context">
1963 <title>Existentials and type classes</title>
1966 An easy extension is to allow
1967 arbitrary contexts before the constructor. For example:
1973 data Baz = forall a. Eq a => Baz1 a a
1974 | forall b. Show b => Baz2 b (b -> b)
1980 The two constructors have the types you'd expect:
1986 Baz1 :: forall a. Eq a => a -> a -> Baz
1987 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1993 But when pattern matching on <function>Baz1</function> the matched values can be compared
1994 for equality, and when pattern matching on <function>Baz2</function> the first matched
1995 value can be converted to a string (as well as applying the function to it).
1996 So this program is legal:
2003 f (Baz1 p q) | p == q = "Yes"
2005 f (Baz2 v fn) = show (fn v)
2011 Operationally, in a dictionary-passing implementation, the
2012 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2013 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2014 extract it on pattern matching.
2019 <sect3 id="existential-records">
2020 <title>Record Constructors</title>
2023 GHC allows existentials to be used with records syntax as well. For example:
2026 data Counter a = forall self. NewCounter
2028 , _inc :: self -> self
2029 , _display :: self -> IO ()
2033 Here <literal>tag</literal> is a public field, with a well-typed selector
2034 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2035 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2036 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2037 compile-time error. In other words, <emphasis>GHC defines a record selector function
2038 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2039 (This example used an underscore in the fields for which record selectors
2040 will not be defined, but that is only programming style; GHC ignores them.)
2044 To make use of these hidden fields, we need to create some helper functions:
2047 inc :: Counter a -> Counter a
2048 inc (NewCounter x i d t) = NewCounter
2049 { _this = i x, _inc = i, _display = d, tag = t }
2051 display :: Counter a -> IO ()
2052 display NewCounter{ _this = x, _display = d } = d x
2055 Now we can define counters with different underlying implementations:
2058 counterA :: Counter String
2059 counterA = NewCounter
2060 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2062 counterB :: Counter String
2063 counterB = NewCounter
2064 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2067 display (inc counterA) -- prints "1"
2068 display (inc (inc counterB)) -- prints "##"
2071 At the moment, record update syntax is only supported for Haskell 98 data types,
2072 so the following function does <emphasis>not</emphasis> work:
2075 -- This is invalid; use explicit NewCounter instead for now
2076 setTag :: Counter a -> a -> Counter a
2077 setTag obj t = obj{ tag = t }
2086 <title>Restrictions</title>
2089 There are several restrictions on the ways in which existentially-quantified
2090 constructors can be use.
2099 When pattern matching, each pattern match introduces a new,
2100 distinct, type for each existential type variable. These types cannot
2101 be unified with any other type, nor can they escape from the scope of
2102 the pattern match. For example, these fragments are incorrect:
2110 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2111 is the result of <function>f1</function>. One way to see why this is wrong is to
2112 ask what type <function>f1</function> has:
2116 f1 :: Foo -> a -- Weird!
2120 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2125 f1 :: forall a. Foo -> a -- Wrong!
2129 The original program is just plain wrong. Here's another sort of error
2133 f2 (Baz1 a b) (Baz1 p q) = a==q
2137 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2138 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2139 from the two <function>Baz1</function> constructors.
2147 You can't pattern-match on an existentially quantified
2148 constructor in a <literal>let</literal> or <literal>where</literal> group of
2149 bindings. So this is illegal:
2153 f3 x = a==b where { Baz1 a b = x }
2156 Instead, use a <literal>case</literal> expression:
2159 f3 x = case x of Baz1 a b -> a==b
2162 In general, you can only pattern-match
2163 on an existentially-quantified constructor in a <literal>case</literal> expression or
2164 in the patterns of a function definition.
2166 The reason for this restriction is really an implementation one.
2167 Type-checking binding groups is already a nightmare without
2168 existentials complicating the picture. Also an existential pattern
2169 binding at the top level of a module doesn't make sense, because it's
2170 not clear how to prevent the existentially-quantified type "escaping".
2171 So for now, there's a simple-to-state restriction. We'll see how
2179 You can't use existential quantification for <literal>newtype</literal>
2180 declarations. So this is illegal:
2184 newtype T = forall a. Ord a => MkT a
2188 Reason: a value of type <literal>T</literal> must be represented as a
2189 pair of a dictionary for <literal>Ord t</literal> and a value of type
2190 <literal>t</literal>. That contradicts the idea that
2191 <literal>newtype</literal> should have no concrete representation.
2192 You can get just the same efficiency and effect by using
2193 <literal>data</literal> instead of <literal>newtype</literal>. If
2194 there is no overloading involved, then there is more of a case for
2195 allowing an existentially-quantified <literal>newtype</literal>,
2196 because the <literal>data</literal> version does carry an
2197 implementation cost, but single-field existentially quantified
2198 constructors aren't much use. So the simple restriction (no
2199 existential stuff on <literal>newtype</literal>) stands, unless there
2200 are convincing reasons to change it.
2208 You can't use <literal>deriving</literal> to define instances of a
2209 data type with existentially quantified data constructors.
2211 Reason: in most cases it would not make sense. For example:;
2214 data T = forall a. MkT [a] deriving( Eq )
2217 To derive <literal>Eq</literal> in the standard way we would need to have equality
2218 between the single component of two <function>MkT</function> constructors:
2222 (MkT a) == (MkT b) = ???
2225 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2226 It's just about possible to imagine examples in which the derived instance
2227 would make sense, but it seems altogether simpler simply to prohibit such
2228 declarations. Define your own instances!
2239 <!-- ====================== Generalised algebraic data types ======================= -->
2241 <sect2 id="gadt-style">
2242 <title>Declaring data types with explicit constructor signatures</title>
2244 <para>GHC allows you to declare an algebraic data type by
2245 giving the type signatures of constructors explicitly. For example:
2249 Just :: a -> Maybe a
2251 The form is called a "GADT-style declaration"
2252 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2253 can only be declared using this form.</para>
2254 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2255 For example, these two declarations are equivalent:
2257 data Foo = forall a. MkFoo a (a -> Bool)
2258 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2261 <para>Any data type that can be declared in standard Haskell-98 syntax
2262 can also be declared using GADT-style syntax.
2263 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2264 they treat class constraints on the data constructors differently.
2265 Specifically, if the constructor is given a type-class context, that
2266 context is made available by pattern matching. For example:
2269 MkSet :: Eq a => [a] -> Set a
2271 makeSet :: Eq a => [a] -> Set a
2272 makeSet xs = MkSet (nub xs)
2274 insert :: a -> Set a -> Set a
2275 insert a (MkSet as) | a `elem` as = MkSet as
2276 | otherwise = MkSet (a:as)
2278 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2279 gives rise to a <literal>(Eq a)</literal>
2280 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2281 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2282 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2283 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2284 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2285 In the example, the equality dictionary is used to satisfy the equality constraint
2286 generated by the call to <literal>elem</literal>, so that the type of
2287 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2290 For example, one possible application is to reify dictionaries:
2292 data NumInst a where
2293 MkNumInst :: Num a => NumInst a
2295 intInst :: NumInst Int
2298 plus :: NumInst a -> a -> a -> a
2299 plus MkNumInst p q = p + q
2301 Here, a value of type <literal>NumInst a</literal> is equivalent
2302 to an explicit <literal>(Num a)</literal> dictionary.
2305 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2306 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2310 = Num a => MkNumInst (NumInst a)
2312 Notice that, unlike the situation when declaring an existential, there is
2313 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2314 data type's universally quantified type variable <literal>a</literal>.
2315 A constructor may have both universal and existential type variables: for example,
2316 the following two declarations are equivalent:
2319 = forall b. (Num a, Eq b) => MkT1 a b
2321 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2324 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2325 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2326 In Haskell 98 the definition
2328 data Eq a => Set' a = MkSet' [a]
2330 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2331 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2332 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2333 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2334 GHC's behaviour is much more useful, as well as much more intuitive.
2338 The rest of this section gives further details about GADT-style data
2343 The result type of each data constructor must begin with the type constructor being defined.
2344 If the result type of all constructors
2345 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2346 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2347 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2351 The type signature of
2352 each constructor is independent, and is implicitly universally quantified as usual.
2353 Different constructors may have different universally-quantified type variables
2354 and different type-class constraints.
2355 For example, this is fine:
2358 T1 :: Eq b => b -> T b
2359 T2 :: (Show c, Ix c) => c -> [c] -> T c
2364 Unlike a Haskell-98-style
2365 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2366 have no scope. Indeed, one can write a kind signature instead:
2368 data Set :: * -> * where ...
2370 or even a mixture of the two:
2372 data Foo a :: (* -> *) -> * where ...
2374 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2377 data Foo a (b :: * -> *) where ...
2383 You can use strictness annotations, in the obvious places
2384 in the constructor type:
2387 Lit :: !Int -> Term Int
2388 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2389 Pair :: Term a -> Term b -> Term (a,b)
2394 You can use a <literal>deriving</literal> clause on a GADT-style data type
2395 declaration. For example, these two declarations are equivalent
2397 data Maybe1 a where {
2398 Nothing1 :: Maybe1 a ;
2399 Just1 :: a -> Maybe1 a
2400 } deriving( Eq, Ord )
2402 data Maybe2 a = Nothing2 | Just2 a
2408 You can use record syntax on a GADT-style data type declaration:
2412 Adult { name :: String, children :: [Person] } :: Person
2413 Child { name :: String } :: Person
2415 As usual, for every constructor that has a field <literal>f</literal>, the type of
2416 field <literal>f</literal> must be the same (modulo alpha conversion).
2419 At the moment, record updates are not yet possible with GADT-style declarations,
2420 so support is limited to record construction, selection and pattern matching.
2423 aPerson = Adult { name = "Fred", children = [] }
2425 shortName :: Person -> Bool
2426 hasChildren (Adult { children = kids }) = not (null kids)
2427 hasChildren (Child {}) = False
2432 As in the case of existentials declared using the Haskell-98-like record syntax
2433 (<xref linkend="existential-records"/>),
2434 record-selector functions are generated only for those fields that have well-typed
2436 Here is the example of that section, in GADT-style syntax:
2438 data Counter a where
2439 NewCounter { _this :: self
2440 , _inc :: self -> self
2441 , _display :: self -> IO ()
2446 As before, only one selector function is generated here, that for <literal>tag</literal>.
2447 Nevertheless, you can still use all the field names in pattern matching and record construction.
2449 </itemizedlist></para>
2453 <title>Generalised Algebraic Data Types (GADTs)</title>
2455 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2456 by allowing constructors to have richer return types. Here is an example:
2459 Lit :: Int -> Term Int
2460 Succ :: Term Int -> Term Int
2461 IsZero :: Term Int -> Term Bool
2462 If :: Term Bool -> Term a -> Term a -> Term a
2463 Pair :: Term a -> Term b -> Term (a,b)
2465 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2466 case with ordinary data types. This generality allows us to
2467 write a well-typed <literal>eval</literal> function
2468 for these <literal>Terms</literal>:
2472 eval (Succ t) = 1 + eval t
2473 eval (IsZero t) = eval t == 0
2474 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2475 eval (Pair e1 e2) = (eval e1, eval e2)
2477 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2478 For example, in the right hand side of the equation
2483 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2484 A precise specification of the type rules is beyond what this user manual aspires to,
2485 but the design closely follows that described in
2487 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2488 unification-based type inference for GADTs</ulink>,
2490 The general principle is this: <emphasis>type refinement is only carried out
2491 based on user-supplied type annotations</emphasis>.
2492 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2493 and lots of obscure error messages will
2494 occur. However, the refinement is quite general. For example, if we had:
2496 eval :: Term a -> a -> a
2497 eval (Lit i) j = i+j
2499 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2500 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2501 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2504 These and many other examples are given in papers by Hongwei Xi, and
2505 Tim Sheard. There is a longer introduction
2506 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2508 <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
2509 may use different notation to that implemented in GHC.
2512 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2513 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2516 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2517 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2518 The result type of each constructor must begin with the type constructor being defined,
2519 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2520 For example, in the <literal>Term</literal> data
2521 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2522 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2527 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2528 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2529 whose result type is not just <literal>T a b</literal>.
2533 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2534 an ordinary data type.
2538 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2542 Lit { val :: Int } :: Term Int
2543 Succ { num :: Term Int } :: Term Int
2544 Pred { num :: Term Int } :: Term Int
2545 IsZero { arg :: Term Int } :: Term Bool
2546 Pair { arg1 :: Term a
2549 If { cnd :: Term Bool
2554 However, for GADTs there is the following additional constraint:
2555 every constructor that has a field <literal>f</literal> must have
2556 the same result type (modulo alpha conversion)
2557 Hence, in the above example, we cannot merge the <literal>num</literal>
2558 and <literal>arg</literal> fields above into a
2559 single name. Although their field types are both <literal>Term Int</literal>,
2560 their selector functions actually have different types:
2563 num :: Term Int -> Term Int
2564 arg :: Term Bool -> Term Int
2569 When pattern-matching against data constructors drawn from a GADT,
2570 for example in a <literal>case</literal> expression, the following rules apply:
2572 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2573 <listitem><para>The type of the result of the <literal>case</literal> expression must be rigid.</para></listitem>
2574 <listitem><para>The type of any free variable mentioned in any of
2575 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2577 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2578 way to ensure that a variable a rigid type is to give it a type signature.
2587 <!-- ====================== End of Generalised algebraic data types ======================= -->
2589 <sect1 id="deriving">
2590 <title>Extensions to the "deriving" mechanism</title>
2592 <sect2 id="deriving-inferred">
2593 <title>Inferred context for deriving clauses</title>
2596 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2599 data T0 f a = MkT0 a deriving( Eq )
2600 data T1 f a = MkT1 (f a) deriving( Eq )
2601 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2603 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2605 instance Eq a => Eq (T0 f a) where ...
2606 instance Eq (f a) => Eq (T1 f a) where ...
2607 instance Eq (f (f a)) => Eq (T2 f a) where ...
2609 The first of these is obviously fine. The second is still fine, although less obviously.
2610 The third is not Haskell 98, and risks losing termination of instances.
2613 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2614 each constraint in the inferred instance context must consist only of type variables,
2615 with no repetitions.
2618 This rule is applied regardless of flags. If you want a more exotic context, you can write
2619 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2623 <sect2 id="stand-alone-deriving">
2624 <title>Stand-alone deriving declarations</title>
2627 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2629 data Foo a = Bar a | Baz String
2631 deriving instance Eq a => Eq (Foo a)
2633 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2634 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2635 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2636 exactly as you would in an ordinary instance declaration.
2637 (In contrast the context is inferred in a <literal>deriving</literal> clause
2638 attached to a data type declaration.)
2640 A <literal>deriving instance</literal> declaration
2641 must obey the same rules concerning form and termination as ordinary instance declarations,
2642 controlled by the same flags; see <xref linkend="instance-decls"/>.
2645 Unlike a <literal>deriving</literal>
2646 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2647 than the data type (assuming you also use
2648 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2651 data Foo a = Bar a | Baz String
2653 deriving instance Eq a => Eq (Foo [a])
2654 deriving instance Eq a => Eq (Foo (Maybe a))
2656 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2657 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2660 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2661 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2664 newtype Foo a = MkFoo (State Int a)
2666 deriving instance MonadState Int Foo
2668 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2669 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2675 <sect2 id="deriving-typeable">
2676 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2679 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2680 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2681 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2682 classes <literal>Eq</literal>, <literal>Ord</literal>,
2683 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2686 GHC extends this list with two more classes that may be automatically derived
2687 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2688 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2689 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2690 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2692 <para>An instance of <literal>Typeable</literal> can only be derived if the
2693 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2694 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2696 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2697 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2699 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2700 are used, and only <literal>Typeable1</literal> up to
2701 <literal>Typeable7</literal> are provided in the library.)
2702 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2703 class, whose kind suits that of the data type constructor, and
2704 then writing the data type instance by hand.
2708 <sect2 id="newtype-deriving">
2709 <title>Generalised derived instances for newtypes</title>
2712 When you define an abstract type using <literal>newtype</literal>, you may want
2713 the new type to inherit some instances from its representation. In
2714 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2715 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2716 other classes you have to write an explicit instance declaration. For
2717 example, if you define
2720 newtype Dollars = Dollars Int
2723 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2724 explicitly define an instance of <literal>Num</literal>:
2727 instance Num Dollars where
2728 Dollars a + Dollars b = Dollars (a+b)
2731 All the instance does is apply and remove the <literal>newtype</literal>
2732 constructor. It is particularly galling that, since the constructor
2733 doesn't appear at run-time, this instance declaration defines a
2734 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2735 dictionary, only slower!
2739 <sect3> <title> Generalising the deriving clause </title>
2741 GHC now permits such instances to be derived instead,
2742 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2745 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2748 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2749 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2750 derives an instance declaration of the form
2753 instance Num Int => Num Dollars
2756 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2760 We can also derive instances of constructor classes in a similar
2761 way. For example, suppose we have implemented state and failure monad
2762 transformers, such that
2765 instance Monad m => Monad (State s m)
2766 instance Monad m => Monad (Failure m)
2768 In Haskell 98, we can define a parsing monad by
2770 type Parser tok m a = State [tok] (Failure m) a
2773 which is automatically a monad thanks to the instance declarations
2774 above. With the extension, we can make the parser type abstract,
2775 without needing to write an instance of class <literal>Monad</literal>, via
2778 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2781 In this case the derived instance declaration is of the form
2783 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2786 Notice that, since <literal>Monad</literal> is a constructor class, the
2787 instance is a <emphasis>partial application</emphasis> of the new type, not the
2788 entire left hand side. We can imagine that the type declaration is
2789 "eta-converted" to generate the context of the instance
2794 We can even derive instances of multi-parameter classes, provided the
2795 newtype is the last class parameter. In this case, a ``partial
2796 application'' of the class appears in the <literal>deriving</literal>
2797 clause. For example, given the class
2800 class StateMonad s m | m -> s where ...
2801 instance Monad m => StateMonad s (State s m) where ...
2803 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2805 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2806 deriving (Monad, StateMonad [tok])
2809 The derived instance is obtained by completing the application of the
2810 class to the new type:
2813 instance StateMonad [tok] (State [tok] (Failure m)) =>
2814 StateMonad [tok] (Parser tok m)
2819 As a result of this extension, all derived instances in newtype
2820 declarations are treated uniformly (and implemented just by reusing
2821 the dictionary for the representation type), <emphasis>except</emphasis>
2822 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2823 the newtype and its representation.
2827 <sect3> <title> A more precise specification </title>
2829 Derived instance declarations are constructed as follows. Consider the
2830 declaration (after expansion of any type synonyms)
2833 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2839 The <literal>ci</literal> are partial applications of
2840 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2841 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2844 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2847 The type <literal>t</literal> is an arbitrary type.
2850 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2851 nor in the <literal>ci</literal>, and
2854 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2855 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2856 should not "look through" the type or its constructor. You can still
2857 derive these classes for a newtype, but it happens in the usual way, not
2858 via this new mechanism.
2861 Then, for each <literal>ci</literal>, the derived instance
2864 instance ci t => ci (T v1...vk)
2866 As an example which does <emphasis>not</emphasis> work, consider
2868 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2870 Here we cannot derive the instance
2872 instance Monad (State s m) => Monad (NonMonad m)
2875 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2876 and so cannot be "eta-converted" away. It is a good thing that this
2877 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2878 not, in fact, a monad --- for the same reason. Try defining
2879 <literal>>>=</literal> with the correct type: you won't be able to.
2883 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2884 important, since we can only derive instances for the last one. If the
2885 <literal>StateMonad</literal> class above were instead defined as
2888 class StateMonad m s | m -> s where ...
2891 then we would not have been able to derive an instance for the
2892 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2893 classes usually have one "main" parameter for which deriving new
2894 instances is most interesting.
2896 <para>Lastly, all of this applies only for classes other than
2897 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2898 and <literal>Data</literal>, for which the built-in derivation applies (section
2899 4.3.3. of the Haskell Report).
2900 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2901 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2902 the standard method is used or the one described here.)
2909 <!-- TYPE SYSTEM EXTENSIONS -->
2910 <sect1 id="type-class-extensions">
2911 <title>Class and instances declarations</title>
2913 <sect2 id="multi-param-type-classes">
2914 <title>Class declarations</title>
2917 This section, and the next one, documents GHC's type-class extensions.
2918 There's lots of background in the paper <ulink
2919 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2920 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2921 Jones, Erik Meijer).
2924 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2928 <title>Multi-parameter type classes</title>
2930 Multi-parameter type classes are permitted. For example:
2934 class Collection c a where
2935 union :: c a -> c a -> c a
2943 <title>The superclasses of a class declaration</title>
2946 There are no restrictions on the context in a class declaration
2947 (which introduces superclasses), except that the class hierarchy must
2948 be acyclic. So these class declarations are OK:
2952 class Functor (m k) => FiniteMap m k where
2955 class (Monad m, Monad (t m)) => Transform t m where
2956 lift :: m a -> (t m) a
2962 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2963 of "acyclic" involves only the superclass relationships. For example,
2969 op :: D b => a -> b -> b
2972 class C a => D a where { ... }
2976 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2977 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2978 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2985 <sect3 id="class-method-types">
2986 <title>Class method types</title>
2989 Haskell 98 prohibits class method types to mention constraints on the
2990 class type variable, thus:
2993 fromList :: [a] -> s a
2994 elem :: Eq a => a -> s a -> Bool
2996 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2997 contains the constraint <literal>Eq a</literal>, constrains only the
2998 class type variable (in this case <literal>a</literal>).
2999 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3006 <sect2 id="functional-dependencies">
3007 <title>Functional dependencies
3010 <para> Functional dependencies are implemented as described by Mark Jones
3011 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3012 In Proceedings of the 9th European Symposium on Programming,
3013 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3017 Functional dependencies are introduced by a vertical bar in the syntax of a
3018 class declaration; e.g.
3020 class (Monad m) => MonadState s m | m -> s where ...
3022 class Foo a b c | a b -> c where ...
3024 There should be more documentation, but there isn't (yet). Yell if you need it.
3027 <sect3><title>Rules for functional dependencies </title>
3029 In a class declaration, all of the class type variables must be reachable (in the sense
3030 mentioned in <xref linkend="type-restrictions"/>)
3031 from the free variables of each method type.
3035 class Coll s a where
3037 insert :: s -> a -> s
3040 is not OK, because the type of <literal>empty</literal> doesn't mention
3041 <literal>a</literal>. Functional dependencies can make the type variable
3044 class Coll s a | s -> a where
3046 insert :: s -> a -> s
3049 Alternatively <literal>Coll</literal> might be rewritten
3052 class Coll s a where
3054 insert :: s a -> a -> s a
3058 which makes the connection between the type of a collection of
3059 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3060 Occasionally this really doesn't work, in which case you can split the
3068 class CollE s => Coll s a where
3069 insert :: s -> a -> s
3076 <title>Background on functional dependencies</title>
3078 <para>The following description of the motivation and use of functional dependencies is taken
3079 from the Hugs user manual, reproduced here (with minor changes) by kind
3080 permission of Mark Jones.
3083 Consider the following class, intended as part of a
3084 library for collection types:
3086 class Collects e ce where
3088 insert :: e -> ce -> ce
3089 member :: e -> ce -> Bool
3091 The type variable e used here represents the element type, while ce is the type
3092 of the container itself. Within this framework, we might want to define
3093 instances of this class for lists or characteristic functions (both of which
3094 can be used to represent collections of any equality type), bit sets (which can
3095 be used to represent collections of characters), or hash tables (which can be
3096 used to represent any collection whose elements have a hash function). Omitting
3097 standard implementation details, this would lead to the following declarations:
3099 instance Eq e => Collects e [e] where ...
3100 instance Eq e => Collects e (e -> Bool) where ...
3101 instance Collects Char BitSet where ...
3102 instance (Hashable e, Collects a ce)
3103 => Collects e (Array Int ce) where ...
3105 All this looks quite promising; we have a class and a range of interesting
3106 implementations. Unfortunately, there are some serious problems with the class
3107 declaration. First, the empty function has an ambiguous type:
3109 empty :: Collects e ce => ce
3111 By "ambiguous" we mean that there is a type variable e that appears on the left
3112 of the <literal>=></literal> symbol, but not on the right. The problem with
3113 this is that, according to the theoretical foundations of Haskell overloading,
3114 we cannot guarantee a well-defined semantics for any term with an ambiguous
3118 We can sidestep this specific problem by removing the empty member from the
3119 class declaration. However, although the remaining members, insert and member,
3120 do not have ambiguous types, we still run into problems when we try to use
3121 them. For example, consider the following two functions:
3123 f x y = insert x . insert y
3126 for which GHC infers the following types:
3128 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3129 g :: (Collects Bool c, Collects Char c) => c -> c
3131 Notice that the type for f allows the two parameters x and y to be assigned
3132 different types, even though it attempts to insert each of the two values, one
3133 after the other, into the same collection. If we're trying to model collections
3134 that contain only one type of value, then this is clearly an inaccurate
3135 type. Worse still, the definition for g is accepted, without causing a type
3136 error. As a result, the error in this code will not be flagged at the point
3137 where it appears. Instead, it will show up only when we try to use g, which
3138 might even be in a different module.
3141 <sect4><title>An attempt to use constructor classes</title>
3144 Faced with the problems described above, some Haskell programmers might be
3145 tempted to use something like the following version of the class declaration:
3147 class Collects e c where
3149 insert :: e -> c e -> c e
3150 member :: e -> c e -> Bool
3152 The key difference here is that we abstract over the type constructor c that is
3153 used to form the collection type c e, and not over that collection type itself,
3154 represented by ce in the original class declaration. This avoids the immediate
3155 problems that we mentioned above: empty has type <literal>Collects e c => c
3156 e</literal>, which is not ambiguous.
3159 The function f from the previous section has a more accurate type:
3161 f :: (Collects e c) => e -> e -> c e -> c e
3163 The function g from the previous section is now rejected with a type error as
3164 we would hope because the type of f does not allow the two arguments to have
3166 This, then, is an example of a multiple parameter class that does actually work
3167 quite well in practice, without ambiguity problems.
3168 There is, however, a catch. This version of the Collects class is nowhere near
3169 as general as the original class seemed to be: only one of the four instances
3170 for <literal>Collects</literal>
3171 given above can be used with this version of Collects because only one of
3172 them---the instance for lists---has a collection type that can be written in
3173 the form c e, for some type constructor c, and element type e.
3177 <sect4><title>Adding functional dependencies</title>
3180 To get a more useful version of the Collects class, Hugs provides a mechanism
3181 that allows programmers to specify dependencies between the parameters of a
3182 multiple parameter class (For readers with an interest in theoretical
3183 foundations and previous work: The use of dependency information can be seen
3184 both as a generalization of the proposal for `parametric type classes' that was
3185 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3186 later framework for "improvement" of qualified types. The
3187 underlying ideas are also discussed in a more theoretical and abstract setting
3188 in a manuscript [implparam], where they are identified as one point in a
3189 general design space for systems of implicit parameterization.).
3191 To start with an abstract example, consider a declaration such as:
3193 class C a b where ...
3195 which tells us simply that C can be thought of as a binary relation on types
3196 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3197 included in the definition of classes to add information about dependencies
3198 between parameters, as in the following examples:
3200 class D a b | a -> b where ...
3201 class E a b | a -> b, b -> a where ...
3203 The notation <literal>a -> b</literal> used here between the | and where
3204 symbols --- not to be
3205 confused with a function type --- indicates that the a parameter uniquely
3206 determines the b parameter, and might be read as "a determines b." Thus D is
3207 not just a relation, but actually a (partial) function. Similarly, from the two
3208 dependencies that are included in the definition of E, we can see that E
3209 represents a (partial) one-one mapping between types.
3212 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3213 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3214 m>=0, meaning that the y parameters are uniquely determined by the x
3215 parameters. Spaces can be used as separators if more than one variable appears
3216 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3217 annotated with multiple dependencies using commas as separators, as in the
3218 definition of E above. Some dependencies that we can write in this notation are
3219 redundant, and will be rejected because they don't serve any useful
3220 purpose, and may instead indicate an error in the program. Examples of
3221 dependencies like this include <literal>a -> a </literal>,
3222 <literal>a -> a a </literal>,
3223 <literal>a -> </literal>, etc. There can also be
3224 some redundancy if multiple dependencies are given, as in
3225 <literal>a->b</literal>,
3226 <literal>b->c </literal>, <literal>a->c </literal>, and
3227 in which some subset implies the remaining dependencies. Examples like this are
3228 not treated as errors. Note that dependencies appear only in class
3229 declarations, and not in any other part of the language. In particular, the
3230 syntax for instance declarations, class constraints, and types is completely
3234 By including dependencies in a class declaration, we provide a mechanism for
3235 the programmer to specify each multiple parameter class more precisely. The
3236 compiler, on the other hand, is responsible for ensuring that the set of
3237 instances that are in scope at any given point in the program is consistent
3238 with any declared dependencies. For example, the following pair of instance
3239 declarations cannot appear together in the same scope because they violate the
3240 dependency for D, even though either one on its own would be acceptable:
3242 instance D Bool Int where ...
3243 instance D Bool Char where ...
3245 Note also that the following declaration is not allowed, even by itself:
3247 instance D [a] b where ...
3249 The problem here is that this instance would allow one particular choice of [a]
3250 to be associated with more than one choice for b, which contradicts the
3251 dependency specified in the definition of D. More generally, this means that,
3252 in any instance of the form:
3254 instance D t s where ...
3256 for some particular types t and s, the only variables that can appear in s are
3257 the ones that appear in t, and hence, if the type t is known, then s will be
3258 uniquely determined.
3261 The benefit of including dependency information is that it allows us to define
3262 more general multiple parameter classes, without ambiguity problems, and with
3263 the benefit of more accurate types. To illustrate this, we return to the
3264 collection class example, and annotate the original definition of <literal>Collects</literal>
3265 with a simple dependency:
3267 class Collects e ce | ce -> e where
3269 insert :: e -> ce -> ce
3270 member :: e -> ce -> Bool
3272 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3273 determined by the type of the collection ce. Note that both parameters of
3274 Collects are of kind *; there are no constructor classes here. Note too that
3275 all of the instances of Collects that we gave earlier can be used
3276 together with this new definition.
3279 What about the ambiguity problems that we encountered with the original
3280 definition? The empty function still has type Collects e ce => ce, but it is no
3281 longer necessary to regard that as an ambiguous type: Although the variable e
3282 does not appear on the right of the => symbol, the dependency for class
3283 Collects tells us that it is uniquely determined by ce, which does appear on
3284 the right of the => symbol. Hence the context in which empty is used can still
3285 give enough information to determine types for both ce and e, without
3286 ambiguity. More generally, we need only regard a type as ambiguous if it
3287 contains a variable on the left of the => that is not uniquely determined
3288 (either directly or indirectly) by the variables on the right.
3291 Dependencies also help to produce more accurate types for user defined
3292 functions, and hence to provide earlier detection of errors, and less cluttered
3293 types for programmers to work with. Recall the previous definition for a
3296 f x y = insert x y = insert x . insert y
3298 for which we originally obtained a type:
3300 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3302 Given the dependency information that we have for Collects, however, we can
3303 deduce that a and b must be equal because they both appear as the second
3304 parameter in a Collects constraint with the same first parameter c. Hence we
3305 can infer a shorter and more accurate type for f:
3307 f :: (Collects a c) => a -> a -> c -> c
3309 In a similar way, the earlier definition of g will now be flagged as a type error.
3312 Although we have given only a few examples here, it should be clear that the
3313 addition of dependency information can help to make multiple parameter classes
3314 more useful in practice, avoiding ambiguity problems, and allowing more general
3315 sets of instance declarations.
3321 <sect2 id="instance-decls">
3322 <title>Instance declarations</title>
3324 <sect3 id="instance-rules">
3325 <title>Relaxed rules for instance declarations</title>
3327 <para>An instance declaration has the form
3329 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 ...
3331 The part before the "<literal>=></literal>" is the
3332 <emphasis>context</emphasis>, while the part after the
3333 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3337 In Haskell 98 the head of an instance declaration
3338 must be of the form <literal>C (T a1 ... an)</literal>, where
3339 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3340 and the <literal>a1 ... an</literal> are distinct type variables.
3341 Furthermore, the assertions in the context of the instance declaration
3342 must be of the form <literal>C a</literal> where <literal>a</literal>
3343 is a type variable that occurs in the head.
3346 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3347 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3348 the context and head of the instance declaration can each consist of arbitrary
3349 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3353 The Paterson Conditions: for each assertion in the context
3355 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3356 <listitem><para>The assertion has fewer constructors and variables (taken together
3357 and counting repetitions) than the head</para></listitem>
3361 <listitem><para>The Coverage Condition. For each functional dependency,
3362 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3363 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3364 every type variable in
3365 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3366 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3367 substitution mapping each type variable in the class declaration to the
3368 corresponding type in the instance declaration.
3371 These restrictions ensure that context reduction terminates: each reduction
3372 step makes the problem smaller by at least one
3373 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3374 if you give the <option>-XUndecidableInstances</option>
3375 flag (<xref linkend="undecidable-instances"/>).
3376 You can find lots of background material about the reason for these
3377 restrictions in the paper <ulink
3378 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3379 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3382 For example, these are OK:
3384 instance C Int [a] -- Multiple parameters
3385 instance Eq (S [a]) -- Structured type in head
3387 -- Repeated type variable in head
3388 instance C4 a a => C4 [a] [a]
3389 instance Stateful (ST s) (MutVar s)
3391 -- Head can consist of type variables only
3393 instance (Eq a, Show b) => C2 a b
3395 -- Non-type variables in context
3396 instance Show (s a) => Show (Sized s a)
3397 instance C2 Int a => C3 Bool [a]
3398 instance C2 Int a => C3 [a] b
3402 -- Context assertion no smaller than head
3403 instance C a => C a where ...
3404 -- (C b b) has more more occurrences of b than the head
3405 instance C b b => Foo [b] where ...
3410 The same restrictions apply to instances generated by
3411 <literal>deriving</literal> clauses. Thus the following is accepted:
3413 data MinHeap h a = H a (h a)
3416 because the derived instance
3418 instance (Show a, Show (h a)) => Show (MinHeap h a)
3420 conforms to the above rules.
3424 A useful idiom permitted by the above rules is as follows.
3425 If one allows overlapping instance declarations then it's quite
3426 convenient to have a "default instance" declaration that applies if
3427 something more specific does not:
3435 <sect3 id="undecidable-instances">
3436 <title>Undecidable instances</title>
3439 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3440 For example, sometimes you might want to use the following to get the
3441 effect of a "class synonym":
3443 class (C1 a, C2 a, C3 a) => C a where { }
3445 instance (C1 a, C2 a, C3 a) => C a where { }
3447 This allows you to write shorter signatures:
3453 f :: (C1 a, C2 a, C3 a) => ...
3455 The restrictions on functional dependencies (<xref
3456 linkend="functional-dependencies"/>) are particularly troublesome.
3457 It is tempting to introduce type variables in the context that do not appear in
3458 the head, something that is excluded by the normal rules. For example:
3460 class HasConverter a b | a -> b where
3463 data Foo a = MkFoo a
3465 instance (HasConverter a b,Show b) => Show (Foo a) where
3466 show (MkFoo value) = show (convert value)
3468 This is dangerous territory, however. Here, for example, is a program that would make the
3473 instance F [a] [[a]]
3474 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3476 Similarly, it can be tempting to lift the coverage condition:
3478 class Mul a b c | a b -> c where
3479 (.*.) :: a -> b -> c
3481 instance Mul Int Int Int where (.*.) = (*)
3482 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3483 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3485 The third instance declaration does not obey the coverage condition;
3486 and indeed the (somewhat strange) definition:
3488 f = \ b x y -> if b then x .*. [y] else y
3490 makes instance inference go into a loop, because it requires the constraint
3491 <literal>(Mul a [b] b)</literal>.
3494 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3495 the experimental flag <option>-XUndecidableInstances</option>
3496 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3497 both the Paterson Conditions and the Coverage Condition
3498 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3499 fixed-depth recursion stack. If you exceed the stack depth you get a
3500 sort of backtrace, and the opportunity to increase the stack depth
3501 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3507 <sect3 id="instance-overlap">
3508 <title>Overlapping instances</title>
3510 In general, <emphasis>GHC requires that that it be unambiguous which instance
3512 should be used to resolve a type-class constraint</emphasis>. This behaviour
3513 can be modified by two flags: <option>-XOverlappingInstances</option>
3514 <indexterm><primary>-XOverlappingInstances
3515 </primary></indexterm>
3516 and <option>-XIncoherentInstances</option>
3517 <indexterm><primary>-XIncoherentInstances
3518 </primary></indexterm>, as this section discusses. Both these
3519 flags are dynamic flags, and can be set on a per-module basis, using
3520 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3522 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3523 it tries to match every instance declaration against the
3525 by instantiating the head of the instance declaration. For example, consider
3528 instance context1 => C Int a where ... -- (A)
3529 instance context2 => C a Bool where ... -- (B)
3530 instance context3 => C Int [a] where ... -- (C)
3531 instance context4 => C Int [Int] where ... -- (D)
3533 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3534 but (C) and (D) do not. When matching, GHC takes
3535 no account of the context of the instance declaration
3536 (<literal>context1</literal> etc).
3537 GHC's default behaviour is that <emphasis>exactly one instance must match the
3538 constraint it is trying to resolve</emphasis>.
3539 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3540 including both declarations (A) and (B), say); an error is only reported if a
3541 particular constraint matches more than one.
3545 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3546 more than one instance to match, provided there is a most specific one. For
3547 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3548 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3549 most-specific match, the program is rejected.
3552 However, GHC is conservative about committing to an overlapping instance. For example:
3557 Suppose that from the RHS of <literal>f</literal> we get the constraint
3558 <literal>C Int [b]</literal>. But
3559 GHC does not commit to instance (C), because in a particular
3560 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3561 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3562 So GHC rejects the program.
3563 (If you add the flag <option>-XIncoherentInstances</option>,
3564 GHC will instead pick (C), without complaining about
3565 the problem of subsequent instantiations.)
3568 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3569 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3570 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3571 it instead. In this case, GHC will refrain from
3572 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3573 as before) but, rather than rejecting the program, it will infer the type
3575 f :: C Int b => [b] -> [b]
3577 That postpones the question of which instance to pick to the
3578 call site for <literal>f</literal>
3579 by which time more is known about the type <literal>b</literal>.
3582 The willingness to be overlapped or incoherent is a property of
3583 the <emphasis>instance declaration</emphasis> itself, controlled by the
3584 presence or otherwise of the <option>-XOverlappingInstances</option>
3585 and <option>-XIncoherentInstances</option> flags when that module is
3586 being defined. Neither flag is required in a module that imports and uses the
3587 instance declaration. Specifically, during the lookup process:
3590 An instance declaration is ignored during the lookup process if (a) a more specific
3591 match is found, and (b) the instance declaration was compiled with
3592 <option>-XOverlappingInstances</option>. The flag setting for the
3593 more-specific instance does not matter.
3596 Suppose an instance declaration does not match the constraint being looked up, but
3597 does unify with it, so that it might match when the constraint is further
3598 instantiated. Usually GHC will regard this as a reason for not committing to
3599 some other constraint. But if the instance declaration was compiled with
3600 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3601 check for that declaration.
3604 These rules make it possible for a library author to design a library that relies on
3605 overlapping instances without the library client having to know.
3608 If an instance declaration is compiled without
3609 <option>-XOverlappingInstances</option>,
3610 then that instance can never be overlapped. This could perhaps be
3611 inconvenient. Perhaps the rule should instead say that the
3612 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3613 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3614 at a usage site should be permitted regardless of how the instance declarations
3615 are compiled, if the <option>-XOverlappingInstances</option> flag is
3616 used at the usage site. (Mind you, the exact usage site can occasionally be
3617 hard to pin down.) We are interested to receive feedback on these points.
3619 <para>The <option>-XIncoherentInstances</option> flag implies the
3620 <option>-XOverlappingInstances</option> flag, but not vice versa.
3625 <title>Type synonyms in the instance head</title>
3628 <emphasis>Unlike Haskell 98, instance heads may use type
3629 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3630 As always, using a type synonym is just shorthand for
3631 writing the RHS of the type synonym definition. For example:
3635 type Point = (Int,Int)
3636 instance C Point where ...
3637 instance C [Point] where ...
3641 is legal. However, if you added
3645 instance C (Int,Int) where ...
3649 as well, then the compiler will complain about the overlapping
3650 (actually, identical) instance declarations. As always, type synonyms
3651 must be fully applied. You cannot, for example, write:
3656 instance Monad P where ...
3660 This design decision is independent of all the others, and easily
3661 reversed, but it makes sense to me.
3669 <sect2 id="overloaded-strings">
3670 <title>Overloaded string literals
3674 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3675 string literal has type <literal>String</literal>, but with overloaded string
3676 literals enabled (with <literal>-XOverloadedStrings</literal>)
3677 a string literal has type <literal>(IsString a) => a</literal>.
3680 This means that the usual string syntax can be used, e.g., for packed strings
3681 and other variations of string like types. String literals behave very much
3682 like integer literals, i.e., they can be used in both expressions and patterns.
3683 If used in a pattern the literal with be replaced by an equality test, in the same
3684 way as an integer literal is.
3687 The class <literal>IsString</literal> is defined as:
3689 class IsString a where
3690 fromString :: String -> a
3692 The only predefined instance is the obvious one to make strings work as usual:
3694 instance IsString [Char] where
3697 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3698 it explicitly (for example, to give an instance declaration for it), you can import it
3699 from module <literal>GHC.Exts</literal>.
3702 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3706 Each type in a default declaration must be an
3707 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3711 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3712 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3713 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3714 <emphasis>or</emphasis> <literal>IsString</literal>.
3723 import GHC.Exts( IsString(..) )
3725 newtype MyString = MyString String deriving (Eq, Show)
3726 instance IsString MyString where
3727 fromString = MyString
3729 greet :: MyString -> MyString
3730 greet "hello" = "world"
3734 print $ greet "hello"
3735 print $ greet "fool"
3739 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3740 to work since it gets translated into an equality comparison.
3746 <sect1 id="other-type-extensions">
3747 <title>Other type system extensions</title>
3749 <sect2 id="type-restrictions">
3750 <title>Type signatures</title>
3752 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3754 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3755 the form <emphasis>(class type-variable)</emphasis> or
3756 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3757 these type signatures are perfectly OK
3760 g :: Ord (T a ()) => ...
3764 GHC imposes the following restrictions on the constraints in a type signature.
3768 forall tv1..tvn (c1, ...,cn) => type
3771 (Here, we write the "foralls" explicitly, although the Haskell source
3772 language omits them; in Haskell 98, all the free type variables of an
3773 explicit source-language type signature are universally quantified,
3774 except for the class type variables in a class declaration. However,
3775 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3784 <emphasis>Each universally quantified type variable
3785 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3787 A type variable <literal>a</literal> is "reachable" if it appears
3788 in the same constraint as either a type variable free in
3789 <literal>type</literal>, or another reachable type variable.
3790 A value with a type that does not obey
3791 this reachability restriction cannot be used without introducing
3792 ambiguity; that is why the type is rejected.
3793 Here, for example, is an illegal type:
3797 forall a. Eq a => Int
3801 When a value with this type was used, the constraint <literal>Eq tv</literal>
3802 would be introduced where <literal>tv</literal> is a fresh type variable, and
3803 (in the dictionary-translation implementation) the value would be
3804 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3805 can never know which instance of <literal>Eq</literal> to use because we never
3806 get any more information about <literal>tv</literal>.
3810 that the reachability condition is weaker than saying that <literal>a</literal> is
3811 functionally dependent on a type variable free in
3812 <literal>type</literal> (see <xref
3813 linkend="functional-dependencies"/>). The reason for this is there
3814 might be a "hidden" dependency, in a superclass perhaps. So
3815 "reachable" is a conservative approximation to "functionally dependent".
3816 For example, consider:
3818 class C a b | a -> b where ...
3819 class C a b => D a b where ...
3820 f :: forall a b. D a b => a -> a
3822 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3823 but that is not immediately apparent from <literal>f</literal>'s type.
3829 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3830 universally quantified type variables <literal>tvi</literal></emphasis>.
3832 For example, this type is OK because <literal>C a b</literal> mentions the
3833 universally quantified type variable <literal>b</literal>:
3837 forall a. C a b => burble
3841 The next type is illegal because the constraint <literal>Eq b</literal> does not
3842 mention <literal>a</literal>:
3846 forall a. Eq b => burble
3850 The reason for this restriction is milder than the other one. The
3851 excluded types are never useful or necessary (because the offending
3852 context doesn't need to be witnessed at this point; it can be floated
3853 out). Furthermore, floating them out increases sharing. Lastly,
3854 excluding them is a conservative choice; it leaves a patch of
3855 territory free in case we need it later.
3869 <sect2 id="implicit-parameters">
3870 <title>Implicit parameters</title>
3872 <para> Implicit parameters are implemented as described in
3873 "Implicit parameters: dynamic scoping with static types",
3874 J Lewis, MB Shields, E Meijer, J Launchbury,
3875 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3879 <para>(Most of the following, still rather incomplete, documentation is
3880 due to Jeff Lewis.)</para>
3882 <para>Implicit parameter support is enabled with the option
3883 <option>-XImplicitParams</option>.</para>
3886 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3887 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3888 context. In Haskell, all variables are statically bound. Dynamic
3889 binding of variables is a notion that goes back to Lisp, but was later
3890 discarded in more modern incarnations, such as Scheme. Dynamic binding
3891 can be very confusing in an untyped language, and unfortunately, typed
3892 languages, in particular Hindley-Milner typed languages like Haskell,
3893 only support static scoping of variables.
3896 However, by a simple extension to the type class system of Haskell, we
3897 can support dynamic binding. Basically, we express the use of a
3898 dynamically bound variable as a constraint on the type. These
3899 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3900 function uses a dynamically-bound variable <literal>?x</literal>
3901 of type <literal>t'</literal>". For
3902 example, the following expresses the type of a sort function,
3903 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3905 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3907 The dynamic binding constraints are just a new form of predicate in the type class system.
3910 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3911 where <literal>x</literal> is
3912 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3913 Use of this construct also introduces a new
3914 dynamic-binding constraint in the type of the expression.
3915 For example, the following definition
3916 shows how we can define an implicitly parameterized sort function in
3917 terms of an explicitly parameterized <literal>sortBy</literal> function:
3919 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3921 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3927 <title>Implicit-parameter type constraints</title>
3929 Dynamic binding constraints behave just like other type class
3930 constraints in that they are automatically propagated. Thus, when a
3931 function is used, its implicit parameters are inherited by the
3932 function that called it. For example, our <literal>sort</literal> function might be used
3933 to pick out the least value in a list:
3935 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3936 least xs = head (sort xs)
3938 Without lifting a finger, the <literal>?cmp</literal> parameter is
3939 propagated to become a parameter of <literal>least</literal> as well. With explicit
3940 parameters, the default is that parameters must always be explicit
3941 propagated. With implicit parameters, the default is to always
3945 An implicit-parameter type constraint differs from other type class constraints in the
3946 following way: All uses of a particular implicit parameter must have
3947 the same type. This means that the type of <literal>(?x, ?x)</literal>
3948 is <literal>(?x::a) => (a,a)</literal>, and not
3949 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3953 <para> You can't have an implicit parameter in the context of a class or instance
3954 declaration. For example, both these declarations are illegal:
3956 class (?x::Int) => C a where ...
3957 instance (?x::a) => Foo [a] where ...
3959 Reason: exactly which implicit parameter you pick up depends on exactly where
3960 you invoke a function. But the ``invocation'' of instance declarations is done
3961 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3962 Easiest thing is to outlaw the offending types.</para>
3964 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3966 f :: (?x :: [a]) => Int -> Int
3969 g :: (Read a, Show a) => String -> String
3972 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3973 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3974 quite unambiguous, and fixes the type <literal>a</literal>.
3979 <title>Implicit-parameter bindings</title>
3982 An implicit parameter is <emphasis>bound</emphasis> using the standard
3983 <literal>let</literal> or <literal>where</literal> binding forms.
3984 For example, we define the <literal>min</literal> function by binding
3985 <literal>cmp</literal>.
3988 min = let ?cmp = (<=) in least
3992 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3993 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3994 (including in a list comprehension, or do-notation, or pattern guards),
3995 or a <literal>where</literal> clause.
3996 Note the following points:
3999 An implicit-parameter binding group must be a
4000 collection of simple bindings to implicit-style variables (no
4001 function-style bindings, and no type signatures); these bindings are
4002 neither polymorphic or recursive.
4005 You may not mix implicit-parameter bindings with ordinary bindings in a
4006 single <literal>let</literal>
4007 expression; use two nested <literal>let</literal>s instead.
4008 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4012 You may put multiple implicit-parameter bindings in a
4013 single binding group; but they are <emphasis>not</emphasis> treated
4014 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4015 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4016 parameter. The bindings are not nested, and may be re-ordered without changing
4017 the meaning of the program.
4018 For example, consider:
4020 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4022 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4023 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4025 f :: (?x::Int) => Int -> Int
4033 <sect3><title>Implicit parameters and polymorphic recursion</title>
4036 Consider these two definitions:
4039 len1 xs = let ?acc = 0 in len_acc1 xs
4042 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4047 len2 xs = let ?acc = 0 in len_acc2 xs
4049 len_acc2 :: (?acc :: Int) => [a] -> Int
4051 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4053 The only difference between the two groups is that in the second group
4054 <literal>len_acc</literal> is given a type signature.
4055 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4056 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4057 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4058 has a type signature, the recursive call is made to the
4059 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4060 as an implicit parameter. So we get the following results in GHCi:
4067 Adding a type signature dramatically changes the result! This is a rather
4068 counter-intuitive phenomenon, worth watching out for.
4072 <sect3><title>Implicit parameters and monomorphism</title>
4074 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4075 Haskell Report) to implicit parameters. For example, consider:
4083 Since the binding for <literal>y</literal> falls under the Monomorphism
4084 Restriction it is not generalised, so the type of <literal>y</literal> is
4085 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4086 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4087 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4088 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4089 <literal>y</literal> in the body of the <literal>let</literal> will see the
4090 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4091 <literal>14</literal>.
4096 <!-- ======================= COMMENTED OUT ========================
4098 We intend to remove linear implicit parameters, so I'm at least removing
4099 them from the 6.6 user manual
4101 <sect2 id="linear-implicit-parameters">
4102 <title>Linear implicit parameters</title>
4104 Linear implicit parameters are an idea developed by Koen Claessen,
4105 Mark Shields, and Simon PJ. They address the long-standing
4106 problem that monads seem over-kill for certain sorts of problem, notably:
4109 <listitem> <para> distributing a supply of unique names </para> </listitem>
4110 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4111 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4115 Linear implicit parameters are just like ordinary implicit parameters,
4116 except that they are "linear"; that is, they cannot be copied, and
4117 must be explicitly "split" instead. Linear implicit parameters are
4118 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4119 (The '/' in the '%' suggests the split!)
4124 import GHC.Exts( Splittable )
4126 data NameSupply = ...
4128 splitNS :: NameSupply -> (NameSupply, NameSupply)
4129 newName :: NameSupply -> Name
4131 instance Splittable NameSupply where
4135 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4136 f env (Lam x e) = Lam x' (f env e)
4139 env' = extend env x x'
4140 ...more equations for f...
4142 Notice that the implicit parameter %ns is consumed
4144 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4145 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4149 So the translation done by the type checker makes
4150 the parameter explicit:
4152 f :: NameSupply -> Env -> Expr -> Expr
4153 f ns env (Lam x e) = Lam x' (f ns1 env e)
4155 (ns1,ns2) = splitNS ns
4157 env = extend env x x'
4159 Notice the call to 'split' introduced by the type checker.
4160 How did it know to use 'splitNS'? Because what it really did
4161 was to introduce a call to the overloaded function 'split',
4162 defined by the class <literal>Splittable</literal>:
4164 class Splittable a where
4167 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4168 split for name supplies. But we can simply write
4174 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4176 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4177 <literal>GHC.Exts</literal>.
4182 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4183 are entirely distinct implicit parameters: you
4184 can use them together and they won't interfere with each other. </para>
4187 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4189 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4190 in the context of a class or instance declaration. </para></listitem>
4194 <sect3><title>Warnings</title>
4197 The monomorphism restriction is even more important than usual.
4198 Consider the example above:
4200 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4201 f env (Lam x e) = Lam x' (f env e)
4204 env' = extend env x x'
4206 If we replaced the two occurrences of x' by (newName %ns), which is
4207 usually a harmless thing to do, we get:
4209 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4210 f env (Lam x e) = Lam (newName %ns) (f env e)
4212 env' = extend env x (newName %ns)
4214 But now the name supply is consumed in <emphasis>three</emphasis> places
4215 (the two calls to newName,and the recursive call to f), so
4216 the result is utterly different. Urk! We don't even have
4220 Well, this is an experimental change. With implicit
4221 parameters we have already lost beta reduction anyway, and
4222 (as John Launchbury puts it) we can't sensibly reason about
4223 Haskell programs without knowing their typing.
4228 <sect3><title>Recursive functions</title>
4229 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4232 foo :: %x::T => Int -> [Int]
4234 foo n = %x : foo (n-1)
4236 where T is some type in class Splittable.</para>
4238 Do you get a list of all the same T's or all different T's
4239 (assuming that split gives two distinct T's back)?
4241 If you supply the type signature, taking advantage of polymorphic
4242 recursion, you get what you'd probably expect. Here's the
4243 translated term, where the implicit param is made explicit:
4246 foo x n = let (x1,x2) = split x
4247 in x1 : foo x2 (n-1)
4249 But if you don't supply a type signature, GHC uses the Hindley
4250 Milner trick of using a single monomorphic instance of the function
4251 for the recursive calls. That is what makes Hindley Milner type inference
4252 work. So the translation becomes
4256 foom n = x : foom (n-1)
4260 Result: 'x' is not split, and you get a list of identical T's. So the
4261 semantics of the program depends on whether or not foo has a type signature.
4264 You may say that this is a good reason to dislike linear implicit parameters
4265 and you'd be right. That is why they are an experimental feature.
4271 ================ END OF Linear Implicit Parameters commented out -->
4273 <sect2 id="kinding">
4274 <title>Explicitly-kinded quantification</title>
4277 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4278 to give the kind explicitly as (machine-checked) documentation,
4279 just as it is nice to give a type signature for a function. On some occasions,
4280 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4281 John Hughes had to define the data type:
4283 data Set cxt a = Set [a]
4284 | Unused (cxt a -> ())
4286 The only use for the <literal>Unused</literal> constructor was to force the correct
4287 kind for the type variable <literal>cxt</literal>.
4290 GHC now instead allows you to specify the kind of a type variable directly, wherever
4291 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4294 This flag enables kind signatures in the following places:
4296 <listitem><para><literal>data</literal> declarations:
4298 data Set (cxt :: * -> *) a = Set [a]
4299 </screen></para></listitem>
4300 <listitem><para><literal>type</literal> declarations:
4302 type T (f :: * -> *) = f Int
4303 </screen></para></listitem>
4304 <listitem><para><literal>class</literal> declarations:
4306 class (Eq a) => C (f :: * -> *) a where ...
4307 </screen></para></listitem>
4308 <listitem><para><literal>forall</literal>'s in type signatures:
4310 f :: forall (cxt :: * -> *). Set cxt Int
4311 </screen></para></listitem>
4316 The parentheses are required. Some of the spaces are required too, to
4317 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4318 will get a parse error, because "<literal>::*->*</literal>" is a
4319 single lexeme in Haskell.
4323 As part of the same extension, you can put kind annotations in types
4326 f :: (Int :: *) -> Int
4327 g :: forall a. a -> (a :: *)
4331 atype ::= '(' ctype '::' kind ')
4333 The parentheses are required.
4338 <sect2 id="universal-quantification">
4339 <title>Arbitrary-rank polymorphism
4343 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4344 allows us to say exactly what this means. For example:
4352 g :: forall b. (b -> b)
4354 The two are treated identically.
4358 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4359 explicit universal quantification in
4361 For example, all the following types are legal:
4363 f1 :: forall a b. a -> b -> a
4364 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4366 f2 :: (forall a. a->a) -> Int -> Int
4367 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4369 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4371 f4 :: Int -> (forall a. a -> a)
4373 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4374 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4375 The <literal>forall</literal> makes explicit the universal quantification that
4376 is implicitly added by Haskell.
4379 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4380 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4381 shows, the polymorphic type on the left of the function arrow can be overloaded.
4384 The function <literal>f3</literal> has a rank-3 type;
4385 it has rank-2 types on the left of a function arrow.
4388 GHC has three flags to control higher-rank types:
4391 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4394 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4397 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4398 That is, you can nest <literal>forall</literal>s
4399 arbitrarily deep in function arrows.
4400 In particular, a forall-type (also called a "type scheme"),
4401 including an operational type class context, is legal:
4403 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4404 of a function arrow </para> </listitem>
4405 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4406 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4407 field type signatures.</para> </listitem>
4408 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4409 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4413 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4414 a type variable any more!
4423 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4424 the types of the constructor arguments. Here are several examples:
4430 data T a = T1 (forall b. b -> b -> b) a
4432 data MonadT m = MkMonad { return :: forall a. a -> m a,
4433 bind :: forall a b. m a -> (a -> m b) -> m b
4436 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4442 The constructors have rank-2 types:
4448 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4449 MkMonad :: forall m. (forall a. a -> m a)
4450 -> (forall a b. m a -> (a -> m b) -> m b)
4452 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4458 Notice that you don't need to use a <literal>forall</literal> if there's an
4459 explicit context. For example in the first argument of the
4460 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4461 prefixed to the argument type. The implicit <literal>forall</literal>
4462 quantifies all type variables that are not already in scope, and are
4463 mentioned in the type quantified over.
4467 As for type signatures, implicit quantification happens for non-overloaded
4468 types too. So if you write this:
4471 data T a = MkT (Either a b) (b -> b)
4474 it's just as if you had written this:
4477 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4480 That is, since the type variable <literal>b</literal> isn't in scope, it's
4481 implicitly universally quantified. (Arguably, it would be better
4482 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4483 where that is what is wanted. Feedback welcomed.)
4487 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4488 the constructor to suitable values, just as usual. For example,
4499 a3 = MkSwizzle reverse
4502 a4 = let r x = Just x
4509 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4510 mkTs f x y = [T1 f x, T1 f y]
4516 The type of the argument can, as usual, be more general than the type
4517 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4518 does not need the <literal>Ord</literal> constraint.)
4522 When you use pattern matching, the bound variables may now have
4523 polymorphic types. For example:
4529 f :: T a -> a -> (a, Char)
4530 f (T1 w k) x = (w k x, w 'c' 'd')
4532 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4533 g (MkSwizzle s) xs f = s (map f (s xs))
4535 h :: MonadT m -> [m a] -> m [a]
4536 h m [] = return m []
4537 h m (x:xs) = bind m x $ \y ->
4538 bind m (h m xs) $ \ys ->
4545 In the function <function>h</function> we use the record selectors <literal>return</literal>
4546 and <literal>bind</literal> to extract the polymorphic bind and return functions
4547 from the <literal>MonadT</literal> data structure, rather than using pattern
4553 <title>Type inference</title>
4556 In general, type inference for arbitrary-rank types is undecidable.
4557 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4558 to get a decidable algorithm by requiring some help from the programmer.
4559 We do not yet have a formal specification of "some help" but the rule is this:
4562 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4563 provides an explicit polymorphic type for x, or GHC's type inference will assume
4564 that x's type has no foralls in it</emphasis>.
4567 What does it mean to "provide" an explicit type for x? You can do that by
4568 giving a type signature for x directly, using a pattern type signature
4569 (<xref linkend="scoped-type-variables"/>), thus:
4571 \ f :: (forall a. a->a) -> (f True, f 'c')
4573 Alternatively, you can give a type signature to the enclosing
4574 context, which GHC can "push down" to find the type for the variable:
4576 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4578 Here the type signature on the expression can be pushed inwards
4579 to give a type signature for f. Similarly, and more commonly,
4580 one can give a type signature for the function itself:
4582 h :: (forall a. a->a) -> (Bool,Char)
4583 h f = (f True, f 'c')
4585 You don't need to give a type signature if the lambda bound variable
4586 is a constructor argument. Here is an example we saw earlier:
4588 f :: T a -> a -> (a, Char)
4589 f (T1 w k) x = (w k x, w 'c' 'd')
4591 Here we do not need to give a type signature to <literal>w</literal>, because
4592 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4599 <sect3 id="implicit-quant">
4600 <title>Implicit quantification</title>
4603 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4604 user-written types, if and only if there is no explicit <literal>forall</literal>,
4605 GHC finds all the type variables mentioned in the type that are not already
4606 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4610 f :: forall a. a -> a
4617 h :: forall b. a -> b -> b
4623 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4626 f :: (a -> a) -> Int
4628 f :: forall a. (a -> a) -> Int
4630 f :: (forall a. a -> a) -> Int
4633 g :: (Ord a => a -> a) -> Int
4634 -- MEANS the illegal type
4635 g :: forall a. (Ord a => a -> a) -> Int
4637 g :: (forall a. Ord a => a -> a) -> Int
4639 The latter produces an illegal type, which you might think is silly,
4640 but at least the rule is simple. If you want the latter type, you
4641 can write your for-alls explicitly. Indeed, doing so is strongly advised
4648 <sect2 id="impredicative-polymorphism">
4649 <title>Impredicative polymorphism
4651 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4652 enabled with <option>-XImpredicativeTypes</option>.
4654 that you can call a polymorphic function at a polymorphic type, and
4655 parameterise data structures over polymorphic types. For example:
4657 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4658 f (Just g) = Just (g [3], g "hello")
4661 Notice here that the <literal>Maybe</literal> type is parameterised by the
4662 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4665 <para>The technical details of this extension are described in the paper
4666 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4667 type inference for higher-rank types and impredicativity</ulink>,
4668 which appeared at ICFP 2006.
4672 <sect2 id="scoped-type-variables">
4673 <title>Lexically scoped type variables
4677 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4678 which some type signatures are simply impossible to write. For example:
4680 f :: forall a. [a] -> [a]
4686 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4687 the entire definition of <literal>f</literal>.
4688 In particular, it is in scope at the type signature for <varname>ys</varname>.
4689 In Haskell 98 it is not possible to declare
4690 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4691 it becomes possible to do so.
4693 <para>Lexically-scoped type variables are enabled by
4694 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4696 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4697 variables work, compared to earlier releases. Read this section
4701 <title>Overview</title>
4703 <para>The design follows the following principles
4705 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4706 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4707 design.)</para></listitem>
4708 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4709 type variables. This means that every programmer-written type signature
4710 (including one that contains free scoped type variables) denotes a
4711 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4712 checker, and no inference is involved.</para></listitem>
4713 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4714 changing the program.</para></listitem>
4718 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4720 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4721 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4722 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4723 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4727 In Haskell, a programmer-written type signature is implicitly quantified over
4728 its free type variables (<ulink
4729 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4731 of the Haskell Report).
4732 Lexically scoped type variables affect this implicit quantification rules
4733 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4734 quantified. For example, if type variable <literal>a</literal> is in scope,
4737 (e :: a -> a) means (e :: a -> a)
4738 (e :: b -> b) means (e :: forall b. b->b)
4739 (e :: a -> b) means (e :: forall b. a->b)
4747 <sect3 id="decl-type-sigs">
4748 <title>Declaration type signatures</title>
4749 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4750 quantification (using <literal>forall</literal>) brings into scope the
4751 explicitly-quantified
4752 type variables, in the definition of the named function. For example:
4754 f :: forall a. [a] -> [a]
4755 f (x:xs) = xs ++ [ x :: a ]
4757 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4758 the definition of "<literal>f</literal>".
4760 <para>This only happens if:
4762 <listitem><para> The quantification in <literal>f</literal>'s type
4763 signature is explicit. For example:
4766 g (x:xs) = xs ++ [ x :: a ]
4768 This program will be rejected, because "<literal>a</literal>" does not scope
4769 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4770 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4771 quantification rules.
4773 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4774 not a pattern binding.
4777 f1 :: forall a. [a] -> [a]
4778 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4780 f2 :: forall a. [a] -> [a]
4781 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4783 f3 :: forall a. [a] -> [a]
4784 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4786 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4787 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4788 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4789 the type signature brings <literal>a</literal> into scope.
4795 <sect3 id="exp-type-sigs">
4796 <title>Expression type signatures</title>
4798 <para>An expression type signature that has <emphasis>explicit</emphasis>
4799 quantification (using <literal>forall</literal>) brings into scope the
4800 explicitly-quantified
4801 type variables, in the annotated expression. For example:
4803 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4805 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4806 type variable <literal>s</literal> into scope, in the annotated expression
4807 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4812 <sect3 id="pattern-type-sigs">
4813 <title>Pattern type signatures</title>
4815 A type signature may occur in any pattern; this is a <emphasis>pattern type
4816 signature</emphasis>.
4819 -- f and g assume that 'a' is already in scope
4820 f = \(x::Int, y::a) -> x
4822 h ((x,y) :: (Int,Bool)) = (y,x)
4824 In the case where all the type variables in the pattern type signature are
4825 already in scope (i.e. bound by the enclosing context), matters are simple: the
4826 signature simply constrains the type of the pattern in the obvious way.
4829 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4830 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4831 that are already in scope. For example:
4833 f :: forall a. [a] -> (Int, [a])
4836 (ys::[a], n) = (reverse xs, length xs) -- OK
4837 zs::[a] = xs ++ ys -- OK
4839 Just (v::b) = ... -- Not OK; b is not in scope
4841 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4842 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4846 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4847 type signature may mention a type variable that is not in scope; in this case,
4848 <emphasis>the signature brings that type variable into scope</emphasis>.
4849 This is particularly important for existential data constructors. For example:
4851 data T = forall a. MkT [a]
4854 k (MkT [t::a]) = MkT t3
4858 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4859 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4860 because it is bound by the pattern match. GHC's rule is that in this situation
4861 (and only then), a pattern type signature can mention a type variable that is
4862 not already in scope; the effect is to bring it into scope, standing for the
4863 existentially-bound type variable.
4866 When a pattern type signature binds a type variable in this way, GHC insists that the
4867 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4868 This means that any user-written type signature always stands for a completely known type.
4871 If all this seems a little odd, we think so too. But we must have
4872 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4873 could not name existentially-bound type variables in subsequent type signatures.
4876 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4877 signature is allowed to mention a lexical variable that is not already in
4879 For example, both <literal>f</literal> and <literal>g</literal> would be
4880 illegal if <literal>a</literal> was not already in scope.
4886 <!-- ==================== Commented out part about result type signatures
4888 <sect3 id="result-type-sigs">
4889 <title>Result type signatures</title>
4892 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4895 {- f assumes that 'a' is already in scope -}
4896 f x y :: [a] = [x,y,x]
4898 g = \ x :: [Int] -> [3,4]
4900 h :: forall a. [a] -> a
4904 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4905 the result of the function. Similarly, the body of the lambda in the RHS of
4906 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4907 alternative in <literal>h</literal> is <literal>a</literal>.
4909 <para> A result type signature never brings new type variables into scope.</para>
4911 There are a couple of syntactic wrinkles. First, notice that all three
4912 examples would parse quite differently with parentheses:
4914 {- f assumes that 'a' is already in scope -}
4915 f x (y :: [a]) = [x,y,x]
4917 g = \ (x :: [Int]) -> [3,4]
4919 h :: forall a. [a] -> a
4923 Now the signature is on the <emphasis>pattern</emphasis>; and
4924 <literal>h</literal> would certainly be ill-typed (since the pattern
4925 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4927 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4928 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4929 token or a parenthesised type of some sort). To see why,
4930 consider how one would parse this:
4939 <sect3 id="cls-inst-scoped-tyvars">
4940 <title>Class and instance declarations</title>
4943 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4944 scope over the methods defined in the <literal>where</literal> part. For example:
4962 <sect2 id="typing-binds">
4963 <title>Generalised typing of mutually recursive bindings</title>
4966 The Haskell Report specifies that a group of bindings (at top level, or in a
4967 <literal>let</literal> or <literal>where</literal>) should be sorted into
4968 strongly-connected components, and then type-checked in dependency order
4969 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4970 Report, Section 4.5.1</ulink>).
4971 As each group is type-checked, any binders of the group that
4973 an explicit type signature are put in the type environment with the specified
4975 and all others are monomorphic until the group is generalised
4976 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4979 <para>Following a suggestion of Mark Jones, in his paper
4980 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4982 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4984 <emphasis>the dependency analysis ignores references to variables that have an explicit
4985 type signature</emphasis>.
4986 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4987 typecheck. For example, consider:
4989 f :: Eq a => a -> Bool
4990 f x = (x == x) || g True || g "Yes"
4992 g y = (y <= y) || f True
4994 This is rejected by Haskell 98, but under Jones's scheme the definition for
4995 <literal>g</literal> is typechecked first, separately from that for
4996 <literal>f</literal>,
4997 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4998 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4999 type is generalised, to get
5001 g :: Ord a => a -> Bool
5003 Now, the definition for <literal>f</literal> is typechecked, with this type for
5004 <literal>g</literal> in the type environment.
5008 The same refined dependency analysis also allows the type signatures of
5009 mutually-recursive functions to have different contexts, something that is illegal in
5010 Haskell 98 (Section 4.5.2, last sentence). With
5011 <option>-XRelaxedPolyRec</option>
5012 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5013 type signatures; in practice this means that only variables bound by the same
5014 pattern binding must have the same context. For example, this is fine:
5016 f :: Eq a => a -> Bool
5017 f x = (x == x) || g True
5019 g :: Ord a => a -> Bool
5020 g y = (y <= y) || f True
5025 <sect2 id="type-families">
5026 <title>Type families
5030 GHC supports the definition of type families indexed by types. They may be
5031 seen as an extension of Haskell 98's class-based overloading of values to
5032 types. When type families are declared in classes, they are also known as
5036 There are two forms of type families: data families and type synonym families.
5037 Currently, only the former are fully implemented, while we are still working
5038 on the latter. As a result, the specification of the language extension is
5039 also still to some degree in flux. Hence, a more detailed description of
5040 the language extension and its use is currently available
5041 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
5042 wiki page on type families</ulink>. The material will be moved to this user's
5043 guide when it has stabilised.
5046 Type families are enabled by the flag <option>-XTypeFamilies</option>.
5053 <!-- ==================== End of type system extensions ================= -->
5055 <!-- ====================== TEMPLATE HASKELL ======================= -->
5057 <sect1 id="template-haskell">
5058 <title>Template Haskell</title>
5060 <para>Template Haskell allows you to do compile-time meta-programming in
5063 the main technical innovations is discussed in "<ulink
5064 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5065 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5068 There is a Wiki page about
5069 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5070 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5074 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5075 Haskell library reference material</ulink>
5076 (look for module <literal>Language.Haskell.TH</literal>).
5077 Many changes to the original design are described in
5078 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5079 Notes on Template Haskell version 2</ulink>.
5080 Not all of these changes are in GHC, however.
5083 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5084 as a worked example to help get you started.
5088 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5089 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5094 <title>Syntax</title>
5096 <para> Template Haskell has the following new syntactic
5097 constructions. You need to use the flag
5098 <option>-XTemplateHaskell</option>
5099 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5100 </indexterm>to switch these syntactic extensions on
5101 (<option>-XTemplateHaskell</option> is no longer implied by
5102 <option>-fglasgow-exts</option>).</para>
5106 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5107 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5108 There must be no space between the "$" and the identifier or parenthesis. This use
5109 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5110 of "." as an infix operator. If you want the infix operator, put spaces around it.
5112 <para> A splice can occur in place of
5114 <listitem><para> an expression; the spliced expression must
5115 have type <literal>Q Exp</literal></para></listitem>
5116 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5119 Inside a splice you can can only call functions defined in imported modules,
5120 not functions defined elsewhere in the same module.</listitem>
5124 A expression quotation is written in Oxford brackets, thus:
5126 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5127 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5128 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5129 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5130 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5131 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5132 </itemizedlist></para></listitem>
5135 A quasi-quotation can appear in either a pattern context or an
5136 expression context and is also written in Oxford brackets:
5138 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5139 where the "..." is an arbitrary string; a full description of the
5140 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5141 </itemizedlist></para></listitem>
5144 A name can be quoted with either one or two prefix single quotes:
5146 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5147 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5148 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5150 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5151 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5154 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5155 may also be given as an argument to the <literal>reify</literal> function.
5161 (Compared to the original paper, there are many differences of detail.
5162 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5163 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5164 Type splices are not implemented, and neither are pattern splices or quotations.
5168 <sect2> <title> Using Template Haskell </title>
5172 The data types and monadic constructor functions for Template Haskell are in the library
5173 <literal>Language.Haskell.THSyntax</literal>.
5177 You can only run a function at compile time if it is imported from another module. That is,
5178 you can't define a function in a module, and call it from within a splice in the same module.
5179 (It would make sense to do so, but it's hard to implement.)
5183 You can only run a function at compile time if it is imported
5184 from another module <emphasis>that is not part of a mutually-recursive group of modules
5185 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5186 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5187 splice is to be run.</para>
5189 For example, when compiling module A,
5190 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5191 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5195 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5198 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5199 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5200 compiles and runs a program, and then looks at the result. So it's important that
5201 the program it compiles produces results whose representations are identical to
5202 those of the compiler itself.
5206 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5207 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5212 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5213 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5214 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5221 -- Import our template "pr"
5222 import Printf ( pr )
5224 -- The splice operator $ takes the Haskell source code
5225 -- generated at compile time by "pr" and splices it into
5226 -- the argument of "putStrLn".
5227 main = putStrLn ( $(pr "Hello") )
5233 -- Skeletal printf from the paper.
5234 -- It needs to be in a separate module to the one where
5235 -- you intend to use it.
5237 -- Import some Template Haskell syntax
5238 import Language.Haskell.TH
5240 -- Describe a format string
5241 data Format = D | S | L String
5243 -- Parse a format string. This is left largely to you
5244 -- as we are here interested in building our first ever
5245 -- Template Haskell program and not in building printf.
5246 parse :: String -> [Format]
5249 -- Generate Haskell source code from a parsed representation
5250 -- of the format string. This code will be spliced into
5251 -- the module which calls "pr", at compile time.
5252 gen :: [Format] -> Q Exp
5253 gen [D] = [| \n -> show n |]
5254 gen [S] = [| \s -> s |]
5255 gen [L s] = stringE s
5257 -- Here we generate the Haskell code for the splice
5258 -- from an input format string.
5259 pr :: String -> Q Exp
5260 pr s = gen (parse s)
5263 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5266 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5269 <para>Run "main.exe" and here is your output:</para>
5279 <title>Using Template Haskell with Profiling</title>
5280 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5282 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5283 interpreter to run the splice expressions. The bytecode interpreter
5284 runs the compiled expression on top of the same runtime on which GHC
5285 itself is running; this means that the compiled code referred to by
5286 the interpreted expression must be compatible with this runtime, and
5287 in particular this means that object code that is compiled for
5288 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5289 expression, because profiled object code is only compatible with the
5290 profiling version of the runtime.</para>
5292 <para>This causes difficulties if you have a multi-module program
5293 containing Template Haskell code and you need to compile it for
5294 profiling, because GHC cannot load the profiled object code and use it
5295 when executing the splices. Fortunately GHC provides a workaround.
5296 The basic idea is to compile the program twice:</para>
5300 <para>Compile the program or library first the normal way, without
5301 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5304 <para>Then compile it again with <option>-prof</option>, and
5305 additionally use <option>-osuf
5306 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5307 to name the object files differently (you can choose any suffix
5308 that isn't the normal object suffix here). GHC will automatically
5309 load the object files built in the first step when executing splice
5310 expressions. If you omit the <option>-osuf</option> flag when
5311 building with <option>-prof</option> and Template Haskell is used,
5312 GHC will emit an error message. </para>
5317 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5318 <para>Quasi-quotation allows patterns and expressions to be written using
5319 programmer-defined concrete syntax; the motivation behind the extension and
5320 several examples are documented in
5321 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5322 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5323 2007). The example below shows how to write a quasiquoter for a simple
5324 expression language.</para>
5327 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5328 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5329 functions for quoting expressions and patterns, respectively. The first argument
5330 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5331 context of the quasi-quotation statement determines which of the two parsers is
5332 called: if the quasi-quotation occurs in an expression context, the expression
5333 parser is called, and if it occurs in a pattern context, the pattern parser is
5337 Note that in the example we make use of an antiquoted
5338 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5339 (this syntax for anti-quotation was defined by the parser's
5340 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5341 integer value argument of the constructor <literal>IntExpr</literal> when
5342 pattern matching. Please see the referenced paper for further details regarding
5343 anti-quotation as well as the description of a technique that uses SYB to
5344 leverage a single parser of type <literal>String -> a</literal> to generate both
5345 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5346 pattern parser that returns a value of type <literal>Q Pat</literal>.
5349 <para>In general, a quasi-quote has the form
5350 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5351 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5352 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5353 can be arbitrary, and may contain newlines.
5356 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5357 the example, <literal>expr</literal> cannot be defined
5358 in <literal>Main.hs</literal> where it is used, but must be imported.
5369 main = do { print $ eval [$expr|1 + 2|]
5371 { [$expr|'int:n|] -> print n
5380 import qualified Language.Haskell.TH as TH
5381 import Language.Haskell.TH.Quasi
5383 data Expr = IntExpr Integer
5384 | AntiIntExpr String
5385 | BinopExpr BinOp Expr Expr
5387 deriving(Show, Typeable, Data)
5393 deriving(Show, Typeable, Data)
5395 eval :: Expr -> Integer
5396 eval (IntExpr n) = n
5397 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5404 expr = QuasiQuoter parseExprExp parseExprPat
5406 -- Parse an Expr, returning its representation as
5407 -- either a Q Exp or a Q Pat. See the referenced paper
5408 -- for how to use SYB to do this by writing a single
5409 -- parser of type String -> Expr instead of two
5410 -- separate parsers.
5412 parseExprExp :: String -> Q Exp
5415 parseExprPat :: String -> Q Pat
5419 <para>Now run the compiler:
5422 $ ghc --make -XQuasiQuotes Main.hs -o main
5425 <para>Run "main" and here is your output:</para>
5437 <!-- ===================== Arrow notation =================== -->
5439 <sect1 id="arrow-notation">
5440 <title>Arrow notation
5443 <para>Arrows are a generalization of monads introduced by John Hughes.
5444 For more details, see
5449 “Generalising Monads to Arrows”,
5450 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5451 pp67–111, May 2000.
5457 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5458 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5464 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5465 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5471 and the arrows web page at
5472 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5473 With the <option>-XArrows</option> flag, GHC supports the arrow
5474 notation described in the second of these papers.
5475 What follows is a brief introduction to the notation;
5476 it won't make much sense unless you've read Hughes's paper.
5477 This notation is translated to ordinary Haskell,
5478 using combinators from the
5479 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5483 <para>The extension adds a new kind of expression for defining arrows:
5485 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5486 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5488 where <literal>proc</literal> is a new keyword.
5489 The variables of the pattern are bound in the body of the
5490 <literal>proc</literal>-expression,
5491 which is a new sort of thing called a <firstterm>command</firstterm>.
5492 The syntax of commands is as follows:
5494 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5495 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5496 | <replaceable>cmd</replaceable><superscript>0</superscript>
5498 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5499 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5500 infix operators as for expressions, and
5502 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5503 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5504 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5505 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5506 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5507 | <replaceable>fcmd</replaceable>
5509 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5510 | ( <replaceable>cmd</replaceable> )
5511 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5513 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5514 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5515 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5516 | <replaceable>cmd</replaceable>
5518 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5519 except that the bodies are commands instead of expressions.
5523 Commands produce values, but (like monadic computations)
5524 may yield more than one value,
5525 or none, and may do other things as well.
5526 For the most part, familiarity with monadic notation is a good guide to
5528 However the values of expressions, even monadic ones,
5529 are determined by the values of the variables they contain;
5530 this is not necessarily the case for commands.
5534 A simple example of the new notation is the expression
5536 proc x -> f -< x+1
5538 We call this a <firstterm>procedure</firstterm> or
5539 <firstterm>arrow abstraction</firstterm>.
5540 As with a lambda expression, the variable <literal>x</literal>
5541 is a new variable bound within the <literal>proc</literal>-expression.
5542 It refers to the input to the arrow.
5543 In the above example, <literal>-<</literal> is not an identifier but an
5544 new reserved symbol used for building commands from an expression of arrow
5545 type and an expression to be fed as input to that arrow.
5546 (The weird look will make more sense later.)
5547 It may be read as analogue of application for arrows.
5548 The above example is equivalent to the Haskell expression
5550 arr (\ x -> x+1) >>> f
5552 That would make no sense if the expression to the left of
5553 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5554 More generally, the expression to the left of <literal>-<</literal>
5555 may not involve any <firstterm>local variable</firstterm>,
5556 i.e. a variable bound in the current arrow abstraction.
5557 For such a situation there is a variant <literal>-<<</literal>, as in
5559 proc x -> f x -<< x+1
5561 which is equivalent to
5563 arr (\ x -> (f x, x+1)) >>> app
5565 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5567 Such an arrow is equivalent to a monad, so if you're using this form
5568 you may find a monadic formulation more convenient.
5572 <title>do-notation for commands</title>
5575 Another form of command is a form of <literal>do</literal>-notation.
5576 For example, you can write
5585 You can read this much like ordinary <literal>do</literal>-notation,
5586 but with commands in place of monadic expressions.
5587 The first line sends the value of <literal>x+1</literal> as an input to
5588 the arrow <literal>f</literal>, and matches its output against
5589 <literal>y</literal>.
5590 In the next line, the output is discarded.
5591 The arrow <function>returnA</function> is defined in the
5592 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5593 module as <literal>arr id</literal>.
5594 The above example is treated as an abbreviation for
5596 arr (\ x -> (x, x)) >>>
5597 first (arr (\ x -> x+1) >>> f) >>>
5598 arr (\ (y, x) -> (y, (x, y))) >>>
5599 first (arr (\ y -> 2*y) >>> g) >>>
5601 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5602 first (arr (\ (x, z) -> x*z) >>> h) >>>
5603 arr (\ (t, z) -> t+z) >>>
5606 Note that variables not used later in the composition are projected out.
5607 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5609 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5610 module, this reduces to
5612 arr (\ x -> (x+1, x)) >>>
5614 arr (\ (y, x) -> (2*y, (x, y))) >>>
5616 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5618 arr (\ (t, z) -> t+z)
5620 which is what you might have written by hand.
5621 With arrow notation, GHC keeps track of all those tuples of variables for you.
5625 Note that although the above translation suggests that
5626 <literal>let</literal>-bound variables like <literal>z</literal> must be
5627 monomorphic, the actual translation produces Core,
5628 so polymorphic variables are allowed.
5632 It's also possible to have mutually recursive bindings,
5633 using the new <literal>rec</literal> keyword, as in the following example:
5635 counter :: ArrowCircuit a => a Bool Int
5636 counter = proc reset -> do
5637 rec output <- returnA -< if reset then 0 else next
5638 next <- delay 0 -< output+1
5639 returnA -< output
5641 The translation of such forms uses the <function>loop</function> combinator,
5642 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5648 <title>Conditional commands</title>
5651 In the previous example, we used a conditional expression to construct the
5653 Sometimes we want to conditionally execute different commands, as in
5660 which is translated to
5662 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5663 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5665 Since the translation uses <function>|||</function>,
5666 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5670 There are also <literal>case</literal> commands, like
5676 y <- h -< (x1, x2)
5680 The syntax is the same as for <literal>case</literal> expressions,
5681 except that the bodies of the alternatives are commands rather than expressions.
5682 The translation is similar to that of <literal>if</literal> commands.
5688 <title>Defining your own control structures</title>
5691 As we're seen, arrow notation provides constructs,
5692 modelled on those for expressions,
5693 for sequencing, value recursion and conditionals.
5694 But suitable combinators,
5695 which you can define in ordinary Haskell,
5696 may also be used to build new commands out of existing ones.
5697 The basic idea is that a command defines an arrow from environments to values.
5698 These environments assign values to the free local variables of the command.
5699 Thus combinators that produce arrows from arrows
5700 may also be used to build commands from commands.
5701 For example, the <literal>ArrowChoice</literal> class includes a combinator
5703 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5705 so we can use it to build commands:
5707 expr' = proc x -> do
5710 symbol Plus -< ()
5711 y <- term -< ()
5714 symbol Minus -< ()
5715 y <- term -< ()
5718 (The <literal>do</literal> on the first line is needed to prevent the first
5719 <literal><+> ...</literal> from being interpreted as part of the
5720 expression on the previous line.)
5721 This is equivalent to
5723 expr' = (proc x -> returnA -< x)
5724 <+> (proc x -> do
5725 symbol Plus -< ()
5726 y <- term -< ()
5728 <+> (proc x -> do
5729 symbol Minus -< ()
5730 y <- term -< ()
5733 It is essential that this operator be polymorphic in <literal>e</literal>
5734 (representing the environment input to the command
5735 and thence to its subcommands)
5736 and satisfy the corresponding naturality property
5738 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5740 at least for strict <literal>k</literal>.
5741 (This should be automatic if you're not using <function>seq</function>.)
5742 This ensures that environments seen by the subcommands are environments
5743 of the whole command,
5744 and also allows the translation to safely trim these environments.
5745 The operator must also not use any variable defined within the current
5750 We could define our own operator
5752 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5753 untilA body cond = proc x ->
5754 if cond x then returnA -< ()
5757 untilA body cond -< x
5759 and use it in the same way.
5760 Of course this infix syntax only makes sense for binary operators;
5761 there is also a more general syntax involving special brackets:
5765 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5772 <title>Primitive constructs</title>
5775 Some operators will need to pass additional inputs to their subcommands.
5776 For example, in an arrow type supporting exceptions,
5777 the operator that attaches an exception handler will wish to pass the
5778 exception that occurred to the handler.
5779 Such an operator might have a type
5781 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5783 where <literal>Ex</literal> is the type of exceptions handled.
5784 You could then use this with arrow notation by writing a command
5786 body `handleA` \ ex -> handler
5788 so that if an exception is raised in the command <literal>body</literal>,
5789 the variable <literal>ex</literal> is bound to the value of the exception
5790 and the command <literal>handler</literal>,
5791 which typically refers to <literal>ex</literal>, is entered.
5792 Though the syntax here looks like a functional lambda,
5793 we are talking about commands, and something different is going on.
5794 The input to the arrow represented by a command consists of values for
5795 the free local variables in the command, plus a stack of anonymous values.
5796 In all the prior examples, this stack was empty.
5797 In the second argument to <function>handleA</function>,
5798 this stack consists of one value, the value of the exception.
5799 The command form of lambda merely gives this value a name.
5804 the values on the stack are paired to the right of the environment.
5805 So operators like <function>handleA</function> that pass
5806 extra inputs to their subcommands can be designed for use with the notation
5807 by pairing the values with the environment in this way.
5808 More precisely, the type of each argument of the operator (and its result)
5809 should have the form
5811 a (...(e,t1), ... tn) t
5813 where <replaceable>e</replaceable> is a polymorphic variable
5814 (representing the environment)
5815 and <replaceable>ti</replaceable> are the types of the values on the stack,
5816 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5817 The polymorphic variable <replaceable>e</replaceable> must not occur in
5818 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5819 <replaceable>t</replaceable>.
5820 However the arrows involved need not be the same.
5821 Here are some more examples of suitable operators:
5823 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5824 runReader :: ... => a e c -> a' (e,State) c
5825 runState :: ... => a e c -> a' (e,State) (c,State)
5827 We can supply the extra input required by commands built with the last two
5828 by applying them to ordinary expressions, as in
5832 (|runReader (do { ... })|) s
5834 which adds <literal>s</literal> to the stack of inputs to the command
5835 built using <function>runReader</function>.
5839 The command versions of lambda abstraction and application are analogous to
5840 the expression versions.
5841 In particular, the beta and eta rules describe equivalences of commands.
5842 These three features (operators, lambda abstraction and application)
5843 are the core of the notation; everything else can be built using them,
5844 though the results would be somewhat clumsy.
5845 For example, we could simulate <literal>do</literal>-notation by defining
5847 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5848 u `bind` f = returnA &&& u >>> f
5850 bind_ :: Arrow a => a e b -> a e c -> a e c
5851 u `bind_` f = u `bind` (arr fst >>> f)
5853 We could simulate <literal>if</literal> by defining
5855 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5856 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5863 <title>Differences with the paper</title>
5868 <para>Instead of a single form of arrow application (arrow tail) with two
5869 translations, the implementation provides two forms
5870 <quote><literal>-<</literal></quote> (first-order)
5871 and <quote><literal>-<<</literal></quote> (higher-order).
5876 <para>User-defined operators are flagged with banana brackets instead of
5877 a new <literal>form</literal> keyword.
5886 <title>Portability</title>
5889 Although only GHC implements arrow notation directly,
5890 there is also a preprocessor
5892 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5893 that translates arrow notation into Haskell 98
5894 for use with other Haskell systems.
5895 You would still want to check arrow programs with GHC;
5896 tracing type errors in the preprocessor output is not easy.
5897 Modules intended for both GHC and the preprocessor must observe some
5898 additional restrictions:
5903 The module must import
5904 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5910 The preprocessor cannot cope with other Haskell extensions.
5911 These would have to go in separate modules.
5917 Because the preprocessor targets Haskell (rather than Core),
5918 <literal>let</literal>-bound variables are monomorphic.
5929 <!-- ==================== BANG PATTERNS ================= -->
5931 <sect1 id="bang-patterns">
5932 <title>Bang patterns
5933 <indexterm><primary>Bang patterns</primary></indexterm>
5935 <para>GHC supports an extension of pattern matching called <emphasis>bang
5936 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5938 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5939 prime feature description</ulink> contains more discussion and examples
5940 than the material below.
5943 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5946 <sect2 id="bang-patterns-informal">
5947 <title>Informal description of bang patterns
5950 The main idea is to add a single new production to the syntax of patterns:
5954 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5955 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5960 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5961 whereas without the bang it would be lazy.
5962 Bang patterns can be nested of course:
5966 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5967 <literal>y</literal>.
5968 A bang only really has an effect if it precedes a variable or wild-card pattern:
5973 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5974 forces evaluation anyway does nothing.
5976 Bang patterns work in <literal>case</literal> expressions too, of course:
5978 g5 x = let y = f x in body
5979 g6 x = case f x of { y -> body }
5980 g7 x = case f x of { !y -> body }
5982 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5983 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5984 result, and then evaluates <literal>body</literal>.
5986 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5987 definitions too. For example:
5991 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5992 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5993 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5994 in a function argument <literal>![x,y]</literal> means the
5995 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5996 is part of the syntax of <literal>let</literal> bindings.
6001 <sect2 id="bang-patterns-sem">
6002 <title>Syntax and semantics
6006 We add a single new production to the syntax of patterns:
6010 There is one problem with syntactic ambiguity. Consider:
6014 Is this a definition of the infix function "<literal>(!)</literal>",
6015 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6016 ambiguity in favour of the latter. If you want to define
6017 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6022 The semantics of Haskell pattern matching is described in <ulink
6023 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6024 Section 3.17.2</ulink> of the Haskell Report. To this description add
6025 one extra item 10, saying:
6026 <itemizedlist><listitem><para>Matching
6027 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6028 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6029 <listitem><para>otherwise, <literal>pat</literal> is matched against
6030 <literal>v</literal></para></listitem>
6032 </para></listitem></itemizedlist>
6033 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6034 Section 3.17.3</ulink>, add a new case (t):
6036 case v of { !pat -> e; _ -> e' }
6037 = v `seq` case v of { pat -> e; _ -> e' }
6040 That leaves let expressions, whose translation is given in
6041 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6043 of the Haskell Report.
6044 In the translation box, first apply
6045 the following transformation: for each pattern <literal>pi</literal> that is of
6046 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6047 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6048 have a bang at the top, apply the rules in the existing box.
6050 <para>The effect of the let rule is to force complete matching of the pattern
6051 <literal>qi</literal> before evaluation of the body is begun. The bang is
6052 retained in the translated form in case <literal>qi</literal> is a variable,
6060 The let-binding can be recursive. However, it is much more common for
6061 the let-binding to be non-recursive, in which case the following law holds:
6062 <literal>(let !p = rhs in body)</literal>
6064 <literal>(case rhs of !p -> body)</literal>
6067 A pattern with a bang at the outermost level is not allowed at the top level of
6073 <!-- ==================== ASSERTIONS ================= -->
6075 <sect1 id="assertions">
6077 <indexterm><primary>Assertions</primary></indexterm>
6081 If you want to make use of assertions in your standard Haskell code, you
6082 could define a function like the following:
6088 assert :: Bool -> a -> a
6089 assert False x = error "assertion failed!"
6096 which works, but gives you back a less than useful error message --
6097 an assertion failed, but which and where?
6101 One way out is to define an extended <function>assert</function> function which also
6102 takes a descriptive string to include in the error message and
6103 perhaps combine this with the use of a pre-processor which inserts
6104 the source location where <function>assert</function> was used.
6108 Ghc offers a helping hand here, doing all of this for you. For every
6109 use of <function>assert</function> in the user's source:
6115 kelvinToC :: Double -> Double
6116 kelvinToC k = assert (k >= 0.0) (k+273.15)
6122 Ghc will rewrite this to also include the source location where the
6129 assert pred val ==> assertError "Main.hs|15" pred val
6135 The rewrite is only performed by the compiler when it spots
6136 applications of <function>Control.Exception.assert</function>, so you
6137 can still define and use your own versions of
6138 <function>assert</function>, should you so wish. If not, import
6139 <literal>Control.Exception</literal> to make use
6140 <function>assert</function> in your code.
6144 GHC ignores assertions when optimisation is turned on with the
6145 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6146 <literal>assert pred e</literal> will be rewritten to
6147 <literal>e</literal>. You can also disable assertions using the
6148 <option>-fignore-asserts</option>
6149 option<indexterm><primary><option>-fignore-asserts</option></primary>
6150 </indexterm>.</para>
6153 Assertion failures can be caught, see the documentation for the
6154 <literal>Control.Exception</literal> library for the details.
6160 <!-- =============================== PRAGMAS =========================== -->
6162 <sect1 id="pragmas">
6163 <title>Pragmas</title>
6165 <indexterm><primary>pragma</primary></indexterm>
6167 <para>GHC supports several pragmas, or instructions to the
6168 compiler placed in the source code. Pragmas don't normally affect
6169 the meaning of the program, but they might affect the efficiency
6170 of the generated code.</para>
6172 <para>Pragmas all take the form
6174 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6176 where <replaceable>word</replaceable> indicates the type of
6177 pragma, and is followed optionally by information specific to that
6178 type of pragma. Case is ignored in
6179 <replaceable>word</replaceable>. The various values for
6180 <replaceable>word</replaceable> that GHC understands are described
6181 in the following sections; any pragma encountered with an
6182 unrecognised <replaceable>word</replaceable> is (silently)
6183 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6184 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6186 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6187 pragma must precede the <literal>module</literal> keyword in the file.
6188 There can be as many file-header pragmas as you please, and they can be
6189 preceded or followed by comments.</para>
6191 <sect2 id="language-pragma">
6192 <title>LANGUAGE pragma</title>
6194 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6195 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6197 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6199 It is the intention that all Haskell compilers support the
6200 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6201 all extensions are supported by all compilers, of
6202 course. The <literal>LANGUAGE</literal> pragma should be used instead
6203 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6205 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6207 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6209 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6211 <para>Every language extension can also be turned into a command-line flag
6212 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6213 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6216 <para>A list of all supported language extensions can be obtained by invoking
6217 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6219 <para>Any extension from the <literal>Extension</literal> type defined in
6221 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6222 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6226 <sect2 id="options-pragma">
6227 <title>OPTIONS_GHC pragma</title>
6228 <indexterm><primary>OPTIONS_GHC</primary>
6230 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6233 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6234 additional options that are given to the compiler when compiling
6235 this source file. See <xref linkend="source-file-options"/> for
6238 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6239 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6242 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6244 <sect2 id="include-pragma">
6245 <title>INCLUDE pragma</title>
6247 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6248 of C header files that should be <literal>#include</literal>'d into
6249 the C source code generated by the compiler for the current module (if
6250 compiling via C). For example:</para>
6253 {-# INCLUDE "foo.h" #-}
6254 {-# INCLUDE <stdio.h> #-}</programlisting>
6256 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6258 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6259 to the <option>-#include</option> option (<xref
6260 linkend="options-C-compiler" />), because the
6261 <literal>INCLUDE</literal> pragma is understood by other
6262 compilers. Yet another alternative is to add the include file to each
6263 <literal>foreign import</literal> declaration in your code, but we
6264 don't recommend using this approach with GHC.</para>
6267 <sect2 id="warning-deprecated-pragma">
6268 <title>WARNING and DEPRECATED pragmas</title>
6269 <indexterm><primary>WARNING</primary></indexterm>
6270 <indexterm><primary>DEPRECATED</primary></indexterm>
6272 <para>The WARNING pragma allows you to attach an arbitrary warning
6273 to a particular function, class, or type.
6274 A DEPRECATED pragma lets you specify that
6275 a particular function, class, or type is deprecated.
6276 There are two ways of using these pragmas.
6280 <para>You can work on an entire module thus:</para>
6282 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6287 module Wibble {-# WARNING "This is an unstable interface." #-} where
6290 <para>When you compile any module that import
6291 <literal>Wibble</literal>, GHC will print the specified
6296 <para>You can attach a warning to a function, class, type, or data constructor, with the
6297 following top-level declarations:</para>
6299 {-# DEPRECATED f, C, T "Don't use these" #-}
6300 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6302 <para>When you compile any module that imports and uses any
6303 of the specified entities, GHC will print the specified
6305 <para> You can only attach to entities declared at top level in the module
6306 being compiled, and you can only use unqualified names in the list of
6307 entities. A capitalised name, such as <literal>T</literal>
6308 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6309 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6310 both are in scope. If both are in scope, there is currently no way to
6311 specify one without the other (c.f. fixities
6312 <xref linkend="infix-tycons"/>).</para>
6315 Warnings and deprecations are not reported for
6316 (a) uses within the defining module, and
6317 (b) uses in an export list.
6318 The latter reduces spurious complaints within a library
6319 in which one module gathers together and re-exports
6320 the exports of several others.
6322 <para>You can suppress the warnings with the flag
6323 <option>-fno-warn-warnings-deprecations</option>.</para>
6326 <sect2 id="inline-noinline-pragma">
6327 <title>INLINE and NOINLINE pragmas</title>
6329 <para>These pragmas control the inlining of function
6332 <sect3 id="inline-pragma">
6333 <title>INLINE pragma</title>
6334 <indexterm><primary>INLINE</primary></indexterm>
6336 <para>GHC (with <option>-O</option>, as always) tries to
6337 inline (or “unfold”) functions/values that are
6338 “small enough,” thus avoiding the call overhead
6339 and possibly exposing other more-wonderful optimisations.
6340 Normally, if GHC decides a function is “too
6341 expensive” to inline, it will not do so, nor will it
6342 export that unfolding for other modules to use.</para>
6344 <para>The sledgehammer you can bring to bear is the
6345 <literal>INLINE</literal><indexterm><primary>INLINE
6346 pragma</primary></indexterm> pragma, used thusly:</para>
6349 key_function :: Int -> String -> (Bool, Double)
6350 {-# INLINE key_function #-}
6353 <para>The major effect of an <literal>INLINE</literal> pragma
6354 is to declare a function's “cost” to be very low.
6355 The normal unfolding machinery will then be very keen to
6356 inline it. However, an <literal>INLINE</literal> pragma for a
6357 function "<literal>f</literal>" has a number of other effects:
6360 No functions are inlined into <literal>f</literal>. Otherwise
6361 GHC might inline a big function into <literal>f</literal>'s right hand side,
6362 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6365 The float-in, float-out, and common-sub-expression transformations are not
6366 applied to the body of <literal>f</literal>.
6369 An INLINE function is not worker/wrappered by strictness analysis.
6370 It's going to be inlined wholesale instead.
6373 All of these effects are aimed at ensuring that what gets inlined is
6374 exactly what you asked for, no more and no less.
6376 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6377 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6378 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6379 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6380 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6381 when there is no choice even an INLINE function can be selected, in which case
6382 the INLINE pragma is ignored.
6383 For example, for a self-recursive function, the loop breaker can only be the function
6384 itself, so an INLINE pragma is always ignored.</para>
6386 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6387 function can be put anywhere its type signature could be
6390 <para><literal>INLINE</literal> pragmas are a particularly
6392 <literal>then</literal>/<literal>return</literal> (or
6393 <literal>bind</literal>/<literal>unit</literal>) functions in
6394 a monad. For example, in GHC's own
6395 <literal>UniqueSupply</literal> monad code, we have:</para>
6398 {-# INLINE thenUs #-}
6399 {-# INLINE returnUs #-}
6402 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6403 linkend="noinline-pragma"/>).</para>
6405 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6406 so if you want your code to be HBC-compatible you'll have to surround
6407 the pragma with C pre-processor directives
6408 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6412 <sect3 id="noinline-pragma">
6413 <title>NOINLINE pragma</title>
6415 <indexterm><primary>NOINLINE</primary></indexterm>
6416 <indexterm><primary>NOTINLINE</primary></indexterm>
6418 <para>The <literal>NOINLINE</literal> pragma does exactly what
6419 you'd expect: it stops the named function from being inlined
6420 by the compiler. You shouldn't ever need to do this, unless
6421 you're very cautious about code size.</para>
6423 <para><literal>NOTINLINE</literal> is a synonym for
6424 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6425 specified by Haskell 98 as the standard way to disable
6426 inlining, so it should be used if you want your code to be
6430 <sect3 id="phase-control">
6431 <title>Phase control</title>
6433 <para> Sometimes you want to control exactly when in GHC's
6434 pipeline the INLINE pragma is switched on. Inlining happens
6435 only during runs of the <emphasis>simplifier</emphasis>. Each
6436 run of the simplifier has a different <emphasis>phase
6437 number</emphasis>; the phase number decreases towards zero.
6438 If you use <option>-dverbose-core2core</option> you'll see the
6439 sequence of phase numbers for successive runs of the
6440 simplifier. In an INLINE pragma you can optionally specify a
6444 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6445 <literal>f</literal>
6446 until phase <literal>k</literal>, but from phase
6447 <literal>k</literal> onwards be very keen to inline it.
6450 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6451 <literal>f</literal>
6452 until phase <literal>k</literal>, but from phase
6453 <literal>k</literal> onwards do not inline it.
6456 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6457 <literal>f</literal>
6458 until phase <literal>k</literal>, but from phase
6459 <literal>k</literal> onwards be willing to inline it (as if
6460 there was no pragma).
6463 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6464 <literal>f</literal>
6465 until phase <literal>k</literal>, but from phase
6466 <literal>k</literal> onwards do not inline it.
6469 The same information is summarised here:
6471 -- Before phase 2 Phase 2 and later
6472 {-# INLINE [2] f #-} -- No Yes
6473 {-# INLINE [~2] f #-} -- Yes No
6474 {-# NOINLINE [2] f #-} -- No Maybe
6475 {-# NOINLINE [~2] f #-} -- Maybe No
6477 {-# INLINE f #-} -- Yes Yes
6478 {-# NOINLINE f #-} -- No No
6480 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6481 function body is small, or it is applied to interesting-looking arguments etc).
6482 Another way to understand the semantics is this:
6484 <listitem><para>For both INLINE and NOINLINE, the phase number says
6485 when inlining is allowed at all.</para></listitem>
6486 <listitem><para>The INLINE pragma has the additional effect of making the
6487 function body look small, so that when inlining is allowed it is very likely to
6492 <para>The same phase-numbering control is available for RULES
6493 (<xref linkend="rewrite-rules"/>).</para>
6497 <sect2 id="line-pragma">
6498 <title>LINE pragma</title>
6500 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6501 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6502 <para>This pragma is similar to C's <literal>#line</literal>
6503 pragma, and is mainly for use in automatically generated Haskell
6504 code. It lets you specify the line number and filename of the
6505 original code; for example</para>
6507 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6509 <para>if you'd generated the current file from something called
6510 <filename>Foo.vhs</filename> and this line corresponds to line
6511 42 in the original. GHC will adjust its error messages to refer
6512 to the line/file named in the <literal>LINE</literal>
6517 <title>RULES pragma</title>
6519 <para>The RULES pragma lets you specify rewrite rules. It is
6520 described in <xref linkend="rewrite-rules"/>.</para>
6523 <sect2 id="specialize-pragma">
6524 <title>SPECIALIZE pragma</title>
6526 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6527 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6528 <indexterm><primary>overloading, death to</primary></indexterm>
6530 <para>(UK spelling also accepted.) For key overloaded
6531 functions, you can create extra versions (NB: more code space)
6532 specialised to particular types. Thus, if you have an
6533 overloaded function:</para>
6536 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6539 <para>If it is heavily used on lists with
6540 <literal>Widget</literal> keys, you could specialise it as
6544 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6547 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6548 be put anywhere its type signature could be put.</para>
6550 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6551 (a) a specialised version of the function and (b) a rewrite rule
6552 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6553 un-specialised function into a call to the specialised one.</para>
6555 <para>The type in a SPECIALIZE pragma can be any type that is less
6556 polymorphic than the type of the original function. In concrete terms,
6557 if the original function is <literal>f</literal> then the pragma
6559 {-# SPECIALIZE f :: <type> #-}
6561 is valid if and only if the definition
6563 f_spec :: <type>
6566 is valid. Here are some examples (where we only give the type signature
6567 for the original function, not its code):
6569 f :: Eq a => a -> b -> b
6570 {-# SPECIALISE f :: Int -> b -> b #-}
6572 g :: (Eq a, Ix b) => a -> b -> b
6573 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6575 h :: Eq a => a -> a -> a
6576 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6578 The last of these examples will generate a
6579 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6580 well. If you use this kind of specialisation, let us know how well it works.
6583 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6584 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6585 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6586 The <literal>INLINE</literal> pragma affects the specialised version of the
6587 function (only), and applies even if the function is recursive. The motivating
6590 -- A GADT for arrays with type-indexed representation
6592 ArrInt :: !Int -> ByteArray# -> Arr Int
6593 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6595 (!:) :: Arr e -> Int -> e
6596 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6597 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6598 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6599 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6601 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6602 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6603 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6604 the specialised function will be inlined. It has two calls to
6605 <literal>(!:)</literal>,
6606 both at type <literal>Int</literal>. Both these calls fire the first
6607 specialisation, whose body is also inlined. The result is a type-based
6608 unrolling of the indexing function.</para>
6609 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6610 on an ordinarily-recursive function.</para>
6612 <para>Note: In earlier versions of GHC, it was possible to provide your own
6613 specialised function for a given type:
6616 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6619 This feature has been removed, as it is now subsumed by the
6620 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6624 <sect2 id="specialize-instance-pragma">
6625 <title>SPECIALIZE instance pragma
6629 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6630 <indexterm><primary>overloading, death to</primary></indexterm>
6631 Same idea, except for instance declarations. For example:
6634 instance (Eq a) => Eq (Foo a) where {
6635 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6639 The pragma must occur inside the <literal>where</literal> part
6640 of the instance declaration.
6643 Compatible with HBC, by the way, except perhaps in the placement
6649 <sect2 id="unpack-pragma">
6650 <title>UNPACK pragma</title>
6652 <indexterm><primary>UNPACK</primary></indexterm>
6654 <para>The <literal>UNPACK</literal> indicates to the compiler
6655 that it should unpack the contents of a constructor field into
6656 the constructor itself, removing a level of indirection. For
6660 data T = T {-# UNPACK #-} !Float
6661 {-# UNPACK #-} !Float
6664 <para>will create a constructor <literal>T</literal> containing
6665 two unboxed floats. This may not always be an optimisation: if
6666 the <function>T</function> constructor is scrutinised and the
6667 floats passed to a non-strict function for example, they will
6668 have to be reboxed (this is done automatically by the
6671 <para>Unpacking constructor fields should only be used in
6672 conjunction with <option>-O</option>, in order to expose
6673 unfoldings to the compiler so the reboxing can be removed as
6674 often as possible. For example:</para>
6678 f (T f1 f2) = f1 + f2
6681 <para>The compiler will avoid reboxing <function>f1</function>
6682 and <function>f2</function> by inlining <function>+</function>
6683 on floats, but only when <option>-O</option> is on.</para>
6685 <para>Any single-constructor data is eligible for unpacking; for
6689 data T = T {-# UNPACK #-} !(Int,Int)
6692 <para>will store the two <literal>Int</literal>s directly in the
6693 <function>T</function> constructor, by flattening the pair.
6694 Multi-level unpacking is also supported:
6697 data T = T {-# UNPACK #-} !S
6698 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6701 will store two unboxed <literal>Int#</literal>s
6702 directly in the <function>T</function> constructor. The
6703 unpacker can see through newtypes, too.</para>
6705 <para>If a field cannot be unpacked, you will not get a warning,
6706 so it might be an idea to check the generated code with
6707 <option>-ddump-simpl</option>.</para>
6709 <para>See also the <option>-funbox-strict-fields</option> flag,
6710 which essentially has the effect of adding
6711 <literal>{-# UNPACK #-}</literal> to every strict
6712 constructor field.</para>
6715 <sect2 id="source-pragma">
6716 <title>SOURCE pragma</title>
6718 <indexterm><primary>SOURCE</primary></indexterm>
6719 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6720 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6726 <!-- ======================= REWRITE RULES ======================== -->
6728 <sect1 id="rewrite-rules">
6729 <title>Rewrite rules
6731 <indexterm><primary>RULES pragma</primary></indexterm>
6732 <indexterm><primary>pragma, RULES</primary></indexterm>
6733 <indexterm><primary>rewrite rules</primary></indexterm></title>
6736 The programmer can specify rewrite rules as part of the source program
6742 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6747 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6748 If you need more information, then <option>-ddump-rule-firings</option> shows you
6749 each individual rule firing in detail.
6753 <title>Syntax</title>
6756 From a syntactic point of view:
6762 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6763 may be generated by the layout rule).
6769 The layout rule applies in a pragma.
6770 Currently no new indentation level
6771 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6772 you must lay out the starting in the same column as the enclosing definitions.
6775 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6776 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6779 Furthermore, the closing <literal>#-}</literal>
6780 should start in a column to the right of the opening <literal>{-#</literal>.
6786 Each rule has a name, enclosed in double quotes. The name itself has
6787 no significance at all. It is only used when reporting how many times the rule fired.
6793 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6794 immediately after the name of the rule. Thus:
6797 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6800 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6801 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6810 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6811 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6812 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6813 by spaces, just like in a type <literal>forall</literal>.
6819 A pattern variable may optionally have a type signature.
6820 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6821 For example, here is the <literal>foldr/build</literal> rule:
6824 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6825 foldr k z (build g) = g k z
6828 Since <function>g</function> has a polymorphic type, it must have a type signature.
6835 The left hand side of a rule must consist of a top-level variable applied
6836 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6839 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6840 "wrong2" forall f. f True = True
6843 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6850 A rule does not need to be in the same module as (any of) the
6851 variables it mentions, though of course they need to be in scope.
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
6868 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
6869 any other flag settings. Furthermore, inside a RULE, the language extension
6870 <option>-XScopedTypeVariables</option> is automatically enabled; see
6871 <xref linkend="scoped-type-variables"/>.
6877 Like other pragmas, RULE pragmas are always checked for scope errors, and
6878 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
6879 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
6880 if the <option>-fenable-rewrite-rules</option> flag is
6881 on (see <xref linkend="rule-semantics"/>).
6890 <sect2 id="rule-semantics">
6891 <title>Semantics</title>
6894 From a semantic point of view:
6899 Rules are enabled (that is, used during optimisation)
6900 by the <option>-fenable-rewrite-rules</option> flag.
6901 This flag is implied by <option>-O</option>, and may be switched
6902 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
6903 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
6904 may not do what you expect, though, because without <option>-O</option> GHC
6905 ignores all optimisation information in interface files;
6906 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
6907 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
6908 has no effect on parsing or typechecking.
6914 Rules are regarded as left-to-right rewrite rules.
6915 When GHC finds an expression that is a substitution instance of the LHS
6916 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6917 By "a substitution instance" we mean that the LHS can be made equal to the
6918 expression by substituting for the pattern variables.
6925 GHC makes absolutely no attempt to verify that the LHS and RHS
6926 of a rule have the same meaning. That is undecidable in general, and
6927 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6934 GHC makes no attempt to make sure that the rules are confluent or
6935 terminating. For example:
6938 "loop" forall x y. f x y = f y x
6941 This rule will cause the compiler to go into an infinite loop.
6948 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6954 GHC currently uses a very simple, syntactic, matching algorithm
6955 for matching a rule LHS with an expression. It seeks a substitution
6956 which makes the LHS and expression syntactically equal modulo alpha
6957 conversion. The pattern (rule), but not the expression, is eta-expanded if
6958 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6959 But not beta conversion (that's called higher-order matching).
6963 Matching is carried out on GHC's intermediate language, which includes
6964 type abstractions and applications. So a rule only matches if the
6965 types match too. See <xref linkend="rule-spec"/> below.
6971 GHC keeps trying to apply the rules as it optimises the program.
6972 For example, consider:
6981 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6982 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6983 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6984 not be substituted, and the rule would not fire.
6991 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6992 results. Consider this (artificial) example
6995 {-# RULES "f" f True = False #-}
7001 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7006 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7008 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7009 would have been a better chance that <literal>f</literal>'s RULE might fire.
7012 The way to get predictable behaviour is to use a NOINLINE
7013 pragma on <literal>f</literal>, to ensure
7014 that it is not inlined until its RULEs have had a chance to fire.
7024 <title>List fusion</title>
7027 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7028 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7029 intermediate list should be eliminated entirely.
7033 The following are good producers:
7045 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7051 Explicit lists (e.g. <literal>[True, False]</literal>)
7057 The cons constructor (e.g <literal>3:4:[]</literal>)
7063 <function>++</function>
7069 <function>map</function>
7075 <function>take</function>, <function>filter</function>
7081 <function>iterate</function>, <function>repeat</function>
7087 <function>zip</function>, <function>zipWith</function>
7096 The following are good consumers:
7108 <function>array</function> (on its second argument)
7114 <function>++</function> (on its first argument)
7120 <function>foldr</function>
7126 <function>map</function>
7132 <function>take</function>, <function>filter</function>
7138 <function>concat</function>
7144 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7150 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7151 will fuse with one but not the other)
7157 <function>partition</function>
7163 <function>head</function>
7169 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7175 <function>sequence_</function>
7181 <function>msum</function>
7187 <function>sortBy</function>
7196 So, for example, the following should generate no intermediate lists:
7199 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7205 This list could readily be extended; if there are Prelude functions that you use
7206 a lot which are not included, please tell us.
7210 If you want to write your own good consumers or producers, look at the
7211 Prelude definitions of the above functions to see how to do so.
7216 <sect2 id="rule-spec">
7217 <title>Specialisation
7221 Rewrite rules can be used to get the same effect as a feature
7222 present in earlier versions of GHC.
7223 For example, suppose that:
7226 genericLookup :: Ord a => Table a b -> a -> b
7227 intLookup :: Table Int b -> Int -> b
7230 where <function>intLookup</function> is an implementation of
7231 <function>genericLookup</function> that works very fast for
7232 keys of type <literal>Int</literal>. You might wish
7233 to tell GHC to use <function>intLookup</function> instead of
7234 <function>genericLookup</function> whenever the latter was called with
7235 type <literal>Table Int b -> Int -> b</literal>.
7236 It used to be possible to write
7239 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7242 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7245 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7248 This slightly odd-looking rule instructs GHC to replace
7249 <function>genericLookup</function> by <function>intLookup</function>
7250 <emphasis>whenever the types match</emphasis>.
7251 What is more, this rule does not need to be in the same
7252 file as <function>genericLookup</function>, unlike the
7253 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7254 have an original definition available to specialise).
7257 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7258 <function>intLookup</function> really behaves as a specialised version
7259 of <function>genericLookup</function>!!!</para>
7261 <para>An example in which using <literal>RULES</literal> for
7262 specialisation will Win Big:
7265 toDouble :: Real a => a -> Double
7266 toDouble = fromRational . toRational
7268 {-# RULES "toDouble/Int" toDouble = i2d #-}
7269 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7272 The <function>i2d</function> function is virtually one machine
7273 instruction; the default conversion—via an intermediate
7274 <literal>Rational</literal>—is obscenely expensive by
7281 <title>Controlling what's going on</title>
7289 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7295 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7296 If you add <option>-dppr-debug</option> you get a more detailed listing.
7302 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7305 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7306 {-# INLINE build #-}
7310 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7311 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7312 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7313 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7320 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7321 see how to write rules that will do fusion and yet give an efficient
7322 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7332 <sect2 id="core-pragma">
7333 <title>CORE pragma</title>
7335 <indexterm><primary>CORE pragma</primary></indexterm>
7336 <indexterm><primary>pragma, CORE</primary></indexterm>
7337 <indexterm><primary>core, annotation</primary></indexterm>
7340 The external core format supports <quote>Note</quote> annotations;
7341 the <literal>CORE</literal> pragma gives a way to specify what these
7342 should be in your Haskell source code. Syntactically, core
7343 annotations are attached to expressions and take a Haskell string
7344 literal as an argument. The following function definition shows an
7348 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7351 Semantically, this is equivalent to:
7359 However, when external core is generated (via
7360 <option>-fext-core</option>), there will be Notes attached to the
7361 expressions <function>show</function> and <varname>x</varname>.
7362 The core function declaration for <function>f</function> is:
7366 f :: %forall a . GHCziShow.ZCTShow a ->
7367 a -> GHCziBase.ZMZN GHCziBase.Char =
7368 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7370 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7372 (tpl1::GHCziBase.Int ->
7374 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7376 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7377 (tpl3::GHCziBase.ZMZN a ->
7378 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7386 Here, we can see that the function <function>show</function> (which
7387 has been expanded out to a case expression over the Show dictionary)
7388 has a <literal>%note</literal> attached to it, as does the
7389 expression <varname>eta</varname> (which used to be called
7390 <varname>x</varname>).
7397 <sect1 id="special-ids">
7398 <title>Special built-in functions</title>
7399 <para>GHC has a few built-in functions with special behaviour. These
7400 are now described in the module <ulink
7401 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7402 in the library documentation.</para>
7406 <sect1 id="generic-classes">
7407 <title>Generic classes</title>
7410 The ideas behind this extension are described in detail in "Derivable type classes",
7411 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7412 An example will give the idea:
7420 fromBin :: [Int] -> (a, [Int])
7422 toBin {| Unit |} Unit = []
7423 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7424 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7425 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7427 fromBin {| Unit |} bs = (Unit, bs)
7428 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7429 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7430 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7431 (y,bs'') = fromBin bs'
7434 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7435 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7436 which are defined thus in the library module <literal>Generics</literal>:
7440 data a :+: b = Inl a | Inr b
7441 data a :*: b = a :*: b
7444 Now you can make a data type into an instance of Bin like this:
7446 instance (Bin a, Bin b) => Bin (a,b)
7447 instance Bin a => Bin [a]
7449 That is, just leave off the "where" clause. Of course, you can put in the
7450 where clause and over-ride whichever methods you please.
7454 <title> Using generics </title>
7455 <para>To use generics you need to</para>
7458 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7459 <option>-XGenerics</option> (to generate extra per-data-type code),
7460 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7464 <para>Import the module <literal>Generics</literal> from the
7465 <literal>lang</literal> package. This import brings into
7466 scope the data types <literal>Unit</literal>,
7467 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7468 don't need this import if you don't mention these types
7469 explicitly; for example, if you are simply giving instance
7470 declarations.)</para>
7475 <sect2> <title> Changes wrt the paper </title>
7477 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7478 can be written infix (indeed, you can now use
7479 any operator starting in a colon as an infix type constructor). Also note that
7480 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7481 Finally, note that the syntax of the type patterns in the class declaration
7482 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7483 alone would ambiguous when they appear on right hand sides (an extension we
7484 anticipate wanting).
7488 <sect2> <title>Terminology and restrictions</title>
7490 Terminology. A "generic default method" in a class declaration
7491 is one that is defined using type patterns as above.
7492 A "polymorphic default method" is a default method defined as in Haskell 98.
7493 A "generic class declaration" is a class declaration with at least one
7494 generic default method.
7502 Alas, we do not yet implement the stuff about constructor names and
7509 A generic class can have only one parameter; you can't have a generic
7510 multi-parameter class.
7516 A default method must be defined entirely using type patterns, or entirely
7517 without. So this is illegal:
7520 op :: a -> (a, Bool)
7521 op {| Unit |} Unit = (Unit, True)
7524 However it is perfectly OK for some methods of a generic class to have
7525 generic default methods and others to have polymorphic default methods.
7531 The type variable(s) in the type pattern for a generic method declaration
7532 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:
7536 op {| p :*: q |} (x :*: y) = op (x :: p)
7544 The type patterns in a generic default method must take one of the forms:
7550 where "a" and "b" are type variables. Furthermore, all the type patterns for
7551 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7552 must use the same type variables. So this is illegal:
7556 op {| a :+: b |} (Inl x) = True
7557 op {| p :+: q |} (Inr y) = False
7559 The type patterns must be identical, even in equations for different methods of the class.
7560 So this too is illegal:
7564 op1 {| a :*: b |} (x :*: y) = True
7567 op2 {| p :*: q |} (x :*: y) = False
7569 (The reason for this restriction is that we gather all the equations for a particular type constructor
7570 into a single generic instance declaration.)
7576 A generic method declaration must give a case for each of the three type constructors.
7582 The type for a generic method can be built only from:
7584 <listitem> <para> Function arrows </para> </listitem>
7585 <listitem> <para> Type variables </para> </listitem>
7586 <listitem> <para> Tuples </para> </listitem>
7587 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7589 Here are some example type signatures for generic methods:
7592 op2 :: Bool -> (a,Bool)
7593 op3 :: [Int] -> a -> a
7596 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7600 This restriction is an implementation restriction: we just haven't got around to
7601 implementing the necessary bidirectional maps over arbitrary type constructors.
7602 It would be relatively easy to add specific type constructors, such as Maybe and list,
7603 to the ones that are allowed.</para>
7608 In an instance declaration for a generic class, the idea is that the compiler
7609 will fill in the methods for you, based on the generic templates. However it can only
7614 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7619 No constructor of the instance type has unboxed fields.
7623 (Of course, these things can only arise if you are already using GHC extensions.)
7624 However, you can still give an instance declarations for types which break these rules,
7625 provided you give explicit code to override any generic default methods.
7633 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7634 what the compiler does with generic declarations.
7639 <sect2> <title> Another example </title>
7641 Just to finish with, here's another example I rather like:
7645 nCons {| Unit |} _ = 1
7646 nCons {| a :*: b |} _ = 1
7647 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7650 tag {| Unit |} _ = 1
7651 tag {| a :*: b |} _ = 1
7652 tag {| a :+: b |} (Inl x) = tag x
7653 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7659 <sect1 id="monomorphism">
7660 <title>Control over monomorphism</title>
7662 <para>GHC supports two flags that control the way in which generalisation is
7663 carried out at let and where bindings.
7667 <title>Switching off the dreaded Monomorphism Restriction</title>
7668 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7670 <para>Haskell's monomorphism restriction (see
7671 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7673 of the Haskell Report)
7674 can be completely switched off by
7675 <option>-XNoMonomorphismRestriction</option>.
7680 <title>Monomorphic pattern bindings</title>
7681 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7682 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7684 <para> As an experimental change, we are exploring the possibility of
7685 making pattern bindings monomorphic; that is, not generalised at all.
7686 A pattern binding is a binding whose LHS has no function arguments,
7687 and is not a simple variable. For example:
7689 f x = x -- Not a pattern binding
7690 f = \x -> x -- Not a pattern binding
7691 f :: Int -> Int = \x -> x -- Not a pattern binding
7693 (g,h) = e -- A pattern binding
7694 (f) = e -- A pattern binding
7695 [x] = e -- A pattern binding
7697 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7698 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7707 ;;; Local Variables: ***
7709 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7710 ;;; ispell-local-dictionary: "british" ***
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