1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individually.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
137 <para> These two flags control how generalisation is done.
138 See <xref linkend="monomorphism"/>.
145 <option>-XExtendedDefaultRules</option>:
146 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
149 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
150 Independent of the <option>-fglasgow-exts</option>
157 <option>-XOverlappingInstances</option>
158 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
161 <option>-XUndecidableInstances</option>
162 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
165 <option>-XIncoherentInstances</option>
166 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
169 <option>-fcontext-stack=N</option>
170 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
173 <para> See <xref linkend="instance-decls"/>. Only relevant
174 if you also use <option>-fglasgow-exts</option>.</para>
180 <option>-finline-phase</option>
181 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
184 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
185 you also use <option>-fglasgow-exts</option>.</para>
191 <option>-XArrows</option>
192 <indexterm><primary><option>-XArrows</option></primary></indexterm>
195 <para>See <xref linkend="arrow-notation"/>. Independent of
196 <option>-fglasgow-exts</option>.</para>
198 <para>New reserved words/symbols: <literal>rec</literal>,
199 <literal>proc</literal>, <literal>-<</literal>,
200 <literal>>-</literal>, <literal>-<<</literal>,
201 <literal>>>-</literal>.</para>
203 <para>Other syntax stolen: <literal>(|</literal>,
204 <literal>|)</literal>.</para>
210 <option>-XGenerics</option>
211 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
214 <para>See <xref linkend="generic-classes"/>. Independent of
215 <option>-fglasgow-exts</option>.</para>
220 <term><option>-XNoImplicitPrelude</option></term>
222 <para><indexterm><primary>-XNoImplicitPrelude
223 option</primary></indexterm> GHC normally imports
224 <filename>Prelude.hi</filename> files for you. If you'd
225 rather it didn't, then give it a
226 <option>-XNoImplicitPrelude</option> option. The idea is
227 that you can then import a Prelude of your own. (But don't
228 call it <literal>Prelude</literal>; the Haskell module
229 namespace is flat, and you must not conflict with any
230 Prelude module.)</para>
232 <para>Even though you have not imported the Prelude, most of
233 the built-in syntax still refers to the built-in Haskell
234 Prelude types and values, as specified by the Haskell
235 Report. For example, the type <literal>[Int]</literal>
236 still means <literal>Prelude.[] Int</literal>; tuples
237 continue to refer to the standard Prelude tuples; the
238 translation for list comprehensions continues to use
239 <literal>Prelude.map</literal> etc.</para>
241 <para>However, <option>-XNoImplicitPrelude</option> does
242 change the handling of certain built-in syntax: see <xref
243 linkend="rebindable-syntax"/>.</para>
248 <term><option>-XImplicitParams</option></term>
250 <para>Enables implicit parameters (see <xref
251 linkend="implicit-parameters"/>). Currently also implied by
252 <option>-fglasgow-exts</option>.</para>
255 <literal>?<replaceable>varid</replaceable></literal>,
256 <literal>%<replaceable>varid</replaceable></literal>.</para>
261 <term><option>-XOverloadedStrings</option></term>
263 <para>Enables overloaded string literals (see <xref
264 linkend="overloaded-strings"/>).</para>
269 <term><option>-XScopedTypeVariables</option></term>
271 <para>Enables lexically-scoped type variables (see <xref
272 linkend="scoped-type-variables"/>). Implied by
273 <option>-fglasgow-exts</option>.</para>
278 <term><option>-XTemplateHaskell</option></term>
280 <para>Enables Template Haskell (see <xref
281 linkend="template-haskell"/>). This flag must
282 be given explicitly; it is no longer implied by
283 <option>-fglasgow-exts</option>.</para>
285 <para>Syntax stolen: <literal>[|</literal>,
286 <literal>[e|</literal>, <literal>[p|</literal>,
287 <literal>[d|</literal>, <literal>[t|</literal>,
288 <literal>$(</literal>,
289 <literal>$<replaceable>varid</replaceable></literal>.</para>
294 <term><option>-XQuasiQuotes</option></term>
296 <para>Enables quasiquotation (see <xref
297 linkend="th-quasiquotation"/>).</para>
300 <literal>[:<replaceable>varid</replaceable>|</literal>.</para>
307 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
308 <sect1 id="primitives">
309 <title>Unboxed types and primitive operations</title>
311 <para>GHC is built on a raft of primitive data types and operations.
312 While you really can use this stuff to write fast code,
313 we generally find it a lot less painful, and more satisfying in the
314 long run, to use higher-level language features and libraries. With
315 any luck, the code you write will be optimised to the efficient
316 unboxed version in any case. And if it isn't, we'd like to know
319 <para>We do not currently have good, up-to-date documentation about the
320 primitives, perhaps because they are mainly intended for internal use.
321 There used to be a long section about them here in the User Guide, but it
322 became out of date, and wrong information is worse than none.</para>
324 <para>The Real Truth about what primitive types there are, and what operations
325 work over those types, is held in the file
326 <filename>compiler/prelude/primops.txt.pp</filename>.
327 This file is used directly to generate GHC's primitive-operation definitions, so
328 it is always correct! It is also intended for processing into text.</para>
331 the result of such processing is part of the description of the
333 url="http://www.haskell.org/ghc/docs/papers/core.ps.gz">External
334 Core language</ulink>.
335 So that document is a good place to look for a type-set version.
336 We would be very happy if someone wanted to volunteer to produce an XML
337 back end to the program that processes <filename>primops.txt</filename> so that
338 we could include the results here in the User Guide.</para>
340 <para>What follows here is a brief summary of some main points.</para>
342 <sect2 id="glasgow-unboxed">
347 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
350 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
351 that values of that type are represented by a pointer to a heap
352 object. The representation of a Haskell <literal>Int</literal>, for
353 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
354 type, however, is represented by the value itself, no pointers or heap
355 allocation are involved.
359 Unboxed types correspond to the “raw machine” types you
360 would use in C: <literal>Int#</literal> (long int),
361 <literal>Double#</literal> (double), <literal>Addr#</literal>
362 (void *), etc. The <emphasis>primitive operations</emphasis>
363 (PrimOps) on these types are what you might expect; e.g.,
364 <literal>(+#)</literal> is addition on
365 <literal>Int#</literal>s, and is the machine-addition that we all
366 know and love—usually one instruction.
369 <para> For some primitive types we have special syntax for literals.
370 Anything that would be an integer lexeme followed by a
371 <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
372 <literal>32#</literal> and <literal>-0x3A#</literal>. Likewise,
373 any non-negative integer literal followed by
374 <literal>##</literal> is a <literal>Word#</literal> literal.
375 Likewise, any floating point literal followed by a
376 <literal>#</literal> is a <literal>Float#</literal> literal, and
377 followed by <literal>##</literal> is a
378 <literal>Double#</literal>. Finally, a string literal followed by a
379 <literal>#</literal>, e.g. <literal>"foo"#</literal>,
380 is a <literal>Addr#</literal> literal.
384 Primitive (unboxed) types cannot be defined in Haskell, and are
385 therefore built into the language and compiler. Primitive types are
386 always unlifted; that is, a value of a primitive type cannot be
387 bottom. We use the convention that primitive types, values, and
388 operations have a <literal>#</literal> suffix.
392 Primitive values are often represented by a simple bit-pattern, such
393 as <literal>Int#</literal>, <literal>Float#</literal>,
394 <literal>Double#</literal>. But this is not necessarily the case:
395 a primitive value might be represented by a pointer to a
396 heap-allocated object. Examples include
397 <literal>Array#</literal>, the type of primitive arrays. A
398 primitive array is heap-allocated because it is too big a value to fit
399 in a register, and would be too expensive to copy around; in a sense,
400 it is accidental that it is represented by a pointer. If a pointer
401 represents a primitive value, then it really does point to that value:
402 no unevaluated thunks, no indirections…nothing can be at the
403 other end of the pointer than the primitive value.
404 A numerically-intensive program using unboxed types can
405 go a <emphasis>lot</emphasis> faster than its “standard”
406 counterpart—we saw a threefold speedup on one example.
410 There are some restrictions on the use of primitive types:
412 <listitem><para>The main restriction
413 is that you can't pass a primitive value to a polymorphic
414 function or store one in a polymorphic data type. This rules out
415 things like <literal>[Int#]</literal> (i.e. lists of primitive
416 integers). The reason for this restriction is that polymorphic
417 arguments and constructor fields are assumed to be pointers: if an
418 unboxed integer is stored in one of these, the garbage collector would
419 attempt to follow it, leading to unpredictable space leaks. Or a
420 <function>seq</function> operation on the polymorphic component may
421 attempt to dereference the pointer, with disastrous results. Even
422 worse, the unboxed value might be larger than a pointer
423 (<literal>Double#</literal> for instance).
426 <listitem><para> You cannot define a newtype whose representation type
427 (the argument type of the data constructor) is an unboxed type. Thus,
433 <listitem><para> You cannot bind a variable with an unboxed type
434 in a <emphasis>top-level</emphasis> binding.
436 <listitem><para> You cannot bind a variable with an unboxed type
437 in a <emphasis>recursive</emphasis> binding.
439 <listitem><para> You may bind unboxed variables in a (non-recursive,
440 non-top-level) pattern binding, but any such variable causes the entire
442 to become strict. For example:
444 data Foo = Foo Int Int#
446 f x = let (Foo a b, w) = ..rhs.. in ..body..
448 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
450 is strict, and the program behaves as if you had written
452 data Foo = Foo Int Int#
454 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
463 <sect2 id="unboxed-tuples">
464 <title>Unboxed Tuples
468 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
469 they're available by default with <option>-fglasgow-exts</option>. An
470 unboxed tuple looks like this:
482 where <literal>e_1..e_n</literal> are expressions of any
483 type (primitive or non-primitive). The type of an unboxed tuple looks
488 Unboxed tuples are used for functions that need to return multiple
489 values, but they avoid the heap allocation normally associated with
490 using fully-fledged tuples. When an unboxed tuple is returned, the
491 components are put directly into registers or on the stack; the
492 unboxed tuple itself does not have a composite representation. Many
493 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
495 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
496 tuples to avoid unnecessary allocation during sequences of operations.
500 There are some pretty stringent restrictions on the use of unboxed tuples:
505 Values of unboxed tuple types are subject to the same restrictions as
506 other unboxed types; i.e. they may not be stored in polymorphic data
507 structures or passed to polymorphic functions.
514 No variable can have an unboxed tuple type, nor may a constructor or function
515 argument have an unboxed tuple type. The following are all illegal:
519 data Foo = Foo (# Int, Int #)
521 f :: (# Int, Int #) -> (# Int, Int #)
524 g :: (# Int, Int #) -> Int
527 h x = let y = (# x,x #) in ...
534 The typical use of unboxed tuples is simply to return multiple values,
535 binding those multiple results with a <literal>case</literal> expression, thus:
537 f x y = (# x+1, y-1 #)
538 g x = case f x x of { (# a, b #) -> a + b }
540 You can have an unboxed tuple in a pattern binding, thus
542 f x = let (# p,q #) = h x in ..body..
544 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
545 the resulting binding is lazy like any other Haskell pattern binding. The
546 above example desugars like this:
548 f x = let t = case h x o f{ (# p,q #) -> (p,q)
553 Indeed, the bindings can even be recursive.
560 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
562 <sect1 id="syntax-extns">
563 <title>Syntactic extensions</title>
565 <!-- ====================== HIERARCHICAL MODULES ======================= -->
567 <sect2 id="hierarchical-modules">
568 <title>Hierarchical Modules</title>
570 <para>GHC supports a small extension to the syntax of module
571 names: a module name is allowed to contain a dot
572 <literal>‘.’</literal>. This is also known as the
573 “hierarchical module namespace” extension, because
574 it extends the normally flat Haskell module namespace into a
575 more flexible hierarchy of modules.</para>
577 <para>This extension has very little impact on the language
578 itself; modules names are <emphasis>always</emphasis> fully
579 qualified, so you can just think of the fully qualified module
580 name as <quote>the module name</quote>. In particular, this
581 means that the full module name must be given after the
582 <literal>module</literal> keyword at the beginning of the
583 module; for example, the module <literal>A.B.C</literal> must
586 <programlisting>module A.B.C</programlisting>
589 <para>It is a common strategy to use the <literal>as</literal>
590 keyword to save some typing when using qualified names with
591 hierarchical modules. For example:</para>
594 import qualified Control.Monad.ST.Strict as ST
597 <para>For details on how GHC searches for source and interface
598 files in the presence of hierarchical modules, see <xref
599 linkend="search-path"/>.</para>
601 <para>GHC comes with a large collection of libraries arranged
602 hierarchically; see the accompanying <ulink
603 url="../libraries/index.html">library
604 documentation</ulink>. More libraries to install are available
606 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
609 <!-- ====================== PATTERN GUARDS ======================= -->
611 <sect2 id="pattern-guards">
612 <title>Pattern guards</title>
615 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
616 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
620 Suppose we have an abstract data type of finite maps, with a
624 lookup :: FiniteMap -> Int -> Maybe Int
627 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
628 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
632 clunky env var1 var2 | ok1 && ok2 = val1 + val2
633 | otherwise = var1 + var2
644 The auxiliary functions are
648 maybeToBool :: Maybe a -> Bool
649 maybeToBool (Just x) = True
650 maybeToBool Nothing = False
652 expectJust :: Maybe a -> a
653 expectJust (Just x) = x
654 expectJust Nothing = error "Unexpected Nothing"
658 What is <function>clunky</function> doing? The guard <literal>ok1 &&
659 ok2</literal> checks that both lookups succeed, using
660 <function>maybeToBool</function> to convert the <function>Maybe</function>
661 types to booleans. The (lazily evaluated) <function>expectJust</function>
662 calls extract the values from the results of the lookups, and binds the
663 returned values to <varname>val1</varname> and <varname>val2</varname>
664 respectively. If either lookup fails, then clunky takes the
665 <literal>otherwise</literal> case and returns the sum of its arguments.
669 This is certainly legal Haskell, but it is a tremendously verbose and
670 un-obvious way to achieve the desired effect. Arguably, a more direct way
671 to write clunky would be to use case expressions:
675 clunky env var1 var2 = case lookup env var1 of
677 Just val1 -> case lookup env var2 of
679 Just val2 -> val1 + val2
685 This is a bit shorter, but hardly better. Of course, we can rewrite any set
686 of pattern-matching, guarded equations as case expressions; that is
687 precisely what the compiler does when compiling equations! The reason that
688 Haskell provides guarded equations is because they allow us to write down
689 the cases we want to consider, one at a time, independently of each other.
690 This structure is hidden in the case version. Two of the right-hand sides
691 are really the same (<function>fail</function>), and the whole expression
692 tends to become more and more indented.
696 Here is how I would write clunky:
701 | Just val1 <- lookup env var1
702 , Just val2 <- lookup env var2
704 ...other equations for clunky...
708 The semantics should be clear enough. The qualifiers are matched in order.
709 For a <literal><-</literal> qualifier, which I call a pattern guard, the
710 right hand side is evaluated and matched against the pattern on the left.
711 If the match fails then the whole guard fails and the next equation is
712 tried. If it succeeds, then the appropriate binding takes place, and the
713 next qualifier is matched, in the augmented environment. Unlike list
714 comprehensions, however, the type of the expression to the right of the
715 <literal><-</literal> is the same as the type of the pattern to its
716 left. The bindings introduced by pattern guards scope over all the
717 remaining guard qualifiers, and over the right hand side of the equation.
721 Just as with list comprehensions, boolean expressions can be freely mixed
722 with among the pattern guards. For example:
733 Haskell's current guards therefore emerge as a special case, in which the
734 qualifier list has just one element, a boolean expression.
738 <!-- ===================== View patterns =================== -->
740 <sect2 id="view-patterns">
745 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
746 More information and examples of view patterns can be found on the
747 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
752 View patterns are somewhat like pattern guards that can be nested inside
753 of other patterns. They are a convenient way of pattern-matching
754 against values of abstract types. For example, in a programming language
755 implementation, we might represent the syntax of the types of the
764 view :: Type -> TypeView
766 -- additional operations for constructing Typ's ...
769 The representation of Typ is held abstract, permitting implementations
770 to use a fancy representation (e.g., hash-consing to manage sharing).
772 Without view patterns, using this signature a little inconvenient:
774 size :: Typ -> Integer
775 size t = case view t of
777 Arrow t1 t2 -> size t1 + size t2
780 It is necessary to iterate the case, rather than using an equational
781 function definition. And the situation is even worse when the matching
782 against <literal>t</literal> is buried deep inside another pattern.
786 View patterns permit calling the view function inside the pattern and
787 matching against the result:
789 size (view -> Unit) = 1
790 size (view -> Arrow t1 t2) = size t1 + size t2
793 That is, we add a new form of pattern, written
794 <replaceable>expression</replaceable> <literal>-></literal>
795 <replaceable>pattern</replaceable> that means "apply the expression to
796 whatever we're trying to match against, and then match the result of
797 that application against the pattern". The expression can be any Haskell
798 expression of function type, and view patterns can be used wherever
803 The semantics of a pattern <literal>(</literal>
804 <replaceable>exp</replaceable> <literal>-></literal>
805 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
811 <para>The variables bound by the view pattern are the variables bound by
812 <replaceable>pat</replaceable>.
816 Any variables in <replaceable>exp</replaceable> are bound occurrences,
817 but variables bound "to the left" in a pattern are in scope. This
818 feature permits, for example, one argument to a function to be used in
819 the view of another argument. For example, the function
820 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
821 written using view patterns as follows:
824 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
825 ...other equations for clunky...
830 More precisely, the scoping rules are:
834 In a single pattern, variables bound by patterns to the left of a view
835 pattern expression are in scope. For example:
837 example :: Maybe ((String -> Integer,Integer), String) -> Bool
838 example Just ((f,_), f -> 4) = True
841 Additionally, in function definitions, variables bound by matching earlier curried
842 arguments may be used in view pattern expressions in later arguments:
844 example :: (String -> Integer) -> String -> Bool
845 example f (f -> 4) = True
847 That is, the scoping is the same as it would be if the curried arguments
848 were collected into a tuple.
854 In mutually recursive bindings, such as <literal>let</literal>,
855 <literal>where</literal>, or the top level, view patterns in one
856 declaration may not mention variables bound by other declarations. That
857 is, each declaration must be self-contained. For example, the following
858 program is not allowed:
865 restriction in the future; the only cost is that type checking patterns
866 would get a little more complicated.)
876 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
877 <replaceable>T1</replaceable> <literal>-></literal>
878 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
879 a <replaceable>T2</replaceable>, then the whole view pattern matches a
880 <replaceable>T1</replaceable>.
883 <listitem><para> Matching: To the equations in Section 3.17.3 of the
884 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
885 Report</ulink>, add the following:
887 case v of { (e -> p) -> e1 ; _ -> e2 }
889 case (e v) of { p -> e1 ; _ -> e2 }
891 That is, to match a variable <replaceable>v</replaceable> against a pattern
892 <literal>(</literal> <replaceable>exp</replaceable>
893 <literal>-></literal> <replaceable>pat</replaceable>
894 <literal>)</literal>, evaluate <literal>(</literal>
895 <replaceable>exp</replaceable> <replaceable> v</replaceable>
896 <literal>)</literal> and match the result against
897 <replaceable>pat</replaceable>.
900 <listitem><para> Efficiency: When the same view function is applied in
901 multiple branches of a function definition or a case expression (e.g.,
902 in <literal>size</literal> above), GHC makes an attempt to collect these
903 applications into a single nested case expression, so that the view
904 function is only applied once. Pattern compilation in GHC follows the
905 matrix algorithm described in Chapter 4 of <ulink
906 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
907 Implementation of Functional Programming Languages</ulink>. When the
908 top rows of the first column of a matrix are all view patterns with the
909 "same" expression, these patterns are transformed into a single nested
910 case. This includes, for example, adjacent view patterns that line up
913 f ((view -> A, p1), p2) = e1
914 f ((view -> B, p3), p4) = e2
918 <para> The current notion of when two view pattern expressions are "the
919 same" is very restricted: it is not even full syntactic equality.
920 However, it does include variables, literals, applications, and tuples;
921 e.g., two instances of <literal>view ("hi", "there")</literal> will be
922 collected. However, the current implementation does not compare up to
923 alpha-equivalence, so two instances of <literal>(x, view x ->
924 y)</literal> will not be coalesced.
934 <!-- ===================== Recursive do-notation =================== -->
936 <sect2 id="mdo-notation">
937 <title>The recursive do-notation
940 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
941 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
942 by Levent Erkok, John Launchbury,
943 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
944 This paper is essential reading for anyone making non-trivial use of mdo-notation,
945 and we do not repeat it here.
948 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
949 that is, the variables bound in a do-expression are visible only in the textually following
950 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
951 group. It turns out that several applications can benefit from recursive bindings in
952 the do-notation, and this extension provides the necessary syntactic support.
955 Here is a simple (yet contrived) example:
958 import Control.Monad.Fix
960 justOnes = mdo xs <- Just (1:xs)
964 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
968 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
971 class Monad m => MonadFix m where
972 mfix :: (a -> m a) -> m a
975 The function <literal>mfix</literal>
976 dictates how the required recursion operation should be performed. For example,
977 <literal>justOnes</literal> desugars as follows:
979 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
981 For full details of the way in which mdo is typechecked and desugared, see
982 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
983 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
986 If recursive bindings are required for a monad,
987 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
988 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
989 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
990 for Haskell's internal state monad (strict and lazy, respectively).
993 Here are some important points in using the recursive-do notation:
996 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
997 than <literal>do</literal>).
1001 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
1002 <literal>-fglasgow-exts</literal>.
1006 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
1007 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
1008 be distinct (Section 3.3 of the paper).
1012 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
1013 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
1014 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
1015 and improve termination (Section 3.2 of the paper).
1021 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb/">http://www.cse.ogi.edu/PacSoft/projects/rmb/</ulink>
1022 contains up to date information on recursive monadic bindings.
1026 Historical note: The old implementation of the mdo-notation (and most
1027 of the existing documents) used the name
1028 <literal>MonadRec</literal> for the class and the corresponding library.
1029 This name is not supported by GHC.
1035 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1037 <sect2 id="parallel-list-comprehensions">
1038 <title>Parallel List Comprehensions</title>
1039 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1041 <indexterm><primary>parallel list comprehensions</primary>
1044 <para>Parallel list comprehensions are a natural extension to list
1045 comprehensions. List comprehensions can be thought of as a nice
1046 syntax for writing maps and filters. Parallel comprehensions
1047 extend this to include the zipWith family.</para>
1049 <para>A parallel list comprehension has multiple independent
1050 branches of qualifier lists, each separated by a `|' symbol. For
1051 example, the following zips together two lists:</para>
1054 [ (x, y) | x <- xs | y <- ys ]
1057 <para>The behavior of parallel list comprehensions follows that of
1058 zip, in that the resulting list will have the same length as the
1059 shortest branch.</para>
1061 <para>We can define parallel list comprehensions by translation to
1062 regular comprehensions. Here's the basic idea:</para>
1064 <para>Given a parallel comprehension of the form: </para>
1067 [ e | p1 <- e11, p2 <- e12, ...
1068 | q1 <- e21, q2 <- e22, ...
1073 <para>This will be translated to: </para>
1076 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1077 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1082 <para>where `zipN' is the appropriate zip for the given number of
1087 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1089 <sect2 id="generalised-list-comprehensions">
1090 <title>Generalised (SQL-Like) List Comprehensions</title>
1091 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1093 <indexterm><primary>extended list comprehensions</primary>
1095 <indexterm><primary>group</primary></indexterm>
1096 <indexterm><primary>sql</primary></indexterm>
1099 <para>Generalised list comprehensions are a further enhancement to the
1100 list comprehension syntatic sugar to allow operations such as sorting
1101 and grouping which are familiar from SQL. They are fully described in the
1102 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1103 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1104 except that the syntax we use differs slightly from the paper.</para>
1105 <para>Here is an example:
1107 employees = [ ("Simon", "MS", 80)
1108 , ("Erik", "MS", 100)
1109 , ("Phil", "Ed", 40)
1110 , ("Gordon", "Ed", 45)
1111 , ("Paul", "Yale", 60)]
1113 output = [ (the dept, sum salary)
1114 | (name, dept, salary) <- employees
1115 , then group by dept
1116 , then sortWith by (sum salary)
1119 In this example, the list <literal>output</literal> would take on
1123 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1126 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1127 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1128 function that is exported by <literal>GHC.Exts</literal>.)</para>
1130 <para>There are five new forms of comprehension qualifier,
1131 all introduced by the (existing) keyword <literal>then</literal>:
1139 This statement requires that <literal>f</literal> have the type <literal>
1140 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1141 motivating example, as this form is used to apply <literal>take 5</literal>.
1152 This form is similar to the previous one, but allows you to create a function
1153 which will be passed as the first argument to f. As a consequence f must have
1154 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1155 from the type, this function lets f "project out" some information
1156 from the elements of the list it is transforming.</para>
1158 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1159 is supplied with a function that lets it find out the <literal>sum salary</literal>
1160 for any item in the list comprehension it transforms.</para>
1168 then group by e using f
1171 <para>This is the most general of the grouping-type statements. In this form,
1172 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1173 As with the <literal>then f by e</literal> case above, the first argument
1174 is a function supplied to f by the compiler which lets it compute e on every
1175 element of the list being transformed. However, unlike the non-grouping case,
1176 f additionally partitions the list into a number of sublists: this means that
1177 at every point after this statement, binders occurring before it in the comprehension
1178 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1179 this, let's look at an example:</para>
1182 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1183 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1184 groupRuns f = groupBy (\x y -> f x == f y)
1186 output = [ (the x, y)
1187 | x <- ([1..3] ++ [1..2])
1189 , then group by x using groupRuns ]
1192 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1195 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1198 <para>Note that we have used the <literal>the</literal> function to change the type
1199 of x from a list to its original numeric type. The variable y, in contrast, is left
1200 unchanged from the list form introduced by the grouping.</para>
1210 <para>This form of grouping is essentially the same as the one described above. However,
1211 since no function to use for the grouping has been supplied it will fall back on the
1212 <literal>groupWith</literal> function defined in
1213 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1214 is the form of the group statement that we made use of in the opening example.</para>
1225 <para>With this form of the group statement, f is required to simply have the type
1226 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1227 comprehension so far directly. An example of this form is as follows:</para>
1233 , then group using inits]
1236 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1239 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1247 <!-- ===================== REBINDABLE SYNTAX =================== -->
1249 <sect2 id="rebindable-syntax">
1250 <title>Rebindable syntax</title>
1252 <para>GHC allows most kinds of built-in syntax to be rebound by
1253 the user, to facilitate replacing the <literal>Prelude</literal>
1254 with a home-grown version, for example.</para>
1256 <para>You may want to define your own numeric class
1257 hierarchy. It completely defeats that purpose if the
1258 literal "1" means "<literal>Prelude.fromInteger
1259 1</literal>", which is what the Haskell Report specifies.
1260 So the <option>-XNoImplicitPrelude</option> flag causes
1261 the following pieces of built-in syntax to refer to
1262 <emphasis>whatever is in scope</emphasis>, not the Prelude
1267 <para>An integer literal <literal>368</literal> means
1268 "<literal>fromInteger (368::Integer)</literal>", rather than
1269 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1272 <listitem><para>Fractional literals are handed in just the same way,
1273 except that the translation is
1274 <literal>fromRational (3.68::Rational)</literal>.
1277 <listitem><para>The equality test in an overloaded numeric pattern
1278 uses whatever <literal>(==)</literal> is in scope.
1281 <listitem><para>The subtraction operation, and the
1282 greater-than-or-equal test, in <literal>n+k</literal> patterns
1283 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1287 <para>Negation (e.g. "<literal>- (f x)</literal>")
1288 means "<literal>negate (f x)</literal>", both in numeric
1289 patterns, and expressions.
1293 <para>"Do" notation is translated using whatever
1294 functions <literal>(>>=)</literal>,
1295 <literal>(>>)</literal>, and <literal>fail</literal>,
1296 are in scope (not the Prelude
1297 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1298 comprehensions, are unaffected. </para></listitem>
1302 notation (see <xref linkend="arrow-notation"/>)
1303 uses whatever <literal>arr</literal>,
1304 <literal>(>>>)</literal>, <literal>first</literal>,
1305 <literal>app</literal>, <literal>(|||)</literal> and
1306 <literal>loop</literal> functions are in scope. But unlike the
1307 other constructs, the types of these functions must match the
1308 Prelude types very closely. Details are in flux; if you want
1312 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1313 even if that is a little unexpected. For example, the
1314 static semantics of the literal <literal>368</literal>
1315 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1316 <literal>fromInteger</literal> to have any of the types:
1318 fromInteger :: Integer -> Integer
1319 fromInteger :: forall a. Foo a => Integer -> a
1320 fromInteger :: Num a => a -> Integer
1321 fromInteger :: Integer -> Bool -> Bool
1325 <para>Be warned: this is an experimental facility, with
1326 fewer checks than usual. Use <literal>-dcore-lint</literal>
1327 to typecheck the desugared program. If Core Lint is happy
1328 you should be all right.</para>
1332 <sect2 id="postfix-operators">
1333 <title>Postfix operators</title>
1336 GHC allows a small extension to the syntax of left operator sections, which
1337 allows you to define postfix operators. The extension is this: the left section
1341 is equivalent (from the point of view of both type checking and execution) to the expression
1345 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1346 The strict Haskell 98 interpretation is that the section is equivalent to
1350 That is, the operator must be a function of two arguments. GHC allows it to
1351 take only one argument, and that in turn allows you to write the function
1354 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1355 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1356 change their behaviour, of course.)
1358 <para>The extension does not extend to the left-hand side of function
1359 definitions; you must define such a function in prefix form.</para>
1363 <sect2 id="disambiguate-fields">
1364 <title>Record field disambiguation</title>
1366 In record construction and record pattern matching
1367 it is entirely unambiguous which field is referred to, even if there are two different
1368 data types in scope with a common field name. For example:
1371 data S = MkS { x :: Int, y :: Bool }
1376 data T = MkT { x :: Int }
1378 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1380 ok2 n = MkT { x = n+1 } -- Unambiguous
1382 bad1 k = k { x = 3 } -- Ambiguous
1383 bad2 k = x k -- Ambiguous
1385 Even though there are two <literal>x</literal>'s in scope,
1386 it is clear that the <literal>x</literal> in the pattern in the
1387 definition of <literal>ok1</literal> can only mean the field
1388 <literal>x</literal> from type <literal>S</literal>. Similarly for
1389 the function <literal>ok2</literal>. However, in the record update
1390 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1391 it is not clear which of the two types is intended.
1394 Haskell 98 regards all four as ambiguous, but with the
1395 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1396 the former two. The rules are precisely the same as those for instance
1397 declarations in Haskell 98, where the method names on the left-hand side
1398 of the method bindings in an instance declaration refer unambiguously
1399 to the method of that class (provided they are in scope at all), even
1400 if there are other variables in scope with the same name.
1401 This reduces the clutter of qualified names when you import two
1402 records from different modules that use the same field name.
1406 <!-- ===================== Record puns =================== -->
1408 <sect2 id="record-puns">
1413 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1417 When using records, it is common to write a pattern that binds a
1418 variable with the same name as a record field, such as:
1421 data C = C {a :: Int}
1427 Record punning permits the variable name to be elided, so one can simply
1434 to mean the same pattern as above. That is, in a record pattern, the
1435 pattern <literal>a</literal> expands into the pattern <literal>a =
1436 a</literal> for the same name <literal>a</literal>.
1440 Note that puns and other patterns can be mixed in the same record:
1442 data C = C {a :: Int, b :: Int}
1443 f (C {a, b = 4}) = a
1445 and that puns can be used wherever record patterns occur (e.g. in
1446 <literal>let</literal> bindings or at the top-level).
1450 Record punning can also be used in an expression, writing, for example,
1456 let a = 1 in C {a = a}
1459 Note that this expansion is purely syntactic, so the record pun
1460 expression refers to the nearest enclosing variable that is spelled the
1461 same as the field name.
1466 <!-- ===================== Record wildcards =================== -->
1468 <sect2 id="record-wildcards">
1469 <title>Record wildcards
1473 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1477 For records with many fields, it can be tiresome to write out each field
1478 individually in a record pattern, as in
1480 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1481 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1486 Record wildcard syntax permits a (<literal>..</literal>) in a record
1487 pattern, where each elided field <literal>f</literal> is replaced by the
1488 pattern <literal>f = f</literal>. For example, the above pattern can be
1491 f (C {a = 1, ..}) = b + c + d
1496 Note that wildcards can be mixed with other patterns, including puns
1497 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1498 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1499 wherever record patterns occur, including in <literal>let</literal>
1500 bindings and at the top-level. For example, the top-level binding
1504 defines <literal>b</literal>, <literal>c</literal>, and
1505 <literal>d</literal>.
1509 Record wildcards can also be used in expressions, writing, for example,
1512 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1518 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1521 Note that this expansion is purely syntactic, so the record wildcard
1522 expression refers to the nearest enclosing variables that are spelled
1523 the same as the omitted field names.
1528 <!-- ===================== Local fixity declarations =================== -->
1530 <sect2 id="local-fixity-declarations">
1531 <title>Local Fixity Declarations
1534 <para>A careful reading of the Haskell 98 Report reveals that fixity
1535 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1536 <literal>infixr</literal>) are permitted to appear inside local bindings
1537 such those introduced by <literal>let</literal> and
1538 <literal>where</literal>. However, the Haskell Report does not specify
1539 the semantics of such bindings very precisely.
1542 <para>In GHC, a fixity declaration may accompany a local binding:
1549 and the fixity declaration applies wherever the binding is in scope.
1550 For example, in a <literal>let</literal>, it applies in the right-hand
1551 sides of other <literal>let</literal>-bindings and the body of the
1552 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1553 expressions (<xref linkend="mdo-notation"/>), the local fixity
1554 declarations of a <literal>let</literal> statement scope over other
1555 statements in the group, just as the bound name does.
1559 Moreover, a local fixity declaration *must* accompany a local binding of
1560 that name: it is not possible to revise the fixity of name bound
1563 let infixr 9 $ in ...
1566 Because local fixity declarations are technically Haskell 98, no flag is
1567 necessary to enable them.
1574 <!-- TYPE SYSTEM EXTENSIONS -->
1575 <sect1 id="data-type-extensions">
1576 <title>Extensions to data types and type synonyms</title>
1578 <sect2 id="nullary-types">
1579 <title>Data types with no constructors</title>
1581 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1582 a data type with no constructors. For example:</para>
1586 data T a -- T :: * -> *
1589 <para>Syntactically, the declaration lacks the "= constrs" part. The
1590 type can be parameterised over types of any kind, but if the kind is
1591 not <literal>*</literal> then an explicit kind annotation must be used
1592 (see <xref linkend="kinding"/>).</para>
1594 <para>Such data types have only one value, namely bottom.
1595 Nevertheless, they can be useful when defining "phantom types".</para>
1598 <sect2 id="infix-tycons">
1599 <title>Infix type constructors, classes, and type variables</title>
1602 GHC allows type constructors, classes, and type variables to be operators, and
1603 to be written infix, very much like expressions. More specifically:
1606 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1607 The lexical syntax is the same as that for data constructors.
1610 Data type and type-synonym declarations can be written infix, parenthesised
1611 if you want further arguments. E.g.
1613 data a :*: b = Foo a b
1614 type a :+: b = Either a b
1615 class a :=: b where ...
1617 data (a :**: b) x = Baz a b x
1618 type (a :++: b) y = Either (a,b) y
1622 Types, and class constraints, can be written infix. For example
1625 f :: (a :=: b) => a -> b
1629 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1630 The lexical syntax is the same as that for variable operators, excluding "(.)",
1631 "(!)", and "(*)". In a binding position, the operator must be
1632 parenthesised. For example:
1634 type T (+) = Int + Int
1638 liftA2 :: Arrow (~>)
1639 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1645 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1646 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1649 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1650 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1651 sets the fixity for a data constructor and the corresponding type constructor. For example:
1655 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1656 and similarly for <literal>:*:</literal>.
1657 <literal>Int `a` Bool</literal>.
1660 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1667 <sect2 id="type-synonyms">
1668 <title>Liberalised type synonyms</title>
1671 Type synonyms are like macros at the type level, and
1672 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1673 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1675 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1676 in a type synonym, thus:
1678 type Discard a = forall b. Show b => a -> b -> (a, String)
1683 g :: Discard Int -> (Int,String) -- A rank-2 type
1690 You can write an unboxed tuple in a type synonym:
1692 type Pr = (# Int, Int #)
1700 You can apply a type synonym to a forall type:
1702 type Foo a = a -> a -> Bool
1704 f :: Foo (forall b. b->b)
1706 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1708 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1713 You can apply a type synonym to a partially applied type synonym:
1715 type Generic i o = forall x. i x -> o x
1718 foo :: Generic Id []
1720 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1722 foo :: forall x. x -> [x]
1730 GHC currently does kind checking before expanding synonyms (though even that
1734 After expanding type synonyms, GHC does validity checking on types, looking for
1735 the following mal-formedness which isn't detected simply by kind checking:
1738 Type constructor applied to a type involving for-alls.
1741 Unboxed tuple on left of an arrow.
1744 Partially-applied type synonym.
1748 this will be rejected:
1750 type Pr = (# Int, Int #)
1755 because GHC does not allow unboxed tuples on the left of a function arrow.
1760 <sect2 id="existential-quantification">
1761 <title>Existentially quantified data constructors
1765 The idea of using existential quantification in data type declarations
1766 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1767 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1768 London, 1991). It was later formalised by Laufer and Odersky
1769 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1770 TOPLAS, 16(5), pp1411-1430, 1994).
1771 It's been in Lennart
1772 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1773 proved very useful. Here's the idea. Consider the declaration:
1779 data Foo = forall a. MkFoo a (a -> Bool)
1786 The data type <literal>Foo</literal> has two constructors with types:
1792 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1799 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1800 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1801 For example, the following expression is fine:
1807 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1813 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1814 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1815 isUpper</function> packages a character with a compatible function. These
1816 two things are each of type <literal>Foo</literal> and can be put in a list.
1820 What can we do with a value of type <literal>Foo</literal>?. In particular,
1821 what happens when we pattern-match on <function>MkFoo</function>?
1827 f (MkFoo val fn) = ???
1833 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1834 are compatible, the only (useful) thing we can do with them is to
1835 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1842 f (MkFoo val fn) = fn val
1848 What this allows us to do is to package heterogeneous values
1849 together with a bunch of functions that manipulate them, and then treat
1850 that collection of packages in a uniform manner. You can express
1851 quite a bit of object-oriented-like programming this way.
1854 <sect3 id="existential">
1855 <title>Why existential?
1859 What has this to do with <emphasis>existential</emphasis> quantification?
1860 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1866 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1872 But Haskell programmers can safely think of the ordinary
1873 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1874 adding a new existential quantification construct.
1879 <sect3 id="existential-with-context">
1880 <title>Existentials and type classes</title>
1883 An easy extension is to allow
1884 arbitrary contexts before the constructor. For example:
1890 data Baz = forall a. Eq a => Baz1 a a
1891 | forall b. Show b => Baz2 b (b -> b)
1897 The two constructors have the types you'd expect:
1903 Baz1 :: forall a. Eq a => a -> a -> Baz
1904 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1910 But when pattern matching on <function>Baz1</function> the matched values can be compared
1911 for equality, and when pattern matching on <function>Baz2</function> the first matched
1912 value can be converted to a string (as well as applying the function to it).
1913 So this program is legal:
1920 f (Baz1 p q) | p == q = "Yes"
1922 f (Baz2 v fn) = show (fn v)
1928 Operationally, in a dictionary-passing implementation, the
1929 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1930 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1931 extract it on pattern matching.
1936 <sect3 id="existential-records">
1937 <title>Record Constructors</title>
1940 GHC allows existentials to be used with records syntax as well. For example:
1943 data Counter a = forall self. NewCounter
1945 , _inc :: self -> self
1946 , _display :: self -> IO ()
1950 Here <literal>tag</literal> is a public field, with a well-typed selector
1951 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1952 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1953 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1954 compile-time error. In other words, <emphasis>GHC defines a record selector function
1955 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1956 (This example used an underscore in the fields for which record selectors
1957 will not be defined, but that is only programming style; GHC ignores them.)
1961 To make use of these hidden fields, we need to create some helper functions:
1964 inc :: Counter a -> Counter a
1965 inc (NewCounter x i d t) = NewCounter
1966 { _this = i x, _inc = i, _display = d, tag = t }
1968 display :: Counter a -> IO ()
1969 display NewCounter{ _this = x, _display = d } = d x
1972 Now we can define counters with different underlying implementations:
1975 counterA :: Counter String
1976 counterA = NewCounter
1977 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1979 counterB :: Counter String
1980 counterB = NewCounter
1981 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1984 display (inc counterA) -- prints "1"
1985 display (inc (inc counterB)) -- prints "##"
1988 At the moment, record update syntax is only supported for Haskell 98 data types,
1989 so the following function does <emphasis>not</emphasis> work:
1992 -- This is invalid; use explicit NewCounter instead for now
1993 setTag :: Counter a -> a -> Counter a
1994 setTag obj t = obj{ tag = t }
2003 <title>Restrictions</title>
2006 There are several restrictions on the ways in which existentially-quantified
2007 constructors can be use.
2016 When pattern matching, each pattern match introduces a new,
2017 distinct, type for each existential type variable. These types cannot
2018 be unified with any other type, nor can they escape from the scope of
2019 the pattern match. For example, these fragments are incorrect:
2027 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2028 is the result of <function>f1</function>. One way to see why this is wrong is to
2029 ask what type <function>f1</function> has:
2033 f1 :: Foo -> a -- Weird!
2037 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2042 f1 :: forall a. Foo -> a -- Wrong!
2046 The original program is just plain wrong. Here's another sort of error
2050 f2 (Baz1 a b) (Baz1 p q) = a==q
2054 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2055 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2056 from the two <function>Baz1</function> constructors.
2064 You can't pattern-match on an existentially quantified
2065 constructor in a <literal>let</literal> or <literal>where</literal> group of
2066 bindings. So this is illegal:
2070 f3 x = a==b where { Baz1 a b = x }
2073 Instead, use a <literal>case</literal> expression:
2076 f3 x = case x of Baz1 a b -> a==b
2079 In general, you can only pattern-match
2080 on an existentially-quantified constructor in a <literal>case</literal> expression or
2081 in the patterns of a function definition.
2083 The reason for this restriction is really an implementation one.
2084 Type-checking binding groups is already a nightmare without
2085 existentials complicating the picture. Also an existential pattern
2086 binding at the top level of a module doesn't make sense, because it's
2087 not clear how to prevent the existentially-quantified type "escaping".
2088 So for now, there's a simple-to-state restriction. We'll see how
2096 You can't use existential quantification for <literal>newtype</literal>
2097 declarations. So this is illegal:
2101 newtype T = forall a. Ord a => MkT a
2105 Reason: a value of type <literal>T</literal> must be represented as a
2106 pair of a dictionary for <literal>Ord t</literal> and a value of type
2107 <literal>t</literal>. That contradicts the idea that
2108 <literal>newtype</literal> should have no concrete representation.
2109 You can get just the same efficiency and effect by using
2110 <literal>data</literal> instead of <literal>newtype</literal>. If
2111 there is no overloading involved, then there is more of a case for
2112 allowing an existentially-quantified <literal>newtype</literal>,
2113 because the <literal>data</literal> version does carry an
2114 implementation cost, but single-field existentially quantified
2115 constructors aren't much use. So the simple restriction (no
2116 existential stuff on <literal>newtype</literal>) stands, unless there
2117 are convincing reasons to change it.
2125 You can't use <literal>deriving</literal> to define instances of a
2126 data type with existentially quantified data constructors.
2128 Reason: in most cases it would not make sense. For example:;
2131 data T = forall a. MkT [a] deriving( Eq )
2134 To derive <literal>Eq</literal> in the standard way we would need to have equality
2135 between the single component of two <function>MkT</function> constructors:
2139 (MkT a) == (MkT b) = ???
2142 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2143 It's just about possible to imagine examples in which the derived instance
2144 would make sense, but it seems altogether simpler simply to prohibit such
2145 declarations. Define your own instances!
2156 <!-- ====================== Generalised algebraic data types ======================= -->
2158 <sect2 id="gadt-style">
2159 <title>Declaring data types with explicit constructor signatures</title>
2161 <para>GHC allows you to declare an algebraic data type by
2162 giving the type signatures of constructors explicitly. For example:
2166 Just :: a -> Maybe a
2168 The form is called a "GADT-style declaration"
2169 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2170 can only be declared using this form.</para>
2171 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2172 For example, these two declarations are equivalent:
2174 data Foo = forall a. MkFoo a (a -> Bool)
2175 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2178 <para>Any data type that can be declared in standard Haskell-98 syntax
2179 can also be declared using GADT-style syntax.
2180 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2181 they treat class constraints on the data constructors differently.
2182 Specifically, if the constructor is given a type-class context, that
2183 context is made available by pattern matching. For example:
2186 MkSet :: Eq a => [a] -> Set a
2188 makeSet :: Eq a => [a] -> Set a
2189 makeSet xs = MkSet (nub xs)
2191 insert :: a -> Set a -> Set a
2192 insert a (MkSet as) | a `elem` as = MkSet as
2193 | otherwise = MkSet (a:as)
2195 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2196 gives rise to a <literal>(Eq a)</literal>
2197 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2198 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2199 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2200 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2201 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2202 In the example, the equality dictionary is used to satisfy the equality constraint
2203 generated by the call to <literal>elem</literal>, so that the type of
2204 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2207 For example, one possible application is to reify dictionaries:
2209 data NumInst a where
2210 MkNumInst :: Num a => NumInst a
2212 intInst :: NumInst Int
2215 plus :: NumInst a -> a -> a -> a
2216 plus MkNumInst p q = p + q
2218 Here, a value of type <literal>NumInst a</literal> is equivalent
2219 to an explicit <literal>(Num a)</literal> dictionary.
2222 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2223 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2227 = Num a => MkNumInst (NumInst a)
2229 Notice that, unlike the situation when declaring an existential, there is
2230 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2231 data type's universally quantified type variable <literal>a</literal>.
2232 A constructor may have both universal and existential type variables: for example,
2233 the following two declarations are equivalent:
2236 = forall b. (Num a, Eq b) => MkT1 a b
2238 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2241 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2242 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2243 In Haskell 98 the definition
2245 data Eq a => Set' a = MkSet' [a]
2247 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2248 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2249 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2250 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2251 GHC's behaviour is much more useful, as well as much more intuitive.
2255 The rest of this section gives further details about GADT-style data
2260 The result type of each data constructor must begin with the type constructor being defined.
2261 If the result type of all constructors
2262 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2263 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2264 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2268 The type signature of
2269 each constructor is independent, and is implicitly universally quantified as usual.
2270 Different constructors may have different universally-quantified type variables
2271 and different type-class constraints.
2272 For example, this is fine:
2275 T1 :: Eq b => b -> T b
2276 T2 :: (Show c, Ix c) => c -> [c] -> T c
2281 Unlike a Haskell-98-style
2282 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2283 have no scope. Indeed, one can write a kind signature instead:
2285 data Set :: * -> * where ...
2287 or even a mixture of the two:
2289 data Foo a :: (* -> *) -> * where ...
2291 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2294 data Foo a (b :: * -> *) where ...
2300 You can use strictness annotations, in the obvious places
2301 in the constructor type:
2304 Lit :: !Int -> Term Int
2305 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2306 Pair :: Term a -> Term b -> Term (a,b)
2311 You can use a <literal>deriving</literal> clause on a GADT-style data type
2312 declaration. For example, these two declarations are equivalent
2314 data Maybe1 a where {
2315 Nothing1 :: Maybe1 a ;
2316 Just1 :: a -> Maybe1 a
2317 } deriving( Eq, Ord )
2319 data Maybe2 a = Nothing2 | Just2 a
2325 You can use record syntax on a GADT-style data type declaration:
2329 Adult { name :: String, children :: [Person] } :: Person
2330 Child { name :: String } :: Person
2332 As usual, for every constructor that has a field <literal>f</literal>, the type of
2333 field <literal>f</literal> must be the same (modulo alpha conversion).
2336 At the moment, record updates are not yet possible with GADT-style declarations,
2337 so support is limited to record construction, selection and pattern matching.
2340 aPerson = Adult { name = "Fred", children = [] }
2342 shortName :: Person -> Bool
2343 hasChildren (Adult { children = kids }) = not (null kids)
2344 hasChildren (Child {}) = False
2349 As in the case of existentials declared using the Haskell-98-like record syntax
2350 (<xref linkend="existential-records"/>),
2351 record-selector functions are generated only for those fields that have well-typed
2353 Here is the example of that section, in GADT-style syntax:
2355 data Counter a where
2356 NewCounter { _this :: self
2357 , _inc :: self -> self
2358 , _display :: self -> IO ()
2363 As before, only one selector function is generated here, that for <literal>tag</literal>.
2364 Nevertheless, you can still use all the field names in pattern matching and record construction.
2366 </itemizedlist></para>
2370 <title>Generalised Algebraic Data Types (GADTs)</title>
2372 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2373 by allowing constructors to have richer return types. Here is an example:
2376 Lit :: Int -> Term Int
2377 Succ :: Term Int -> Term Int
2378 IsZero :: Term Int -> Term Bool
2379 If :: Term Bool -> Term a -> Term a -> Term a
2380 Pair :: Term a -> Term b -> Term (a,b)
2382 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2383 case with ordinary data types. This generality allows us to
2384 write a well-typed <literal>eval</literal> function
2385 for these <literal>Terms</literal>:
2389 eval (Succ t) = 1 + eval t
2390 eval (IsZero t) = eval t == 0
2391 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2392 eval (Pair e1 e2) = (eval e1, eval e2)
2394 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2395 For example, in the right hand side of the equation
2400 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2401 A precise specification of the type rules is beyond what this user manual aspires to,
2402 but the design closely follows that described in
2404 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2405 unification-based type inference for GADTs</ulink>,
2407 The general principle is this: <emphasis>type refinement is only carried out
2408 based on user-supplied type annotations</emphasis>.
2409 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2410 and lots of obscure error messages will
2411 occur. However, the refinement is quite general. For example, if we had:
2413 eval :: Term a -> a -> a
2414 eval (Lit i) j = i+j
2416 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2417 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2418 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2421 These and many other examples are given in papers by Hongwei Xi, and
2422 Tim Sheard. There is a longer introduction
2423 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2425 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
2426 may use different notation to that implemented in GHC.
2429 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2430 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2433 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2434 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2435 The result type of each constructor must begin with the type constructor being defined,
2436 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2437 For example, in the <literal>Term</literal> data
2438 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2439 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
2444 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2445 an ordinary data type.
2449 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2453 Lit { val :: Int } :: Term Int
2454 Succ { num :: Term Int } :: Term Int
2455 Pred { num :: Term Int } :: Term Int
2456 IsZero { arg :: Term Int } :: Term Bool
2457 Pair { arg1 :: Term a
2460 If { cnd :: Term Bool
2465 However, for GADTs there is the following additional constraint:
2466 every constructor that has a field <literal>f</literal> must have
2467 the same result type (modulo alpha conversion)
2468 Hence, in the above example, we cannot merge the <literal>num</literal>
2469 and <literal>arg</literal> fields above into a
2470 single name. Although their field types are both <literal>Term Int</literal>,
2471 their selector functions actually have different types:
2474 num :: Term Int -> Term Int
2475 arg :: Term Bool -> Term Int
2485 <!-- ====================== End of Generalised algebraic data types ======================= -->
2487 <sect1 id="deriving">
2488 <title>Extensions to the "deriving" mechanism</title>
2490 <sect2 id="deriving-inferred">
2491 <title>Inferred context for deriving clauses</title>
2494 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2497 data T0 f a = MkT0 a deriving( Eq )
2498 data T1 f a = MkT1 (f a) deriving( Eq )
2499 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2501 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2503 instance Eq a => Eq (T0 f a) where ...
2504 instance Eq (f a) => Eq (T1 f a) where ...
2505 instance Eq (f (f a)) => Eq (T2 f a) where ...
2507 The first of these is obviously fine. The second is still fine, although less obviously.
2508 The third is not Haskell 98, and risks losing termination of instances.
2511 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2512 each constraint in the inferred instance context must consist only of type variables,
2513 with no repetitions.
2516 This rule is applied regardless of flags. If you want a more exotic context, you can write
2517 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2521 <sect2 id="stand-alone-deriving">
2522 <title>Stand-alone deriving declarations</title>
2525 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2527 data Foo a = Bar a | Baz String
2529 deriving instance Eq a => Eq (Foo a)
2531 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2532 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2533 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2534 exactly as you would in an ordinary instance declaration.
2535 (In contrast the context is inferred in a <literal>deriving</literal> clause
2536 attached to a data type declaration.)
2538 A <literal>deriving instance</literal> declaration
2539 must obey the same rules concerning form and termination as ordinary instance declarations,
2540 controlled by the same flags; see <xref linkend="instance-decls"/>.
2543 Unlike a <literal>deriving</literal>
2544 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2545 than the data type (assuming you also use
2546 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2549 data Foo a = Bar a | Baz String
2551 deriving instance Eq a => Eq (Foo [a])
2552 deriving instance Eq a => Eq (Foo (Maybe a))
2554 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2555 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2558 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2559 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2562 newtype Foo a = MkFoo (State Int a)
2564 deriving instance MonadState Int Foo
2566 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2567 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2573 <sect2 id="deriving-typeable">
2574 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2577 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2578 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2579 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2580 classes <literal>Eq</literal>, <literal>Ord</literal>,
2581 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2584 GHC extends this list with two more classes that may be automatically derived
2585 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2586 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2587 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2588 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2590 <para>An instance of <literal>Typeable</literal> can only be derived if the
2591 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2592 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2594 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2595 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2597 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2598 are used, and only <literal>Typeable1</literal> up to
2599 <literal>Typeable7</literal> are provided in the library.)
2600 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2601 class, whose kind suits that of the data type constructor, and
2602 then writing the data type instance by hand.
2606 <sect2 id="newtype-deriving">
2607 <title>Generalised derived instances for newtypes</title>
2610 When you define an abstract type using <literal>newtype</literal>, you may want
2611 the new type to inherit some instances from its representation. In
2612 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2613 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2614 other classes you have to write an explicit instance declaration. For
2615 example, if you define
2618 newtype Dollars = Dollars Int
2621 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2622 explicitly define an instance of <literal>Num</literal>:
2625 instance Num Dollars where
2626 Dollars a + Dollars b = Dollars (a+b)
2629 All the instance does is apply and remove the <literal>newtype</literal>
2630 constructor. It is particularly galling that, since the constructor
2631 doesn't appear at run-time, this instance declaration defines a
2632 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2633 dictionary, only slower!
2637 <sect3> <title> Generalising the deriving clause </title>
2639 GHC now permits such instances to be derived instead,
2640 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2643 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2646 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2647 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2648 derives an instance declaration of the form
2651 instance Num Int => Num Dollars
2654 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2658 We can also derive instances of constructor classes in a similar
2659 way. For example, suppose we have implemented state and failure monad
2660 transformers, such that
2663 instance Monad m => Monad (State s m)
2664 instance Monad m => Monad (Failure m)
2666 In Haskell 98, we can define a parsing monad by
2668 type Parser tok m a = State [tok] (Failure m) a
2671 which is automatically a monad thanks to the instance declarations
2672 above. With the extension, we can make the parser type abstract,
2673 without needing to write an instance of class <literal>Monad</literal>, via
2676 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2679 In this case the derived instance declaration is of the form
2681 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2684 Notice that, since <literal>Monad</literal> is a constructor class, the
2685 instance is a <emphasis>partial application</emphasis> of the new type, not the
2686 entire left hand side. We can imagine that the type declaration is
2687 "eta-converted" to generate the context of the instance
2692 We can even derive instances of multi-parameter classes, provided the
2693 newtype is the last class parameter. In this case, a ``partial
2694 application'' of the class appears in the <literal>deriving</literal>
2695 clause. For example, given the class
2698 class StateMonad s m | m -> s where ...
2699 instance Monad m => StateMonad s (State s m) where ...
2701 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2703 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2704 deriving (Monad, StateMonad [tok])
2707 The derived instance is obtained by completing the application of the
2708 class to the new type:
2711 instance StateMonad [tok] (State [tok] (Failure m)) =>
2712 StateMonad [tok] (Parser tok m)
2717 As a result of this extension, all derived instances in newtype
2718 declarations are treated uniformly (and implemented just by reusing
2719 the dictionary for the representation type), <emphasis>except</emphasis>
2720 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2721 the newtype and its representation.
2725 <sect3> <title> A more precise specification </title>
2727 Derived instance declarations are constructed as follows. Consider the
2728 declaration (after expansion of any type synonyms)
2731 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2737 The <literal>ci</literal> are partial applications of
2738 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2739 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2742 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2745 The type <literal>t</literal> is an arbitrary type.
2748 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2749 nor in the <literal>ci</literal>, and
2752 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2753 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2754 should not "look through" the type or its constructor. You can still
2755 derive these classes for a newtype, but it happens in the usual way, not
2756 via this new mechanism.
2759 Then, for each <literal>ci</literal>, the derived instance
2762 instance ci t => ci (T v1...vk)
2764 As an example which does <emphasis>not</emphasis> work, consider
2766 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2768 Here we cannot derive the instance
2770 instance Monad (State s m) => Monad (NonMonad m)
2773 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2774 and so cannot be "eta-converted" away. It is a good thing that this
2775 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2776 not, in fact, a monad --- for the same reason. Try defining
2777 <literal>>>=</literal> with the correct type: you won't be able to.
2781 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2782 important, since we can only derive instances for the last one. If the
2783 <literal>StateMonad</literal> class above were instead defined as
2786 class StateMonad m s | m -> s where ...
2789 then we would not have been able to derive an instance for the
2790 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2791 classes usually have one "main" parameter for which deriving new
2792 instances is most interesting.
2794 <para>Lastly, all of this applies only for classes other than
2795 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2796 and <literal>Data</literal>, for which the built-in derivation applies (section
2797 4.3.3. of the Haskell Report).
2798 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2799 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2800 the standard method is used or the one described here.)
2807 <!-- TYPE SYSTEM EXTENSIONS -->
2808 <sect1 id="type-class-extensions">
2809 <title>Class and instances declarations</title>
2811 <sect2 id="multi-param-type-classes">
2812 <title>Class declarations</title>
2815 This section, and the next one, documents GHC's type-class extensions.
2816 There's lots of background in the paper <ulink
2817 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2818 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2819 Jones, Erik Meijer).
2822 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2826 <title>Multi-parameter type classes</title>
2828 Multi-parameter type classes are permitted. For example:
2832 class Collection c a where
2833 union :: c a -> c a -> c a
2841 <title>The superclasses of a class declaration</title>
2844 There are no restrictions on the context in a class declaration
2845 (which introduces superclasses), except that the class hierarchy must
2846 be acyclic. So these class declarations are OK:
2850 class Functor (m k) => FiniteMap m k where
2853 class (Monad m, Monad (t m)) => Transform t m where
2854 lift :: m a -> (t m) a
2860 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2861 of "acyclic" involves only the superclass relationships. For example,
2867 op :: D b => a -> b -> b
2870 class C a => D a where { ... }
2874 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2875 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2876 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2883 <sect3 id="class-method-types">
2884 <title>Class method types</title>
2887 Haskell 98 prohibits class method types to mention constraints on the
2888 class type variable, thus:
2891 fromList :: [a] -> s a
2892 elem :: Eq a => a -> s a -> Bool
2894 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2895 contains the constraint <literal>Eq a</literal>, constrains only the
2896 class type variable (in this case <literal>a</literal>).
2897 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2904 <sect2 id="functional-dependencies">
2905 <title>Functional dependencies
2908 <para> Functional dependencies are implemented as described by Mark Jones
2909 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2910 In Proceedings of the 9th European Symposium on Programming,
2911 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2915 Functional dependencies are introduced by a vertical bar in the syntax of a
2916 class declaration; e.g.
2918 class (Monad m) => MonadState s m | m -> s where ...
2920 class Foo a b c | a b -> c where ...
2922 There should be more documentation, but there isn't (yet). Yell if you need it.
2925 <sect3><title>Rules for functional dependencies </title>
2927 In a class declaration, all of the class type variables must be reachable (in the sense
2928 mentioned in <xref linkend="type-restrictions"/>)
2929 from the free variables of each method type.
2933 class Coll s a where
2935 insert :: s -> a -> s
2938 is not OK, because the type of <literal>empty</literal> doesn't mention
2939 <literal>a</literal>. Functional dependencies can make the type variable
2942 class Coll s a | s -> a where
2944 insert :: s -> a -> s
2947 Alternatively <literal>Coll</literal> might be rewritten
2950 class Coll s a where
2952 insert :: s a -> a -> s a
2956 which makes the connection between the type of a collection of
2957 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2958 Occasionally this really doesn't work, in which case you can split the
2966 class CollE s => Coll s a where
2967 insert :: s -> a -> s
2974 <title>Background on functional dependencies</title>
2976 <para>The following description of the motivation and use of functional dependencies is taken
2977 from the Hugs user manual, reproduced here (with minor changes) by kind
2978 permission of Mark Jones.
2981 Consider the following class, intended as part of a
2982 library for collection types:
2984 class Collects e ce where
2986 insert :: e -> ce -> ce
2987 member :: e -> ce -> Bool
2989 The type variable e used here represents the element type, while ce is the type
2990 of the container itself. Within this framework, we might want to define
2991 instances of this class for lists or characteristic functions (both of which
2992 can be used to represent collections of any equality type), bit sets (which can
2993 be used to represent collections of characters), or hash tables (which can be
2994 used to represent any collection whose elements have a hash function). Omitting
2995 standard implementation details, this would lead to the following declarations:
2997 instance Eq e => Collects e [e] where ...
2998 instance Eq e => Collects e (e -> Bool) where ...
2999 instance Collects Char BitSet where ...
3000 instance (Hashable e, Collects a ce)
3001 => Collects e (Array Int ce) where ...
3003 All this looks quite promising; we have a class and a range of interesting
3004 implementations. Unfortunately, there are some serious problems with the class
3005 declaration. First, the empty function has an ambiguous type:
3007 empty :: Collects e ce => ce
3009 By "ambiguous" we mean that there is a type variable e that appears on the left
3010 of the <literal>=></literal> symbol, but not on the right. The problem with
3011 this is that, according to the theoretical foundations of Haskell overloading,
3012 we cannot guarantee a well-defined semantics for any term with an ambiguous
3016 We can sidestep this specific problem by removing the empty member from the
3017 class declaration. However, although the remaining members, insert and member,
3018 do not have ambiguous types, we still run into problems when we try to use
3019 them. For example, consider the following two functions:
3021 f x y = insert x . insert y
3024 for which GHC infers the following types:
3026 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3027 g :: (Collects Bool c, Collects Char c) => c -> c
3029 Notice that the type for f allows the two parameters x and y to be assigned
3030 different types, even though it attempts to insert each of the two values, one
3031 after the other, into the same collection. If we're trying to model collections
3032 that contain only one type of value, then this is clearly an inaccurate
3033 type. Worse still, the definition for g is accepted, without causing a type
3034 error. As a result, the error in this code will not be flagged at the point
3035 where it appears. Instead, it will show up only when we try to use g, which
3036 might even be in a different module.
3039 <sect4><title>An attempt to use constructor classes</title>
3042 Faced with the problems described above, some Haskell programmers might be
3043 tempted to use something like the following version of the class declaration:
3045 class Collects e c where
3047 insert :: e -> c e -> c e
3048 member :: e -> c e -> Bool
3050 The key difference here is that we abstract over the type constructor c that is
3051 used to form the collection type c e, and not over that collection type itself,
3052 represented by ce in the original class declaration. This avoids the immediate
3053 problems that we mentioned above: empty has type <literal>Collects e c => c
3054 e</literal>, which is not ambiguous.
3057 The function f from the previous section has a more accurate type:
3059 f :: (Collects e c) => e -> e -> c e -> c e
3061 The function g from the previous section is now rejected with a type error as
3062 we would hope because the type of f does not allow the two arguments to have
3064 This, then, is an example of a multiple parameter class that does actually work
3065 quite well in practice, without ambiguity problems.
3066 There is, however, a catch. This version of the Collects class is nowhere near
3067 as general as the original class seemed to be: only one of the four instances
3068 for <literal>Collects</literal>
3069 given above can be used with this version of Collects because only one of
3070 them---the instance for lists---has a collection type that can be written in
3071 the form c e, for some type constructor c, and element type e.
3075 <sect4><title>Adding functional dependencies</title>
3078 To get a more useful version of the Collects class, Hugs provides a mechanism
3079 that allows programmers to specify dependencies between the parameters of a
3080 multiple parameter class (For readers with an interest in theoretical
3081 foundations and previous work: The use of dependency information can be seen
3082 both as a generalization of the proposal for `parametric type classes' that was
3083 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3084 later framework for "improvement" of qualified types. The
3085 underlying ideas are also discussed in a more theoretical and abstract setting
3086 in a manuscript [implparam], where they are identified as one point in a
3087 general design space for systems of implicit parameterization.).
3089 To start with an abstract example, consider a declaration such as:
3091 class C a b where ...
3093 which tells us simply that C can be thought of as a binary relation on types
3094 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3095 included in the definition of classes to add information about dependencies
3096 between parameters, as in the following examples:
3098 class D a b | a -> b where ...
3099 class E a b | a -> b, b -> a where ...
3101 The notation <literal>a -> b</literal> used here between the | and where
3102 symbols --- not to be
3103 confused with a function type --- indicates that the a parameter uniquely
3104 determines the b parameter, and might be read as "a determines b." Thus D is
3105 not just a relation, but actually a (partial) function. Similarly, from the two
3106 dependencies that are included in the definition of E, we can see that E
3107 represents a (partial) one-one mapping between types.
3110 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3111 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3112 m>=0, meaning that the y parameters are uniquely determined by the x
3113 parameters. Spaces can be used as separators if more than one variable appears
3114 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3115 annotated with multiple dependencies using commas as separators, as in the
3116 definition of E above. Some dependencies that we can write in this notation are
3117 redundant, and will be rejected because they don't serve any useful
3118 purpose, and may instead indicate an error in the program. Examples of
3119 dependencies like this include <literal>a -> a </literal>,
3120 <literal>a -> a a </literal>,
3121 <literal>a -> </literal>, etc. There can also be
3122 some redundancy if multiple dependencies are given, as in
3123 <literal>a->b</literal>,
3124 <literal>b->c </literal>, <literal>a->c </literal>, and
3125 in which some subset implies the remaining dependencies. Examples like this are
3126 not treated as errors. Note that dependencies appear only in class
3127 declarations, and not in any other part of the language. In particular, the
3128 syntax for instance declarations, class constraints, and types is completely
3132 By including dependencies in a class declaration, we provide a mechanism for
3133 the programmer to specify each multiple parameter class more precisely. The
3134 compiler, on the other hand, is responsible for ensuring that the set of
3135 instances that are in scope at any given point in the program is consistent
3136 with any declared dependencies. For example, the following pair of instance
3137 declarations cannot appear together in the same scope because they violate the
3138 dependency for D, even though either one on its own would be acceptable:
3140 instance D Bool Int where ...
3141 instance D Bool Char where ...
3143 Note also that the following declaration is not allowed, even by itself:
3145 instance D [a] b where ...
3147 The problem here is that this instance would allow one particular choice of [a]
3148 to be associated with more than one choice for b, which contradicts the
3149 dependency specified in the definition of D. More generally, this means that,
3150 in any instance of the form:
3152 instance D t s where ...
3154 for some particular types t and s, the only variables that can appear in s are
3155 the ones that appear in t, and hence, if the type t is known, then s will be
3156 uniquely determined.
3159 The benefit of including dependency information is that it allows us to define
3160 more general multiple parameter classes, without ambiguity problems, and with
3161 the benefit of more accurate types. To illustrate this, we return to the
3162 collection class example, and annotate the original definition of <literal>Collects</literal>
3163 with a simple dependency:
3165 class Collects e ce | ce -> e where
3167 insert :: e -> ce -> ce
3168 member :: e -> ce -> Bool
3170 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3171 determined by the type of the collection ce. Note that both parameters of
3172 Collects are of kind *; there are no constructor classes here. Note too that
3173 all of the instances of Collects that we gave earlier can be used
3174 together with this new definition.
3177 What about the ambiguity problems that we encountered with the original
3178 definition? The empty function still has type Collects e ce => ce, but it is no
3179 longer necessary to regard that as an ambiguous type: Although the variable e
3180 does not appear on the right of the => symbol, the dependency for class
3181 Collects tells us that it is uniquely determined by ce, which does appear on
3182 the right of the => symbol. Hence the context in which empty is used can still
3183 give enough information to determine types for both ce and e, without
3184 ambiguity. More generally, we need only regard a type as ambiguous if it
3185 contains a variable on the left of the => that is not uniquely determined
3186 (either directly or indirectly) by the variables on the right.
3189 Dependencies also help to produce more accurate types for user defined
3190 functions, and hence to provide earlier detection of errors, and less cluttered
3191 types for programmers to work with. Recall the previous definition for a
3194 f x y = insert x y = insert x . insert y
3196 for which we originally obtained a type:
3198 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3200 Given the dependency information that we have for Collects, however, we can
3201 deduce that a and b must be equal because they both appear as the second
3202 parameter in a Collects constraint with the same first parameter c. Hence we
3203 can infer a shorter and more accurate type for f:
3205 f :: (Collects a c) => a -> a -> c -> c
3207 In a similar way, the earlier definition of g will now be flagged as a type error.
3210 Although we have given only a few examples here, it should be clear that the
3211 addition of dependency information can help to make multiple parameter classes
3212 more useful in practice, avoiding ambiguity problems, and allowing more general
3213 sets of instance declarations.
3219 <sect2 id="instance-decls">
3220 <title>Instance declarations</title>
3222 <sect3 id="instance-rules">
3223 <title>Relaxed rules for instance declarations</title>
3225 <para>An instance declaration has the form
3227 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 ...
3229 The part before the "<literal>=></literal>" is the
3230 <emphasis>context</emphasis>, while the part after the
3231 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3235 In Haskell 98 the head of an instance declaration
3236 must be of the form <literal>C (T a1 ... an)</literal>, where
3237 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3238 and the <literal>a1 ... an</literal> are distinct type variables.
3239 Furthermore, the assertions in the context of the instance declaration
3240 must be of the form <literal>C a</literal> where <literal>a</literal>
3241 is a type variable that occurs in the head.
3244 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3245 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3246 the context and head of the instance declaration can each consist of arbitrary
3247 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3251 The Paterson Conditions: for each assertion in the context
3253 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3254 <listitem><para>The assertion has fewer constructors and variables (taken together
3255 and counting repetitions) than the head</para></listitem>
3259 <listitem><para>The Coverage Condition. For each functional dependency,
3260 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3261 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3262 every type variable in
3263 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3264 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3265 substitution mapping each type variable in the class declaration to the
3266 corresponding type in the instance declaration.
3269 These restrictions ensure that context reduction terminates: each reduction
3270 step makes the problem smaller by at least one
3271 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3272 if you give the <option>-XUndecidableInstances</option>
3273 flag (<xref linkend="undecidable-instances"/>).
3274 You can find lots of background material about the reason for these
3275 restrictions in the paper <ulink
3276 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3277 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3280 For example, these are OK:
3282 instance C Int [a] -- Multiple parameters
3283 instance Eq (S [a]) -- Structured type in head
3285 -- Repeated type variable in head
3286 instance C4 a a => C4 [a] [a]
3287 instance Stateful (ST s) (MutVar s)
3289 -- Head can consist of type variables only
3291 instance (Eq a, Show b) => C2 a b
3293 -- Non-type variables in context
3294 instance Show (s a) => Show (Sized s a)
3295 instance C2 Int a => C3 Bool [a]
3296 instance C2 Int a => C3 [a] b
3300 -- Context assertion no smaller than head
3301 instance C a => C a where ...
3302 -- (C b b) has more more occurrences of b than the head
3303 instance C b b => Foo [b] where ...
3308 The same restrictions apply to instances generated by
3309 <literal>deriving</literal> clauses. Thus the following is accepted:
3311 data MinHeap h a = H a (h a)
3314 because the derived instance
3316 instance (Show a, Show (h a)) => Show (MinHeap h a)
3318 conforms to the above rules.
3322 A useful idiom permitted by the above rules is as follows.
3323 If one allows overlapping instance declarations then it's quite
3324 convenient to have a "default instance" declaration that applies if
3325 something more specific does not:
3333 <sect3 id="undecidable-instances">
3334 <title>Undecidable instances</title>
3337 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3338 For example, sometimes you might want to use the following to get the
3339 effect of a "class synonym":
3341 class (C1 a, C2 a, C3 a) => C a where { }
3343 instance (C1 a, C2 a, C3 a) => C a where { }
3345 This allows you to write shorter signatures:
3351 f :: (C1 a, C2 a, C3 a) => ...
3353 The restrictions on functional dependencies (<xref
3354 linkend="functional-dependencies"/>) are particularly troublesome.
3355 It is tempting to introduce type variables in the context that do not appear in
3356 the head, something that is excluded by the normal rules. For example:
3358 class HasConverter a b | a -> b where
3361 data Foo a = MkFoo a
3363 instance (HasConverter a b,Show b) => Show (Foo a) where
3364 show (MkFoo value) = show (convert value)
3366 This is dangerous territory, however. Here, for example, is a program that would make the
3371 instance F [a] [[a]]
3372 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3374 Similarly, it can be tempting to lift the coverage condition:
3376 class Mul a b c | a b -> c where
3377 (.*.) :: a -> b -> c
3379 instance Mul Int Int Int where (.*.) = (*)
3380 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3381 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3383 The third instance declaration does not obey the coverage condition;
3384 and indeed the (somewhat strange) definition:
3386 f = \ b x y -> if b then x .*. [y] else y
3388 makes instance inference go into a loop, because it requires the constraint
3389 <literal>(Mul a [b] b)</literal>.
3392 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3393 the experimental flag <option>-XUndecidableInstances</option>
3394 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3395 both the Paterson Conditions and the Coverage Condition
3396 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3397 fixed-depth recursion stack. If you exceed the stack depth you get a
3398 sort of backtrace, and the opportunity to increase the stack depth
3399 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3405 <sect3 id="instance-overlap">
3406 <title>Overlapping instances</title>
3408 In general, <emphasis>GHC requires that that it be unambiguous which instance
3410 should be used to resolve a type-class constraint</emphasis>. This behaviour
3411 can be modified by two flags: <option>-XOverlappingInstances</option>
3412 <indexterm><primary>-XOverlappingInstances
3413 </primary></indexterm>
3414 and <option>-XIncoherentInstances</option>
3415 <indexterm><primary>-XIncoherentInstances
3416 </primary></indexterm>, as this section discusses. Both these
3417 flags are dynamic flags, and can be set on a per-module basis, using
3418 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3420 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3421 it tries to match every instance declaration against the
3423 by instantiating the head of the instance declaration. For example, consider
3426 instance context1 => C Int a where ... -- (A)
3427 instance context2 => C a Bool where ... -- (B)
3428 instance context3 => C Int [a] where ... -- (C)
3429 instance context4 => C Int [Int] where ... -- (D)
3431 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3432 but (C) and (D) do not. When matching, GHC takes
3433 no account of the context of the instance declaration
3434 (<literal>context1</literal> etc).
3435 GHC's default behaviour is that <emphasis>exactly one instance must match the
3436 constraint it is trying to resolve</emphasis>.
3437 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3438 including both declarations (A) and (B), say); an error is only reported if a
3439 particular constraint matches more than one.
3443 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3444 more than one instance to match, provided there is a most specific one. For
3445 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3446 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3447 most-specific match, the program is rejected.
3450 However, GHC is conservative about committing to an overlapping instance. For example:
3455 Suppose that from the RHS of <literal>f</literal> we get the constraint
3456 <literal>C Int [b]</literal>. But
3457 GHC does not commit to instance (C), because in a particular
3458 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3459 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3460 So GHC rejects the program.
3461 (If you add the flag <option>-XIncoherentInstances</option>,
3462 GHC will instead pick (C), without complaining about
3463 the problem of subsequent instantiations.)
3466 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3467 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3468 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3469 it instead. In this case, GHC will refrain from
3470 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3471 as before) but, rather than rejecting the program, it will infer the type
3473 f :: C Int b => [b] -> [b]
3475 That postpones the question of which instance to pick to the
3476 call site for <literal>f</literal>
3477 by which time more is known about the type <literal>b</literal>.
3480 The willingness to be overlapped or incoherent is a property of
3481 the <emphasis>instance declaration</emphasis> itself, controlled by the
3482 presence or otherwise of the <option>-XOverlappingInstances</option>
3483 and <option>-XIncoherentInstances</option> flags when that module is
3484 being defined. Neither flag is required in a module that imports and uses the
3485 instance declaration. Specifically, during the lookup process:
3488 An instance declaration is ignored during the lookup process if (a) a more specific
3489 match is found, and (b) the instance declaration was compiled with
3490 <option>-XOverlappingInstances</option>. The flag setting for the
3491 more-specific instance does not matter.
3494 Suppose an instance declaration does not match the constraint being looked up, but
3495 does unify with it, so that it might match when the constraint is further
3496 instantiated. Usually GHC will regard this as a reason for not committing to
3497 some other constraint. But if the instance declaration was compiled with
3498 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3499 check for that declaration.
3502 These rules make it possible for a library author to design a library that relies on
3503 overlapping instances without the library client having to know.
3506 If an instance declaration is compiled without
3507 <option>-XOverlappingInstances</option>,
3508 then that instance can never be overlapped. This could perhaps be
3509 inconvenient. Perhaps the rule should instead say that the
3510 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3511 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3512 at a usage site should be permitted regardless of how the instance declarations
3513 are compiled, if the <option>-XOverlappingInstances</option> flag is
3514 used at the usage site. (Mind you, the exact usage site can occasionally be
3515 hard to pin down.) We are interested to receive feedback on these points.
3517 <para>The <option>-XIncoherentInstances</option> flag implies the
3518 <option>-XOverlappingInstances</option> flag, but not vice versa.
3523 <title>Type synonyms in the instance head</title>
3526 <emphasis>Unlike Haskell 98, instance heads may use type
3527 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3528 As always, using a type synonym is just shorthand for
3529 writing the RHS of the type synonym definition. For example:
3533 type Point = (Int,Int)
3534 instance C Point where ...
3535 instance C [Point] where ...
3539 is legal. However, if you added
3543 instance C (Int,Int) where ...
3547 as well, then the compiler will complain about the overlapping
3548 (actually, identical) instance declarations. As always, type synonyms
3549 must be fully applied. You cannot, for example, write:
3554 instance Monad P where ...
3558 This design decision is independent of all the others, and easily
3559 reversed, but it makes sense to me.
3567 <sect2 id="overloaded-strings">
3568 <title>Overloaded string literals
3572 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3573 string literal has type <literal>String</literal>, but with overloaded string
3574 literals enabled (with <literal>-XOverloadedStrings</literal>)
3575 a string literal has type <literal>(IsString a) => a</literal>.
3578 This means that the usual string syntax can be used, e.g., for packed strings
3579 and other variations of string like types. String literals behave very much
3580 like integer literals, i.e., they can be used in both expressions and patterns.
3581 If used in a pattern the literal with be replaced by an equality test, in the same
3582 way as an integer literal is.
3585 The class <literal>IsString</literal> is defined as:
3587 class IsString a where
3588 fromString :: String -> a
3590 The only predefined instance is the obvious one to make strings work as usual:
3592 instance IsString [Char] where
3595 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3596 it explicitly (for example, to give an instance declaration for it), you can import it
3597 from module <literal>GHC.Exts</literal>.
3600 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3604 Each type in a default declaration must be an
3605 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3609 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3610 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3611 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3612 <emphasis>or</emphasis> <literal>IsString</literal>.
3621 import GHC.Exts( IsString(..) )
3623 newtype MyString = MyString String deriving (Eq, Show)
3624 instance IsString MyString where
3625 fromString = MyString
3627 greet :: MyString -> MyString
3628 greet "hello" = "world"
3632 print $ greet "hello"
3633 print $ greet "fool"
3637 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3638 to work since it gets translated into an equality comparison.
3644 <sect1 id="other-type-extensions">
3645 <title>Other type system extensions</title>
3647 <sect2 id="type-restrictions">
3648 <title>Type signatures</title>
3650 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3652 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3653 the form <emphasis>(class type-variable)</emphasis> or
3654 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3655 these type signatures are perfectly OK
3658 g :: Ord (T a ()) => ...
3662 GHC imposes the following restrictions on the constraints in a type signature.
3666 forall tv1..tvn (c1, ...,cn) => type
3669 (Here, we write the "foralls" explicitly, although the Haskell source
3670 language omits them; in Haskell 98, all the free type variables of an
3671 explicit source-language type signature are universally quantified,
3672 except for the class type variables in a class declaration. However,
3673 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3682 <emphasis>Each universally quantified type variable
3683 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3685 A type variable <literal>a</literal> is "reachable" if it appears
3686 in the same constraint as either a type variable free in
3687 <literal>type</literal>, or another reachable type variable.
3688 A value with a type that does not obey
3689 this reachability restriction cannot be used without introducing
3690 ambiguity; that is why the type is rejected.
3691 Here, for example, is an illegal type:
3695 forall a. Eq a => Int
3699 When a value with this type was used, the constraint <literal>Eq tv</literal>
3700 would be introduced where <literal>tv</literal> is a fresh type variable, and
3701 (in the dictionary-translation implementation) the value would be
3702 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3703 can never know which instance of <literal>Eq</literal> to use because we never
3704 get any more information about <literal>tv</literal>.
3708 that the reachability condition is weaker than saying that <literal>a</literal> is
3709 functionally dependent on a type variable free in
3710 <literal>type</literal> (see <xref
3711 linkend="functional-dependencies"/>). The reason for this is there
3712 might be a "hidden" dependency, in a superclass perhaps. So
3713 "reachable" is a conservative approximation to "functionally dependent".
3714 For example, consider:
3716 class C a b | a -> b where ...
3717 class C a b => D a b where ...
3718 f :: forall a b. D a b => a -> a
3720 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3721 but that is not immediately apparent from <literal>f</literal>'s type.
3727 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3728 universally quantified type variables <literal>tvi</literal></emphasis>.
3730 For example, this type is OK because <literal>C a b</literal> mentions the
3731 universally quantified type variable <literal>b</literal>:
3735 forall a. C a b => burble
3739 The next type is illegal because the constraint <literal>Eq b</literal> does not
3740 mention <literal>a</literal>:
3744 forall a. Eq b => burble
3748 The reason for this restriction is milder than the other one. The
3749 excluded types are never useful or necessary (because the offending
3750 context doesn't need to be witnessed at this point; it can be floated
3751 out). Furthermore, floating them out increases sharing. Lastly,
3752 excluding them is a conservative choice; it leaves a patch of
3753 territory free in case we need it later.
3767 <sect2 id="implicit-parameters">
3768 <title>Implicit parameters</title>
3770 <para> Implicit parameters are implemented as described in
3771 "Implicit parameters: dynamic scoping with static types",
3772 J Lewis, MB Shields, E Meijer, J Launchbury,
3773 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3777 <para>(Most of the following, still rather incomplete, documentation is
3778 due to Jeff Lewis.)</para>
3780 <para>Implicit parameter support is enabled with the option
3781 <option>-XImplicitParams</option>.</para>
3784 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3785 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3786 context. In Haskell, all variables are statically bound. Dynamic
3787 binding of variables is a notion that goes back to Lisp, but was later
3788 discarded in more modern incarnations, such as Scheme. Dynamic binding
3789 can be very confusing in an untyped language, and unfortunately, typed
3790 languages, in particular Hindley-Milner typed languages like Haskell,
3791 only support static scoping of variables.
3794 However, by a simple extension to the type class system of Haskell, we
3795 can support dynamic binding. Basically, we express the use of a
3796 dynamically bound variable as a constraint on the type. These
3797 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3798 function uses a dynamically-bound variable <literal>?x</literal>
3799 of type <literal>t'</literal>". For
3800 example, the following expresses the type of a sort function,
3801 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3803 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3805 The dynamic binding constraints are just a new form of predicate in the type class system.
3808 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3809 where <literal>x</literal> is
3810 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3811 Use of this construct also introduces a new
3812 dynamic-binding constraint in the type of the expression.
3813 For example, the following definition
3814 shows how we can define an implicitly parameterized sort function in
3815 terms of an explicitly parameterized <literal>sortBy</literal> function:
3817 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3819 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3825 <title>Implicit-parameter type constraints</title>
3827 Dynamic binding constraints behave just like other type class
3828 constraints in that they are automatically propagated. Thus, when a
3829 function is used, its implicit parameters are inherited by the
3830 function that called it. For example, our <literal>sort</literal> function might be used
3831 to pick out the least value in a list:
3833 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3834 least xs = head (sort xs)
3836 Without lifting a finger, the <literal>?cmp</literal> parameter is
3837 propagated to become a parameter of <literal>least</literal> as well. With explicit
3838 parameters, the default is that parameters must always be explicit
3839 propagated. With implicit parameters, the default is to always
3843 An implicit-parameter type constraint differs from other type class constraints in the
3844 following way: All uses of a particular implicit parameter must have
3845 the same type. This means that the type of <literal>(?x, ?x)</literal>
3846 is <literal>(?x::a) => (a,a)</literal>, and not
3847 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3851 <para> You can't have an implicit parameter in the context of a class or instance
3852 declaration. For example, both these declarations are illegal:
3854 class (?x::Int) => C a where ...
3855 instance (?x::a) => Foo [a] where ...
3857 Reason: exactly which implicit parameter you pick up depends on exactly where
3858 you invoke a function. But the ``invocation'' of instance declarations is done
3859 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3860 Easiest thing is to outlaw the offending types.</para>
3862 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3864 f :: (?x :: [a]) => Int -> Int
3867 g :: (Read a, Show a) => String -> String
3870 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3871 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3872 quite unambiguous, and fixes the type <literal>a</literal>.
3877 <title>Implicit-parameter bindings</title>
3880 An implicit parameter is <emphasis>bound</emphasis> using the standard
3881 <literal>let</literal> or <literal>where</literal> binding forms.
3882 For example, we define the <literal>min</literal> function by binding
3883 <literal>cmp</literal>.
3886 min = let ?cmp = (<=) in least
3890 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3891 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3892 (including in a list comprehension, or do-notation, or pattern guards),
3893 or a <literal>where</literal> clause.
3894 Note the following points:
3897 An implicit-parameter binding group must be a
3898 collection of simple bindings to implicit-style variables (no
3899 function-style bindings, and no type signatures); these bindings are
3900 neither polymorphic or recursive.
3903 You may not mix implicit-parameter bindings with ordinary bindings in a
3904 single <literal>let</literal>
3905 expression; use two nested <literal>let</literal>s instead.
3906 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3910 You may put multiple implicit-parameter bindings in a
3911 single binding group; but they are <emphasis>not</emphasis> treated
3912 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3913 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3914 parameter. The bindings are not nested, and may be re-ordered without changing
3915 the meaning of the program.
3916 For example, consider:
3918 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3920 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3921 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3923 f :: (?x::Int) => Int -> Int
3931 <sect3><title>Implicit parameters and polymorphic recursion</title>
3934 Consider these two definitions:
3937 len1 xs = let ?acc = 0 in len_acc1 xs
3940 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3945 len2 xs = let ?acc = 0 in len_acc2 xs
3947 len_acc2 :: (?acc :: Int) => [a] -> Int
3949 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3951 The only difference between the two groups is that in the second group
3952 <literal>len_acc</literal> is given a type signature.
3953 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3954 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3955 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3956 has a type signature, the recursive call is made to the
3957 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3958 as an implicit parameter. So we get the following results in GHCi:
3965 Adding a type signature dramatically changes the result! This is a rather
3966 counter-intuitive phenomenon, worth watching out for.
3970 <sect3><title>Implicit parameters and monomorphism</title>
3972 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3973 Haskell Report) to implicit parameters. For example, consider:
3981 Since the binding for <literal>y</literal> falls under the Monomorphism
3982 Restriction it is not generalised, so the type of <literal>y</literal> is
3983 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3984 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3985 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3986 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3987 <literal>y</literal> in the body of the <literal>let</literal> will see the
3988 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3989 <literal>14</literal>.
3994 <!-- ======================= COMMENTED OUT ========================
3996 We intend to remove linear implicit parameters, so I'm at least removing
3997 them from the 6.6 user manual
3999 <sect2 id="linear-implicit-parameters">
4000 <title>Linear implicit parameters</title>
4002 Linear implicit parameters are an idea developed by Koen Claessen,
4003 Mark Shields, and Simon PJ. They address the long-standing
4004 problem that monads seem over-kill for certain sorts of problem, notably:
4007 <listitem> <para> distributing a supply of unique names </para> </listitem>
4008 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4009 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4013 Linear implicit parameters are just like ordinary implicit parameters,
4014 except that they are "linear"; that is, they cannot be copied, and
4015 must be explicitly "split" instead. Linear implicit parameters are
4016 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4017 (The '/' in the '%' suggests the split!)
4022 import GHC.Exts( Splittable )
4024 data NameSupply = ...
4026 splitNS :: NameSupply -> (NameSupply, NameSupply)
4027 newName :: NameSupply -> Name
4029 instance Splittable NameSupply where
4033 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4034 f env (Lam x e) = Lam x' (f env e)
4037 env' = extend env x x'
4038 ...more equations for f...
4040 Notice that the implicit parameter %ns is consumed
4042 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4043 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4047 So the translation done by the type checker makes
4048 the parameter explicit:
4050 f :: NameSupply -> Env -> Expr -> Expr
4051 f ns env (Lam x e) = Lam x' (f ns1 env e)
4053 (ns1,ns2) = splitNS ns
4055 env = extend env x x'
4057 Notice the call to 'split' introduced by the type checker.
4058 How did it know to use 'splitNS'? Because what it really did
4059 was to introduce a call to the overloaded function 'split',
4060 defined by the class <literal>Splittable</literal>:
4062 class Splittable a where
4065 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4066 split for name supplies. But we can simply write
4072 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4074 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4075 <literal>GHC.Exts</literal>.
4080 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4081 are entirely distinct implicit parameters: you
4082 can use them together and they won't interfere with each other. </para>
4085 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4087 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4088 in the context of a class or instance declaration. </para></listitem>
4092 <sect3><title>Warnings</title>
4095 The monomorphism restriction is even more important than usual.
4096 Consider the example above:
4098 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4099 f env (Lam x e) = Lam x' (f env e)
4102 env' = extend env x x'
4104 If we replaced the two occurrences of x' by (newName %ns), which is
4105 usually a harmless thing to do, we get:
4107 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4108 f env (Lam x e) = Lam (newName %ns) (f env e)
4110 env' = extend env x (newName %ns)
4112 But now the name supply is consumed in <emphasis>three</emphasis> places
4113 (the two calls to newName,and the recursive call to f), so
4114 the result is utterly different. Urk! We don't even have
4118 Well, this is an experimental change. With implicit
4119 parameters we have already lost beta reduction anyway, and
4120 (as John Launchbury puts it) we can't sensibly reason about
4121 Haskell programs without knowing their typing.
4126 <sect3><title>Recursive functions</title>
4127 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4130 foo :: %x::T => Int -> [Int]
4132 foo n = %x : foo (n-1)
4134 where T is some type in class Splittable.</para>
4136 Do you get a list of all the same T's or all different T's
4137 (assuming that split gives two distinct T's back)?
4139 If you supply the type signature, taking advantage of polymorphic
4140 recursion, you get what you'd probably expect. Here's the
4141 translated term, where the implicit param is made explicit:
4144 foo x n = let (x1,x2) = split x
4145 in x1 : foo x2 (n-1)
4147 But if you don't supply a type signature, GHC uses the Hindley
4148 Milner trick of using a single monomorphic instance of the function
4149 for the recursive calls. That is what makes Hindley Milner type inference
4150 work. So the translation becomes
4154 foom n = x : foom (n-1)
4158 Result: 'x' is not split, and you get a list of identical T's. So the
4159 semantics of the program depends on whether or not foo has a type signature.
4162 You may say that this is a good reason to dislike linear implicit parameters
4163 and you'd be right. That is why they are an experimental feature.
4169 ================ END OF Linear Implicit Parameters commented out -->
4171 <sect2 id="kinding">
4172 <title>Explicitly-kinded quantification</title>
4175 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4176 to give the kind explicitly as (machine-checked) documentation,
4177 just as it is nice to give a type signature for a function. On some occasions,
4178 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4179 John Hughes had to define the data type:
4181 data Set cxt a = Set [a]
4182 | Unused (cxt a -> ())
4184 The only use for the <literal>Unused</literal> constructor was to force the correct
4185 kind for the type variable <literal>cxt</literal>.
4188 GHC now instead allows you to specify the kind of a type variable directly, wherever
4189 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4192 This flag enables kind signatures in the following places:
4194 <listitem><para><literal>data</literal> declarations:
4196 data Set (cxt :: * -> *) a = Set [a]
4197 </screen></para></listitem>
4198 <listitem><para><literal>type</literal> declarations:
4200 type T (f :: * -> *) = f Int
4201 </screen></para></listitem>
4202 <listitem><para><literal>class</literal> declarations:
4204 class (Eq a) => C (f :: * -> *) a where ...
4205 </screen></para></listitem>
4206 <listitem><para><literal>forall</literal>'s in type signatures:
4208 f :: forall (cxt :: * -> *). Set cxt Int
4209 </screen></para></listitem>
4214 The parentheses are required. Some of the spaces are required too, to
4215 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4216 will get a parse error, because "<literal>::*->*</literal>" is a
4217 single lexeme in Haskell.
4221 As part of the same extension, you can put kind annotations in types
4224 f :: (Int :: *) -> Int
4225 g :: forall a. a -> (a :: *)
4229 atype ::= '(' ctype '::' kind ')
4231 The parentheses are required.
4236 <sect2 id="universal-quantification">
4237 <title>Arbitrary-rank polymorphism
4241 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4242 allows us to say exactly what this means. For example:
4250 g :: forall b. (b -> b)
4252 The two are treated identically.
4256 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4257 explicit universal quantification in
4259 For example, all the following types are legal:
4261 f1 :: forall a b. a -> b -> a
4262 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4264 f2 :: (forall a. a->a) -> Int -> Int
4265 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4267 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4269 f4 :: Int -> (forall a. a -> a)
4271 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4272 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4273 The <literal>forall</literal> makes explicit the universal quantification that
4274 is implicitly added by Haskell.
4277 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4278 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4279 shows, the polymorphic type on the left of the function arrow can be overloaded.
4282 The function <literal>f3</literal> has a rank-3 type;
4283 it has rank-2 types on the left of a function arrow.
4286 GHC has three flags to control higher-rank types:
4289 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4292 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4295 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4296 That is, you can nest <literal>forall</literal>s
4297 arbitrarily deep in function arrows.
4298 In particular, a forall-type (also called a "type scheme"),
4299 including an operational type class context, is legal:
4301 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4302 of a function arrow </para> </listitem>
4303 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4304 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4305 field type signatures.</para> </listitem>
4306 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4307 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4311 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4312 a type variable any more!
4321 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4322 the types of the constructor arguments. Here are several examples:
4328 data T a = T1 (forall b. b -> b -> b) a
4330 data MonadT m = MkMonad { return :: forall a. a -> m a,
4331 bind :: forall a b. m a -> (a -> m b) -> m b
4334 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4340 The constructors have rank-2 types:
4346 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4347 MkMonad :: forall m. (forall a. a -> m a)
4348 -> (forall a b. m a -> (a -> m b) -> m b)
4350 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4356 Notice that you don't need to use a <literal>forall</literal> if there's an
4357 explicit context. For example in the first argument of the
4358 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4359 prefixed to the argument type. The implicit <literal>forall</literal>
4360 quantifies all type variables that are not already in scope, and are
4361 mentioned in the type quantified over.
4365 As for type signatures, implicit quantification happens for non-overloaded
4366 types too. So if you write this:
4369 data T a = MkT (Either a b) (b -> b)
4372 it's just as if you had written this:
4375 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4378 That is, since the type variable <literal>b</literal> isn't in scope, it's
4379 implicitly universally quantified. (Arguably, it would be better
4380 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4381 where that is what is wanted. Feedback welcomed.)
4385 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4386 the constructor to suitable values, just as usual. For example,
4397 a3 = MkSwizzle reverse
4400 a4 = let r x = Just x
4407 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4408 mkTs f x y = [T1 f x, T1 f y]
4414 The type of the argument can, as usual, be more general than the type
4415 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4416 does not need the <literal>Ord</literal> constraint.)
4420 When you use pattern matching, the bound variables may now have
4421 polymorphic types. For example:
4427 f :: T a -> a -> (a, Char)
4428 f (T1 w k) x = (w k x, w 'c' 'd')
4430 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4431 g (MkSwizzle s) xs f = s (map f (s xs))
4433 h :: MonadT m -> [m a] -> m [a]
4434 h m [] = return m []
4435 h m (x:xs) = bind m x $ \y ->
4436 bind m (h m xs) $ \ys ->
4443 In the function <function>h</function> we use the record selectors <literal>return</literal>
4444 and <literal>bind</literal> to extract the polymorphic bind and return functions
4445 from the <literal>MonadT</literal> data structure, rather than using pattern
4451 <title>Type inference</title>
4454 In general, type inference for arbitrary-rank types is undecidable.
4455 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4456 to get a decidable algorithm by requiring some help from the programmer.
4457 We do not yet have a formal specification of "some help" but the rule is this:
4460 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4461 provides an explicit polymorphic type for x, or GHC's type inference will assume
4462 that x's type has no foralls in it</emphasis>.
4465 What does it mean to "provide" an explicit type for x? You can do that by
4466 giving a type signature for x directly, using a pattern type signature
4467 (<xref linkend="scoped-type-variables"/>), thus:
4469 \ f :: (forall a. a->a) -> (f True, f 'c')
4471 Alternatively, you can give a type signature to the enclosing
4472 context, which GHC can "push down" to find the type for the variable:
4474 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4476 Here the type signature on the expression can be pushed inwards
4477 to give a type signature for f. Similarly, and more commonly,
4478 one can give a type signature for the function itself:
4480 h :: (forall a. a->a) -> (Bool,Char)
4481 h f = (f True, f 'c')
4483 You don't need to give a type signature if the lambda bound variable
4484 is a constructor argument. Here is an example we saw earlier:
4486 f :: T a -> a -> (a, Char)
4487 f (T1 w k) x = (w k x, w 'c' 'd')
4489 Here we do not need to give a type signature to <literal>w</literal>, because
4490 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4497 <sect3 id="implicit-quant">
4498 <title>Implicit quantification</title>
4501 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4502 user-written types, if and only if there is no explicit <literal>forall</literal>,
4503 GHC finds all the type variables mentioned in the type that are not already
4504 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4508 f :: forall a. a -> a
4515 h :: forall b. a -> b -> b
4521 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4524 f :: (a -> a) -> Int
4526 f :: forall a. (a -> a) -> Int
4528 f :: (forall a. a -> a) -> Int
4531 g :: (Ord a => a -> a) -> Int
4532 -- MEANS the illegal type
4533 g :: forall a. (Ord a => a -> a) -> Int
4535 g :: (forall a. Ord a => a -> a) -> Int
4537 The latter produces an illegal type, which you might think is silly,
4538 but at least the rule is simple. If you want the latter type, you
4539 can write your for-alls explicitly. Indeed, doing so is strongly advised
4546 <sect2 id="impredicative-polymorphism">
4547 <title>Impredicative polymorphism
4549 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4550 enabled with <option>-XImpredicativeTypes</option>.
4552 that you can call a polymorphic function at a polymorphic type, and
4553 parameterise data structures over polymorphic types. For example:
4555 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4556 f (Just g) = Just (g [3], g "hello")
4559 Notice here that the <literal>Maybe</literal> type is parameterised by the
4560 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4563 <para>The technical details of this extension are described in the paper
4564 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4565 type inference for higher-rank types and impredicativity</ulink>,
4566 which appeared at ICFP 2006.
4570 <sect2 id="scoped-type-variables">
4571 <title>Lexically scoped type variables
4575 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4576 which some type signatures are simply impossible to write. For example:
4578 f :: forall a. [a] -> [a]
4584 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4585 the entire definition of <literal>f</literal>.
4586 In particular, it is in scope at the type signature for <varname>ys</varname>.
4587 In Haskell 98 it is not possible to declare
4588 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4589 it becomes possible to do so.
4591 <para>Lexically-scoped type variables are enabled by
4592 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4594 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4595 variables work, compared to earlier releases. Read this section
4599 <title>Overview</title>
4601 <para>The design follows the following principles
4603 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4604 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4605 design.)</para></listitem>
4606 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4607 type variables. This means that every programmer-written type signature
4608 (including one that contains free scoped type variables) denotes a
4609 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4610 checker, and no inference is involved.</para></listitem>
4611 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4612 changing the program.</para></listitem>
4616 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4618 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4619 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4620 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4621 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4625 In Haskell, a programmer-written type signature is implicitly quantified over
4626 its free type variables (<ulink
4627 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4629 of the Haskell Report).
4630 Lexically scoped type variables affect this implicit quantification rules
4631 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4632 quantified. For example, if type variable <literal>a</literal> is in scope,
4635 (e :: a -> a) means (e :: a -> a)
4636 (e :: b -> b) means (e :: forall b. b->b)
4637 (e :: a -> b) means (e :: forall b. a->b)
4645 <sect3 id="decl-type-sigs">
4646 <title>Declaration type signatures</title>
4647 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4648 quantification (using <literal>forall</literal>) brings into scope the
4649 explicitly-quantified
4650 type variables, in the definition of the named function. For example:
4652 f :: forall a. [a] -> [a]
4653 f (x:xs) = xs ++ [ x :: a ]
4655 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4656 the definition of "<literal>f</literal>".
4658 <para>This only happens if:
4660 <listitem><para> The quantification in <literal>f</literal>'s type
4661 signature is explicit. For example:
4664 g (x:xs) = xs ++ [ x :: a ]
4666 This program will be rejected, because "<literal>a</literal>" does not scope
4667 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4668 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4669 quantification rules.
4671 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4672 not a pattern binding.
4675 f1 :: forall a. [a] -> [a]
4676 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4678 f2 :: forall a. [a] -> [a]
4679 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4681 f3 :: forall a. [a] -> [a]
4682 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4684 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4685 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4686 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4687 the type signature brings <literal>a</literal> into scope.
4693 <sect3 id="exp-type-sigs">
4694 <title>Expression type signatures</title>
4696 <para>An expression type signature that has <emphasis>explicit</emphasis>
4697 quantification (using <literal>forall</literal>) brings into scope the
4698 explicitly-quantified
4699 type variables, in the annotated expression. For example:
4701 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4703 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4704 type variable <literal>s</literal> into scope, in the annotated expression
4705 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4710 <sect3 id="pattern-type-sigs">
4711 <title>Pattern type signatures</title>
4713 A type signature may occur in any pattern; this is a <emphasis>pattern type
4714 signature</emphasis>.
4717 -- f and g assume that 'a' is already in scope
4718 f = \(x::Int, y::a) -> x
4720 h ((x,y) :: (Int,Bool)) = (y,x)
4722 In the case where all the type variables in the pattern type signature are
4723 already in scope (i.e. bound by the enclosing context), matters are simple: the
4724 signature simply constrains the type of the pattern in the obvious way.
4727 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4728 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4729 that are already in scope. For example:
4731 f :: forall a. [a] -> (Int, [a])
4734 (ys::[a], n) = (reverse xs, length xs) -- OK
4735 zs::[a] = xs ++ ys -- OK
4737 Just (v::b) = ... -- Not OK; b is not in scope
4739 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4740 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4744 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4745 type signature may mention a type variable that is not in scope; in this case,
4746 <emphasis>the signature brings that type variable into scope</emphasis>.
4747 This is particularly important for existential data constructors. For example:
4749 data T = forall a. MkT [a]
4752 k (MkT [t::a]) = MkT t3
4756 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4757 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4758 because it is bound by the pattern match. GHC's rule is that in this situation
4759 (and only then), a pattern type signature can mention a type variable that is
4760 not already in scope; the effect is to bring it into scope, standing for the
4761 existentially-bound type variable.
4764 When a pattern type signature binds a type variable in this way, GHC insists that the
4765 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4766 This means that any user-written type signature always stands for a completely known type.
4769 If all this seems a little odd, we think so too. But we must have
4770 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4771 could not name existentially-bound type variables in subsequent type signatures.
4774 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4775 signature is allowed to mention a lexical variable that is not already in
4777 For example, both <literal>f</literal> and <literal>g</literal> would be
4778 illegal if <literal>a</literal> was not already in scope.
4784 <!-- ==================== Commented out part about result type signatures
4786 <sect3 id="result-type-sigs">
4787 <title>Result type signatures</title>
4790 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4793 {- f assumes that 'a' is already in scope -}
4794 f x y :: [a] = [x,y,x]
4796 g = \ x :: [Int] -> [3,4]
4798 h :: forall a. [a] -> a
4802 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4803 the result of the function. Similarly, the body of the lambda in the RHS of
4804 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4805 alternative in <literal>h</literal> is <literal>a</literal>.
4807 <para> A result type signature never brings new type variables into scope.</para>
4809 There are a couple of syntactic wrinkles. First, notice that all three
4810 examples would parse quite differently with parentheses:
4812 {- f assumes that 'a' is already in scope -}
4813 f x (y :: [a]) = [x,y,x]
4815 g = \ (x :: [Int]) -> [3,4]
4817 h :: forall a. [a] -> a
4821 Now the signature is on the <emphasis>pattern</emphasis>; and
4822 <literal>h</literal> would certainly be ill-typed (since the pattern
4823 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4825 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4826 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4827 token or a parenthesised type of some sort). To see why,
4828 consider how one would parse this:
4837 <sect3 id="cls-inst-scoped-tyvars">
4838 <title>Class and instance declarations</title>
4841 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4842 scope over the methods defined in the <literal>where</literal> part. For example:
4860 <sect2 id="typing-binds">
4861 <title>Generalised typing of mutually recursive bindings</title>
4864 The Haskell Report specifies that a group of bindings (at top level, or in a
4865 <literal>let</literal> or <literal>where</literal>) should be sorted into
4866 strongly-connected components, and then type-checked in dependency order
4867 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4868 Report, Section 4.5.1</ulink>).
4869 As each group is type-checked, any binders of the group that
4871 an explicit type signature are put in the type environment with the specified
4873 and all others are monomorphic until the group is generalised
4874 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4877 <para>Following a suggestion of Mark Jones, in his paper
4878 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4880 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4882 <emphasis>the dependency analysis ignores references to variables that have an explicit
4883 type signature</emphasis>.
4884 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4885 typecheck. For example, consider:
4887 f :: Eq a => a -> Bool
4888 f x = (x == x) || g True || g "Yes"
4890 g y = (y <= y) || f True
4892 This is rejected by Haskell 98, but under Jones's scheme the definition for
4893 <literal>g</literal> is typechecked first, separately from that for
4894 <literal>f</literal>,
4895 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4896 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4897 type is generalised, to get
4899 g :: Ord a => a -> Bool
4901 Now, the definition for <literal>f</literal> is typechecked, with this type for
4902 <literal>g</literal> in the type environment.
4906 The same refined dependency analysis also allows the type signatures of
4907 mutually-recursive functions to have different contexts, something that is illegal in
4908 Haskell 98 (Section 4.5.2, last sentence). With
4909 <option>-XRelaxedPolyRec</option>
4910 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4911 type signatures; in practice this means that only variables bound by the same
4912 pattern binding must have the same context. For example, this is fine:
4914 f :: Eq a => a -> Bool
4915 f x = (x == x) || g True
4917 g :: Ord a => a -> Bool
4918 g y = (y <= y) || f True
4923 <sect2 id="type-families">
4924 <title>Type families
4928 GHC supports the definition of type families indexed by types. They may be
4929 seen as an extension of Haskell 98's class-based overloading of values to
4930 types. When type families are declared in classes, they are also known as
4934 There are two forms of type families: data families and type synonym families.
4935 Currently, only the former are fully implemented, while we are still working
4936 on the latter. As a result, the specification of the language extension is
4937 also still to some degree in flux. Hence, a more detailed description of
4938 the language extension and its use is currently available
4939 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4940 wiki page on type families</ulink>. The material will be moved to this user's
4941 guide when it has stabilised.
4944 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4951 <!-- ==================== End of type system extensions ================= -->
4953 <!-- ====================== TEMPLATE HASKELL ======================= -->
4955 <sect1 id="template-haskell">
4956 <title>Template Haskell</title>
4958 <para>Template Haskell allows you to do compile-time meta-programming in
4961 the main technical innovations is discussed in "<ulink
4962 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
4963 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4966 There is a Wiki page about
4967 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
4968 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4972 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4973 Haskell library reference material</ulink>
4974 (look for module <literal>Language.Haskell.TH</literal>).
4975 Many changes to the original design are described in
4976 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4977 Notes on Template Haskell version 2</ulink>.
4978 Not all of these changes are in GHC, however.
4981 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4982 as a worked example to help get you started.
4986 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4987 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4992 <title>Syntax</title>
4994 <para> Template Haskell has the following new syntactic
4995 constructions. You need to use the flag
4996 <option>-XTemplateHaskell</option>
4997 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4998 </indexterm>to switch these syntactic extensions on
4999 (<option>-XTemplateHaskell</option> is no longer implied by
5000 <option>-fglasgow-exts</option>).</para>
5004 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5005 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5006 There must be no space between the "$" and the identifier or parenthesis. This use
5007 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5008 of "." as an infix operator. If you want the infix operator, put spaces around it.
5010 <para> A splice can occur in place of
5012 <listitem><para> an expression; the spliced expression must
5013 have type <literal>Q Exp</literal></para></listitem>
5014 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5017 Inside a splice you can can only call functions defined in imported modules,
5018 not functions defined elsewhere in the same module.</listitem>
5022 A expression quotation is written in Oxford brackets, thus:
5024 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5025 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5026 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5027 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5028 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5029 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5030 </itemizedlist></para></listitem>
5033 A quasi-quotation can appear in either a pattern context or an
5034 expression context and is also written in Oxford brackets:
5036 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5037 where the "..." is an arbitrary string; a full description of the
5038 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5039 </itemizedlist></para></listitem>
5042 A name can be quoted with either one or two prefix single quotes:
5044 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5045 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5046 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5048 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5049 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5052 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5053 may also be given as an argument to the <literal>reify</literal> function.
5059 (Compared to the original paper, there are many differences of detail.
5060 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5061 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5062 Type splices are not implemented, and neither are pattern splices or quotations.
5066 <sect2> <title> Using Template Haskell </title>
5070 The data types and monadic constructor functions for Template Haskell are in the library
5071 <literal>Language.Haskell.THSyntax</literal>.
5075 You can only run a function at compile time if it is imported from another module. That is,
5076 you can't define a function in a module, and call it from within a splice in the same module.
5077 (It would make sense to do so, but it's hard to implement.)
5081 You can only run a function at compile time if it is imported
5082 from another module <emphasis>that is not part of a mutually-recursive group of modules
5083 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5084 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5085 splice is to be run.</para>
5087 For example, when compiling module A,
5088 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5089 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5093 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5096 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5097 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5098 compiles and runs a program, and then looks at the result. So it's important that
5099 the program it compiles produces results whose representations are identical to
5100 those of the compiler itself.
5104 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5105 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5110 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5111 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5112 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5119 -- Import our template "pr"
5120 import Printf ( pr )
5122 -- The splice operator $ takes the Haskell source code
5123 -- generated at compile time by "pr" and splices it into
5124 -- the argument of "putStrLn".
5125 main = putStrLn ( $(pr "Hello") )
5131 -- Skeletal printf from the paper.
5132 -- It needs to be in a separate module to the one where
5133 -- you intend to use it.
5135 -- Import some Template Haskell syntax
5136 import Language.Haskell.TH
5138 -- Describe a format string
5139 data Format = D | S | L String
5141 -- Parse a format string. This is left largely to you
5142 -- as we are here interested in building our first ever
5143 -- Template Haskell program and not in building printf.
5144 parse :: String -> [Format]
5147 -- Generate Haskell source code from a parsed representation
5148 -- of the format string. This code will be spliced into
5149 -- the module which calls "pr", at compile time.
5150 gen :: [Format] -> Q Exp
5151 gen [D] = [| \n -> show n |]
5152 gen [S] = [| \s -> s |]
5153 gen [L s] = stringE s
5155 -- Here we generate the Haskell code for the splice
5156 -- from an input format string.
5157 pr :: String -> Q Exp
5158 pr s = gen (parse s)
5161 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5164 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5167 <para>Run "main.exe" and here is your output:</para>
5177 <title>Using Template Haskell with Profiling</title>
5178 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5180 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5181 interpreter to run the splice expressions. The bytecode interpreter
5182 runs the compiled expression on top of the same runtime on which GHC
5183 itself is running; this means that the compiled code referred to by
5184 the interpreted expression must be compatible with this runtime, and
5185 in particular this means that object code that is compiled for
5186 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5187 expression, because profiled object code is only compatible with the
5188 profiling version of the runtime.</para>
5190 <para>This causes difficulties if you have a multi-module program
5191 containing Template Haskell code and you need to compile it for
5192 profiling, because GHC cannot load the profiled object code and use it
5193 when executing the splices. Fortunately GHC provides a workaround.
5194 The basic idea is to compile the program twice:</para>
5198 <para>Compile the program or library first the normal way, without
5199 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5202 <para>Then compile it again with <option>-prof</option>, and
5203 additionally use <option>-osuf
5204 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5205 to name the object files differently (you can choose any suffix
5206 that isn't the normal object suffix here). GHC will automatically
5207 load the object files built in the first step when executing splice
5208 expressions. If you omit the <option>-osuf</option> flag when
5209 building with <option>-prof</option> and Template Haskell is used,
5210 GHC will emit an error message. </para>
5215 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5216 <para>Quasi-quotation allows patterns and expressions to be written using
5217 programmer-defined concrete syntax; the motivation behind the extension and
5218 several examples are documented in
5219 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5220 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5221 2007). The example below shows how to write a quasiquoter for a simple
5222 expression language.</para>
5225 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5226 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5227 functions for quoting expressions and patterns, respectively. The first argument
5228 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5229 context of the quasi-quotation statement determines which of the two parsers is
5230 called: if the quasi-quotation occurs in an expression context, the expression
5231 parser is called, and if it occurs in a pattern context, the pattern parser is
5235 Note that in the example we make use of an antiquoted
5236 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5237 (this syntax for anti-quotation was defined by the parser's
5238 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5239 integer value argument of the constructor <literal>IntExpr</literal> when
5240 pattern matching. Please see the referenced paper for further details regarding
5241 anti-quotation as well as the description of a technique that uses SYB to
5242 leverage a single parser of type <literal>String -> a</literal> to generate both
5243 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5244 pattern parser that returns a value of type <literal>Q Pat</literal>.
5247 <para>In general, a quasi-quote has the form
5248 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5249 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5250 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5251 can be arbitrary, and may contain newlines.
5254 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5255 the example, <literal>expr</literal> cannot be defined
5256 in <literal>Main.hs</literal> where it is used, but must be imported.
5267 main = do { print $ eval [$expr|1 + 2|]
5269 { [$expr|'int:n|] -> print n
5278 import qualified Language.Haskell.TH as TH
5279 import Language.Haskell.TH.Quasi
5281 data Expr = IntExpr Integer
5282 | AntiIntExpr String
5283 | BinopExpr BinOp Expr Expr
5285 deriving(Show, Typeable, Data)
5291 deriving(Show, Typeable, Data)
5293 eval :: Expr -> Integer
5294 eval (IntExpr n) = n
5295 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5302 expr = QuasiQuoter parseExprExp parseExprPat
5304 -- Parse an Expr, returning its representation as
5305 -- either a Q Exp or a Q Pat. See the referenced paper
5306 -- for how to use SYB to do this by writing a single
5307 -- parser of type String -> Expr instead of two
5308 -- separate parsers.
5310 parseExprExp :: String -> Q Exp
5313 parseExprPat :: String -> Q Pat
5317 <para>Now run the compiler:
5320 $ ghc --make -XQuasiQuotes Main.hs -o main
5323 <para>Run "main" and here is your output:</para>
5335 <!-- ===================== Arrow notation =================== -->
5337 <sect1 id="arrow-notation">
5338 <title>Arrow notation
5341 <para>Arrows are a generalization of monads introduced by John Hughes.
5342 For more details, see
5347 “Generalising Monads to Arrows”,
5348 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5349 pp67–111, May 2000.
5355 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5356 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5362 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5363 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5369 and the arrows web page at
5370 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5371 With the <option>-XArrows</option> flag, GHC supports the arrow
5372 notation described in the second of these papers.
5373 What follows is a brief introduction to the notation;
5374 it won't make much sense unless you've read Hughes's paper.
5375 This notation is translated to ordinary Haskell,
5376 using combinators from the
5377 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5381 <para>The extension adds a new kind of expression for defining arrows:
5383 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5384 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5386 where <literal>proc</literal> is a new keyword.
5387 The variables of the pattern are bound in the body of the
5388 <literal>proc</literal>-expression,
5389 which is a new sort of thing called a <firstterm>command</firstterm>.
5390 The syntax of commands is as follows:
5392 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5393 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5394 | <replaceable>cmd</replaceable><superscript>0</superscript>
5396 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5397 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5398 infix operators as for expressions, and
5400 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5401 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5402 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5403 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5404 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5405 | <replaceable>fcmd</replaceable>
5407 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5408 | ( <replaceable>cmd</replaceable> )
5409 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5411 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5412 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5413 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5414 | <replaceable>cmd</replaceable>
5416 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5417 except that the bodies are commands instead of expressions.
5421 Commands produce values, but (like monadic computations)
5422 may yield more than one value,
5423 or none, and may do other things as well.
5424 For the most part, familiarity with monadic notation is a good guide to
5426 However the values of expressions, even monadic ones,
5427 are determined by the values of the variables they contain;
5428 this is not necessarily the case for commands.
5432 A simple example of the new notation is the expression
5434 proc x -> f -< x+1
5436 We call this a <firstterm>procedure</firstterm> or
5437 <firstterm>arrow abstraction</firstterm>.
5438 As with a lambda expression, the variable <literal>x</literal>
5439 is a new variable bound within the <literal>proc</literal>-expression.
5440 It refers to the input to the arrow.
5441 In the above example, <literal>-<</literal> is not an identifier but an
5442 new reserved symbol used for building commands from an expression of arrow
5443 type and an expression to be fed as input to that arrow.
5444 (The weird look will make more sense later.)
5445 It may be read as analogue of application for arrows.
5446 The above example is equivalent to the Haskell expression
5448 arr (\ x -> x+1) >>> f
5450 That would make no sense if the expression to the left of
5451 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5452 More generally, the expression to the left of <literal>-<</literal>
5453 may not involve any <firstterm>local variable</firstterm>,
5454 i.e. a variable bound in the current arrow abstraction.
5455 For such a situation there is a variant <literal>-<<</literal>, as in
5457 proc x -> f x -<< x+1
5459 which is equivalent to
5461 arr (\ x -> (f x, x+1)) >>> app
5463 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5465 Such an arrow is equivalent to a monad, so if you're using this form
5466 you may find a monadic formulation more convenient.
5470 <title>do-notation for commands</title>
5473 Another form of command is a form of <literal>do</literal>-notation.
5474 For example, you can write
5483 You can read this much like ordinary <literal>do</literal>-notation,
5484 but with commands in place of monadic expressions.
5485 The first line sends the value of <literal>x+1</literal> as an input to
5486 the arrow <literal>f</literal>, and matches its output against
5487 <literal>y</literal>.
5488 In the next line, the output is discarded.
5489 The arrow <function>returnA</function> is defined in the
5490 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5491 module as <literal>arr id</literal>.
5492 The above example is treated as an abbreviation for
5494 arr (\ x -> (x, x)) >>>
5495 first (arr (\ x -> x+1) >>> f) >>>
5496 arr (\ (y, x) -> (y, (x, y))) >>>
5497 first (arr (\ y -> 2*y) >>> g) >>>
5499 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5500 first (arr (\ (x, z) -> x*z) >>> h) >>>
5501 arr (\ (t, z) -> t+z) >>>
5504 Note that variables not used later in the composition are projected out.
5505 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5507 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5508 module, this reduces to
5510 arr (\ x -> (x+1, x)) >>>
5512 arr (\ (y, x) -> (2*y, (x, y))) >>>
5514 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5516 arr (\ (t, z) -> t+z)
5518 which is what you might have written by hand.
5519 With arrow notation, GHC keeps track of all those tuples of variables for you.
5523 Note that although the above translation suggests that
5524 <literal>let</literal>-bound variables like <literal>z</literal> must be
5525 monomorphic, the actual translation produces Core,
5526 so polymorphic variables are allowed.
5530 It's also possible to have mutually recursive bindings,
5531 using the new <literal>rec</literal> keyword, as in the following example:
5533 counter :: ArrowCircuit a => a Bool Int
5534 counter = proc reset -> do
5535 rec output <- returnA -< if reset then 0 else next
5536 next <- delay 0 -< output+1
5537 returnA -< output
5539 The translation of such forms uses the <function>loop</function> combinator,
5540 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5546 <title>Conditional commands</title>
5549 In the previous example, we used a conditional expression to construct the
5551 Sometimes we want to conditionally execute different commands, as in
5558 which is translated to
5560 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5561 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5563 Since the translation uses <function>|||</function>,
5564 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5568 There are also <literal>case</literal> commands, like
5574 y <- h -< (x1, x2)
5578 The syntax is the same as for <literal>case</literal> expressions,
5579 except that the bodies of the alternatives are commands rather than expressions.
5580 The translation is similar to that of <literal>if</literal> commands.
5586 <title>Defining your own control structures</title>
5589 As we're seen, arrow notation provides constructs,
5590 modelled on those for expressions,
5591 for sequencing, value recursion and conditionals.
5592 But suitable combinators,
5593 which you can define in ordinary Haskell,
5594 may also be used to build new commands out of existing ones.
5595 The basic idea is that a command defines an arrow from environments to values.
5596 These environments assign values to the free local variables of the command.
5597 Thus combinators that produce arrows from arrows
5598 may also be used to build commands from commands.
5599 For example, the <literal>ArrowChoice</literal> class includes a combinator
5601 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5603 so we can use it to build commands:
5605 expr' = proc x -> do
5608 symbol Plus -< ()
5609 y <- term -< ()
5612 symbol Minus -< ()
5613 y <- term -< ()
5616 (The <literal>do</literal> on the first line is needed to prevent the first
5617 <literal><+> ...</literal> from being interpreted as part of the
5618 expression on the previous line.)
5619 This is equivalent to
5621 expr' = (proc x -> returnA -< x)
5622 <+> (proc x -> do
5623 symbol Plus -< ()
5624 y <- term -< ()
5626 <+> (proc x -> do
5627 symbol Minus -< ()
5628 y <- term -< ()
5631 It is essential that this operator be polymorphic in <literal>e</literal>
5632 (representing the environment input to the command
5633 and thence to its subcommands)
5634 and satisfy the corresponding naturality property
5636 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5638 at least for strict <literal>k</literal>.
5639 (This should be automatic if you're not using <function>seq</function>.)
5640 This ensures that environments seen by the subcommands are environments
5641 of the whole command,
5642 and also allows the translation to safely trim these environments.
5643 The operator must also not use any variable defined within the current
5648 We could define our own operator
5650 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5651 untilA body cond = proc x ->
5652 if cond x then returnA -< ()
5655 untilA body cond -< x
5657 and use it in the same way.
5658 Of course this infix syntax only makes sense for binary operators;
5659 there is also a more general syntax involving special brackets:
5663 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5670 <title>Primitive constructs</title>
5673 Some operators will need to pass additional inputs to their subcommands.
5674 For example, in an arrow type supporting exceptions,
5675 the operator that attaches an exception handler will wish to pass the
5676 exception that occurred to the handler.
5677 Such an operator might have a type
5679 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5681 where <literal>Ex</literal> is the type of exceptions handled.
5682 You could then use this with arrow notation by writing a command
5684 body `handleA` \ ex -> handler
5686 so that if an exception is raised in the command <literal>body</literal>,
5687 the variable <literal>ex</literal> is bound to the value of the exception
5688 and the command <literal>handler</literal>,
5689 which typically refers to <literal>ex</literal>, is entered.
5690 Though the syntax here looks like a functional lambda,
5691 we are talking about commands, and something different is going on.
5692 The input to the arrow represented by a command consists of values for
5693 the free local variables in the command, plus a stack of anonymous values.
5694 In all the prior examples, this stack was empty.
5695 In the second argument to <function>handleA</function>,
5696 this stack consists of one value, the value of the exception.
5697 The command form of lambda merely gives this value a name.
5702 the values on the stack are paired to the right of the environment.
5703 So operators like <function>handleA</function> that pass
5704 extra inputs to their subcommands can be designed for use with the notation
5705 by pairing the values with the environment in this way.
5706 More precisely, the type of each argument of the operator (and its result)
5707 should have the form
5709 a (...(e,t1), ... tn) t
5711 where <replaceable>e</replaceable> is a polymorphic variable
5712 (representing the environment)
5713 and <replaceable>ti</replaceable> are the types of the values on the stack,
5714 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5715 The polymorphic variable <replaceable>e</replaceable> must not occur in
5716 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5717 <replaceable>t</replaceable>.
5718 However the arrows involved need not be the same.
5719 Here are some more examples of suitable operators:
5721 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5722 runReader :: ... => a e c -> a' (e,State) c
5723 runState :: ... => a e c -> a' (e,State) (c,State)
5725 We can supply the extra input required by commands built with the last two
5726 by applying them to ordinary expressions, as in
5730 (|runReader (do { ... })|) s
5732 which adds <literal>s</literal> to the stack of inputs to the command
5733 built using <function>runReader</function>.
5737 The command versions of lambda abstraction and application are analogous to
5738 the expression versions.
5739 In particular, the beta and eta rules describe equivalences of commands.
5740 These three features (operators, lambda abstraction and application)
5741 are the core of the notation; everything else can be built using them,
5742 though the results would be somewhat clumsy.
5743 For example, we could simulate <literal>do</literal>-notation by defining
5745 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5746 u `bind` f = returnA &&& u >>> f
5748 bind_ :: Arrow a => a e b -> a e c -> a e c
5749 u `bind_` f = u `bind` (arr fst >>> f)
5751 We could simulate <literal>if</literal> by defining
5753 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5754 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5761 <title>Differences with the paper</title>
5766 <para>Instead of a single form of arrow application (arrow tail) with two
5767 translations, the implementation provides two forms
5768 <quote><literal>-<</literal></quote> (first-order)
5769 and <quote><literal>-<<</literal></quote> (higher-order).
5774 <para>User-defined operators are flagged with banana brackets instead of
5775 a new <literal>form</literal> keyword.
5784 <title>Portability</title>
5787 Although only GHC implements arrow notation directly,
5788 there is also a preprocessor
5790 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5791 that translates arrow notation into Haskell 98
5792 for use with other Haskell systems.
5793 You would still want to check arrow programs with GHC;
5794 tracing type errors in the preprocessor output is not easy.
5795 Modules intended for both GHC and the preprocessor must observe some
5796 additional restrictions:
5801 The module must import
5802 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5808 The preprocessor cannot cope with other Haskell extensions.
5809 These would have to go in separate modules.
5815 Because the preprocessor targets Haskell (rather than Core),
5816 <literal>let</literal>-bound variables are monomorphic.
5827 <!-- ==================== BANG PATTERNS ================= -->
5829 <sect1 id="bang-patterns">
5830 <title>Bang patterns
5831 <indexterm><primary>Bang patterns</primary></indexterm>
5833 <para>GHC supports an extension of pattern matching called <emphasis>bang
5834 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5836 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5837 prime feature description</ulink> contains more discussion and examples
5838 than the material below.
5841 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5844 <sect2 id="bang-patterns-informal">
5845 <title>Informal description of bang patterns
5848 The main idea is to add a single new production to the syntax of patterns:
5852 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5853 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5858 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5859 whereas without the bang it would be lazy.
5860 Bang patterns can be nested of course:
5864 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5865 <literal>y</literal>.
5866 A bang only really has an effect if it precedes a variable or wild-card pattern:
5871 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5872 forces evaluation anyway does nothing.
5874 Bang patterns work in <literal>case</literal> expressions too, of course:
5876 g5 x = let y = f x in body
5877 g6 x = case f x of { y -> body }
5878 g7 x = case f x of { !y -> body }
5880 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5881 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5882 result, and then evaluates <literal>body</literal>.
5884 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5885 definitions too. For example:
5889 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5890 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5891 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5892 in a function argument <literal>![x,y]</literal> means the
5893 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5894 is part of the syntax of <literal>let</literal> bindings.
5899 <sect2 id="bang-patterns-sem">
5900 <title>Syntax and semantics
5904 We add a single new production to the syntax of patterns:
5908 There is one problem with syntactic ambiguity. Consider:
5912 Is this a definition of the infix function "<literal>(!)</literal>",
5913 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5914 ambiguity in favour of the latter. If you want to define
5915 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5920 The semantics of Haskell pattern matching is described in <ulink
5921 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5922 Section 3.17.2</ulink> of the Haskell Report. To this description add
5923 one extra item 10, saying:
5924 <itemizedlist><listitem><para>Matching
5925 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5926 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5927 <listitem><para>otherwise, <literal>pat</literal> is matched against
5928 <literal>v</literal></para></listitem>
5930 </para></listitem></itemizedlist>
5931 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5932 Section 3.17.3</ulink>, add a new case (t):
5934 case v of { !pat -> e; _ -> e' }
5935 = v `seq` case v of { pat -> e; _ -> e' }
5938 That leaves let expressions, whose translation is given in
5939 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5941 of the Haskell Report.
5942 In the translation box, first apply
5943 the following transformation: for each pattern <literal>pi</literal> that is of
5944 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5945 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5946 have a bang at the top, apply the rules in the existing box.
5948 <para>The effect of the let rule is to force complete matching of the pattern
5949 <literal>qi</literal> before evaluation of the body is begun. The bang is
5950 retained in the translated form in case <literal>qi</literal> is a variable,
5958 The let-binding can be recursive. However, it is much more common for
5959 the let-binding to be non-recursive, in which case the following law holds:
5960 <literal>(let !p = rhs in body)</literal>
5962 <literal>(case rhs of !p -> body)</literal>
5965 A pattern with a bang at the outermost level is not allowed at the top level of
5971 <!-- ==================== ASSERTIONS ================= -->
5973 <sect1 id="assertions">
5975 <indexterm><primary>Assertions</primary></indexterm>
5979 If you want to make use of assertions in your standard Haskell code, you
5980 could define a function like the following:
5986 assert :: Bool -> a -> a
5987 assert False x = error "assertion failed!"
5994 which works, but gives you back a less than useful error message --
5995 an assertion failed, but which and where?
5999 One way out is to define an extended <function>assert</function> function which also
6000 takes a descriptive string to include in the error message and
6001 perhaps combine this with the use of a pre-processor which inserts
6002 the source location where <function>assert</function> was used.
6006 Ghc offers a helping hand here, doing all of this for you. For every
6007 use of <function>assert</function> in the user's source:
6013 kelvinToC :: Double -> Double
6014 kelvinToC k = assert (k >= 0.0) (k+273.15)
6020 Ghc will rewrite this to also include the source location where the
6027 assert pred val ==> assertError "Main.hs|15" pred val
6033 The rewrite is only performed by the compiler when it spots
6034 applications of <function>Control.Exception.assert</function>, so you
6035 can still define and use your own versions of
6036 <function>assert</function>, should you so wish. If not, import
6037 <literal>Control.Exception</literal> to make use
6038 <function>assert</function> in your code.
6042 GHC ignores assertions when optimisation is turned on with the
6043 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6044 <literal>assert pred e</literal> will be rewritten to
6045 <literal>e</literal>. You can also disable assertions using the
6046 <option>-fignore-asserts</option>
6047 option<indexterm><primary><option>-fignore-asserts</option></primary>
6048 </indexterm>.</para>
6051 Assertion failures can be caught, see the documentation for the
6052 <literal>Control.Exception</literal> library for the details.
6058 <!-- =============================== PRAGMAS =========================== -->
6060 <sect1 id="pragmas">
6061 <title>Pragmas</title>
6063 <indexterm><primary>pragma</primary></indexterm>
6065 <para>GHC supports several pragmas, or instructions to the
6066 compiler placed in the source code. Pragmas don't normally affect
6067 the meaning of the program, but they might affect the efficiency
6068 of the generated code.</para>
6070 <para>Pragmas all take the form
6072 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6074 where <replaceable>word</replaceable> indicates the type of
6075 pragma, and is followed optionally by information specific to that
6076 type of pragma. Case is ignored in
6077 <replaceable>word</replaceable>. The various values for
6078 <replaceable>word</replaceable> that GHC understands are described
6079 in the following sections; any pragma encountered with an
6080 unrecognised <replaceable>word</replaceable> is (silently)
6081 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6082 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6084 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6085 pragma must precede the <literal>module</literal> keyword in the file.
6086 There can be as many file-header pragmas as you please, and they can be
6087 preceded or followed by comments.</para>
6089 <sect2 id="language-pragma">
6090 <title>LANGUAGE pragma</title>
6092 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6093 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6095 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6097 It is the intention that all Haskell compilers support the
6098 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6099 all extensions are supported by all compilers, of
6100 course. The <literal>LANGUAGE</literal> pragma should be used instead
6101 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6103 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6105 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6107 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6109 <para>Every language extension can also be turned into a command-line flag
6110 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6111 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6114 <para>A list of all supported language extensions can be obtained by invoking
6115 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6117 <para>Any extension from the <literal>Extension</literal> type defined in
6119 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6120 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6124 <sect2 id="options-pragma">
6125 <title>OPTIONS_GHC pragma</title>
6126 <indexterm><primary>OPTIONS_GHC</primary>
6128 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6131 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6132 additional options that are given to the compiler when compiling
6133 this source file. See <xref linkend="source-file-options"/> for
6136 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6137 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6140 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6142 <sect2 id="include-pragma">
6143 <title>INCLUDE pragma</title>
6145 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6146 of C header files that should be <literal>#include</literal>'d into
6147 the C source code generated by the compiler for the current module (if
6148 compiling via C). For example:</para>
6151 {-# INCLUDE "foo.h" #-}
6152 {-# INCLUDE <stdio.h> #-}</programlisting>
6154 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6156 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6157 to the <option>-#include</option> option (<xref
6158 linkend="options-C-compiler" />), because the
6159 <literal>INCLUDE</literal> pragma is understood by other
6160 compilers. Yet another alternative is to add the include file to each
6161 <literal>foreign import</literal> declaration in your code, but we
6162 don't recommend using this approach with GHC.</para>
6165 <sect2 id="warning-deprecated-pragma">
6166 <title>WARNING and DEPRECATED pragmas</title>
6167 <indexterm><primary>WARNING</primary></indexterm>
6168 <indexterm><primary>DEPRECATED</primary></indexterm>
6170 <para>The WARNING pragma allows you to attach an arbitrary warning
6171 to a particular function, class, or type.
6172 A DEPRECATED pragma lets you specify that
6173 a particular function, class, or type is deprecated.
6174 There are two ways of using these pragmas.
6178 <para>You can work on an entire module thus:</para>
6180 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6185 module Wibble {-# WARNING "This is an unstable interface." #-} where
6188 <para>When you compile any module that import
6189 <literal>Wibble</literal>, GHC will print the specified
6194 <para>You can attach a warning to a function, class, type, or data constructor, with the
6195 following top-level declarations:</para>
6197 {-# DEPRECATED f, C, T "Don't use these" #-}
6198 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6200 <para>When you compile any module that imports and uses any
6201 of the specified entities, GHC will print the specified
6203 <para> You can only attach to entities declared at top level in the module
6204 being compiled, and you can only use unqualified names in the list of
6205 entities. A capitalised name, such as <literal>T</literal>
6206 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6207 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6208 both are in scope. If both are in scope, there is currently no way to
6209 specify one without the other (c.f. fixities
6210 <xref linkend="infix-tycons"/>).</para>
6213 Warnings and deprecations are not reported for
6214 (a) uses within the defining module, and
6215 (b) uses in an export list.
6216 The latter reduces spurious complaints within a library
6217 in which one module gathers together and re-exports
6218 the exports of several others.
6220 <para>You can suppress the warnings with the flag
6221 <option>-fno-warn-warnings-deprecations</option>.</para>
6224 <sect2 id="inline-noinline-pragma">
6225 <title>INLINE and NOINLINE pragmas</title>
6227 <para>These pragmas control the inlining of function
6230 <sect3 id="inline-pragma">
6231 <title>INLINE pragma</title>
6232 <indexterm><primary>INLINE</primary></indexterm>
6234 <para>GHC (with <option>-O</option>, as always) tries to
6235 inline (or “unfold”) functions/values that are
6236 “small enough,” thus avoiding the call overhead
6237 and possibly exposing other more-wonderful optimisations.
6238 Normally, if GHC decides a function is “too
6239 expensive” to inline, it will not do so, nor will it
6240 export that unfolding for other modules to use.</para>
6242 <para>The sledgehammer you can bring to bear is the
6243 <literal>INLINE</literal><indexterm><primary>INLINE
6244 pragma</primary></indexterm> pragma, used thusly:</para>
6247 key_function :: Int -> String -> (Bool, Double)
6248 {-# INLINE key_function #-}
6251 <para>The major effect of an <literal>INLINE</literal> pragma
6252 is to declare a function's “cost” to be very low.
6253 The normal unfolding machinery will then be very keen to
6254 inline it. However, an <literal>INLINE</literal> pragma for a
6255 function "<literal>f</literal>" has a number of other effects:
6258 No functions are inlined into <literal>f</literal>. Otherwise
6259 GHC might inline a big function into <literal>f</literal>'s right hand side,
6260 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6263 The float-in, float-out, and common-sub-expression transformations are not
6264 applied to the body of <literal>f</literal>.
6267 An INLINE function is not worker/wrappered by strictness analysis.
6268 It's going to be inlined wholesale instead.
6271 All of these effects are aimed at ensuring that what gets inlined is
6272 exactly what you asked for, no more and no less.
6274 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6275 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6276 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6277 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6278 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6279 when there is no choice even an INLINE function can be selected, in which case
6280 the INLINE pragma is ignored.
6281 For example, for a self-recursive function, the loop breaker can only be the function
6282 itself, so an INLINE pragma is always ignored.</para>
6284 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6285 function can be put anywhere its type signature could be
6288 <para><literal>INLINE</literal> pragmas are a particularly
6290 <literal>then</literal>/<literal>return</literal> (or
6291 <literal>bind</literal>/<literal>unit</literal>) functions in
6292 a monad. For example, in GHC's own
6293 <literal>UniqueSupply</literal> monad code, we have:</para>
6296 {-# INLINE thenUs #-}
6297 {-# INLINE returnUs #-}
6300 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6301 linkend="noinline-pragma"/>).</para>
6303 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6304 so if you want your code to be HBC-compatible you'll have to surround
6305 the pragma with C pre-processor directives
6306 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6310 <sect3 id="noinline-pragma">
6311 <title>NOINLINE pragma</title>
6313 <indexterm><primary>NOINLINE</primary></indexterm>
6314 <indexterm><primary>NOTINLINE</primary></indexterm>
6316 <para>The <literal>NOINLINE</literal> pragma does exactly what
6317 you'd expect: it stops the named function from being inlined
6318 by the compiler. You shouldn't ever need to do this, unless
6319 you're very cautious about code size.</para>
6321 <para><literal>NOTINLINE</literal> is a synonym for
6322 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6323 specified by Haskell 98 as the standard way to disable
6324 inlining, so it should be used if you want your code to be
6328 <sect3 id="phase-control">
6329 <title>Phase control</title>
6331 <para> Sometimes you want to control exactly when in GHC's
6332 pipeline the INLINE pragma is switched on. Inlining happens
6333 only during runs of the <emphasis>simplifier</emphasis>. Each
6334 run of the simplifier has a different <emphasis>phase
6335 number</emphasis>; the phase number decreases towards zero.
6336 If you use <option>-dverbose-core2core</option> you'll see the
6337 sequence of phase numbers for successive runs of the
6338 simplifier. In an INLINE pragma you can optionally specify a
6342 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6343 <literal>f</literal>
6344 until phase <literal>k</literal>, but from phase
6345 <literal>k</literal> onwards be very keen to inline it.
6348 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6349 <literal>f</literal>
6350 until phase <literal>k</literal>, but from phase
6351 <literal>k</literal> onwards do not inline it.
6354 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6355 <literal>f</literal>
6356 until phase <literal>k</literal>, but from phase
6357 <literal>k</literal> onwards be willing to inline it (as if
6358 there was no pragma).
6361 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6362 <literal>f</literal>
6363 until phase <literal>k</literal>, but from phase
6364 <literal>k</literal> onwards do not inline it.
6367 The same information is summarised here:
6369 -- Before phase 2 Phase 2 and later
6370 {-# INLINE [2] f #-} -- No Yes
6371 {-# INLINE [~2] f #-} -- Yes No
6372 {-# NOINLINE [2] f #-} -- No Maybe
6373 {-# NOINLINE [~2] f #-} -- Maybe No
6375 {-# INLINE f #-} -- Yes Yes
6376 {-# NOINLINE f #-} -- No No
6378 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6379 function body is small, or it is applied to interesting-looking arguments etc).
6380 Another way to understand the semantics is this:
6382 <listitem><para>For both INLINE and NOINLINE, the phase number says
6383 when inlining is allowed at all.</para></listitem>
6384 <listitem><para>The INLINE pragma has the additional effect of making the
6385 function body look small, so that when inlining is allowed it is very likely to
6390 <para>The same phase-numbering control is available for RULES
6391 (<xref linkend="rewrite-rules"/>).</para>
6395 <sect2 id="line-pragma">
6396 <title>LINE pragma</title>
6398 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6399 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6400 <para>This pragma is similar to C's <literal>#line</literal>
6401 pragma, and is mainly for use in automatically generated Haskell
6402 code. It lets you specify the line number and filename of the
6403 original code; for example</para>
6405 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6407 <para>if you'd generated the current file from something called
6408 <filename>Foo.vhs</filename> and this line corresponds to line
6409 42 in the original. GHC will adjust its error messages to refer
6410 to the line/file named in the <literal>LINE</literal>
6415 <title>RULES pragma</title>
6417 <para>The RULES pragma lets you specify rewrite rules. It is
6418 described in <xref linkend="rewrite-rules"/>.</para>
6421 <sect2 id="specialize-pragma">
6422 <title>SPECIALIZE pragma</title>
6424 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6425 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6426 <indexterm><primary>overloading, death to</primary></indexterm>
6428 <para>(UK spelling also accepted.) For key overloaded
6429 functions, you can create extra versions (NB: more code space)
6430 specialised to particular types. Thus, if you have an
6431 overloaded function:</para>
6434 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6437 <para>If it is heavily used on lists with
6438 <literal>Widget</literal> keys, you could specialise it as
6442 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6445 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6446 be put anywhere its type signature could be put.</para>
6448 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6449 (a) a specialised version of the function and (b) a rewrite rule
6450 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6451 un-specialised function into a call to the specialised one.</para>
6453 <para>The type in a SPECIALIZE pragma can be any type that is less
6454 polymorphic than the type of the original function. In concrete terms,
6455 if the original function is <literal>f</literal> then the pragma
6457 {-# SPECIALIZE f :: <type> #-}
6459 is valid if and only if the definition
6461 f_spec :: <type>
6464 is valid. Here are some examples (where we only give the type signature
6465 for the original function, not its code):
6467 f :: Eq a => a -> b -> b
6468 {-# SPECIALISE f :: Int -> b -> b #-}
6470 g :: (Eq a, Ix b) => a -> b -> b
6471 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6473 h :: Eq a => a -> a -> a
6474 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6476 The last of these examples will generate a
6477 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6478 well. If you use this kind of specialisation, let us know how well it works.
6481 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6482 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6483 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6484 The <literal>INLINE</literal> pragma affects the specialised version of the
6485 function (only), and applies even if the function is recursive. The motivating
6488 -- A GADT for arrays with type-indexed representation
6490 ArrInt :: !Int -> ByteArray# -> Arr Int
6491 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6493 (!:) :: Arr e -> Int -> e
6494 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6495 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6496 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6497 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6499 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6500 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6501 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6502 the specialised function will be inlined. It has two calls to
6503 <literal>(!:)</literal>,
6504 both at type <literal>Int</literal>. Both these calls fire the first
6505 specialisation, whose body is also inlined. The result is a type-based
6506 unrolling of the indexing function.</para>
6507 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6508 on an ordinarily-recursive function.</para>
6510 <para>Note: In earlier versions of GHC, it was possible to provide your own
6511 specialised function for a given type:
6514 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6517 This feature has been removed, as it is now subsumed by the
6518 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6522 <sect2 id="specialize-instance-pragma">
6523 <title>SPECIALIZE instance pragma
6527 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6528 <indexterm><primary>overloading, death to</primary></indexterm>
6529 Same idea, except for instance declarations. For example:
6532 instance (Eq a) => Eq (Foo a) where {
6533 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6537 The pragma must occur inside the <literal>where</literal> part
6538 of the instance declaration.
6541 Compatible with HBC, by the way, except perhaps in the placement
6547 <sect2 id="unpack-pragma">
6548 <title>UNPACK pragma</title>
6550 <indexterm><primary>UNPACK</primary></indexterm>
6552 <para>The <literal>UNPACK</literal> indicates to the compiler
6553 that it should unpack the contents of a constructor field into
6554 the constructor itself, removing a level of indirection. For
6558 data T = T {-# UNPACK #-} !Float
6559 {-# UNPACK #-} !Float
6562 <para>will create a constructor <literal>T</literal> containing
6563 two unboxed floats. This may not always be an optimisation: if
6564 the <function>T</function> constructor is scrutinised and the
6565 floats passed to a non-strict function for example, they will
6566 have to be reboxed (this is done automatically by the
6569 <para>Unpacking constructor fields should only be used in
6570 conjunction with <option>-O</option>, in order to expose
6571 unfoldings to the compiler so the reboxing can be removed as
6572 often as possible. For example:</para>
6576 f (T f1 f2) = f1 + f2
6579 <para>The compiler will avoid reboxing <function>f1</function>
6580 and <function>f2</function> by inlining <function>+</function>
6581 on floats, but only when <option>-O</option> is on.</para>
6583 <para>Any single-constructor data is eligible for unpacking; for
6587 data T = T {-# UNPACK #-} !(Int,Int)
6590 <para>will store the two <literal>Int</literal>s directly in the
6591 <function>T</function> constructor, by flattening the pair.
6592 Multi-level unpacking is also supported:
6595 data T = T {-# UNPACK #-} !S
6596 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6599 will store two unboxed <literal>Int#</literal>s
6600 directly in the <function>T</function> constructor. The
6601 unpacker can see through newtypes, too.</para>
6603 <para>If a field cannot be unpacked, you will not get a warning,
6604 so it might be an idea to check the generated code with
6605 <option>-ddump-simpl</option>.</para>
6607 <para>See also the <option>-funbox-strict-fields</option> flag,
6608 which essentially has the effect of adding
6609 <literal>{-# UNPACK #-}</literal> to every strict
6610 constructor field.</para>
6613 <sect2 id="source-pragma">
6614 <title>SOURCE pragma</title>
6616 <indexterm><primary>SOURCE</primary></indexterm>
6617 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6618 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6624 <!-- ======================= REWRITE RULES ======================== -->
6626 <sect1 id="rewrite-rules">
6627 <title>Rewrite rules
6629 <indexterm><primary>RULES pragma</primary></indexterm>
6630 <indexterm><primary>pragma, RULES</primary></indexterm>
6631 <indexterm><primary>rewrite rules</primary></indexterm></title>
6634 The programmer can specify rewrite rules as part of the source program
6635 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6636 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6637 and (b) the <option>-fno-rewrite-rules</option> flag
6638 (<xref linkend="options-f"/>) is not specified, and (c) the
6639 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6648 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6653 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6654 If you need more information, then <option>-ddump-rule-firings</option> shows you
6655 each individual rule firing in detail.
6659 <title>Syntax</title>
6662 From a syntactic point of view:
6668 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6669 may be generated by the layout rule).
6675 The layout rule applies in a pragma.
6676 Currently no new indentation level
6677 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6678 you must lay out the starting in the same column as the enclosing definitions.
6681 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6682 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6685 Furthermore, the closing <literal>#-}</literal>
6686 should start in a column to the right of the opening <literal>{-#</literal>.
6692 Each rule has a name, enclosed in double quotes. The name itself has
6693 no significance at all. It is only used when reporting how many times the rule fired.
6699 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6700 immediately after the name of the rule. Thus:
6703 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6706 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6707 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6716 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6717 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6718 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6719 by spaces, just like in a type <literal>forall</literal>.
6725 A pattern variable may optionally have a type signature.
6726 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6727 For example, here is the <literal>foldr/build</literal> rule:
6730 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6731 foldr k z (build g) = g k z
6734 Since <function>g</function> has a polymorphic type, it must have a type signature.
6741 The left hand side of a rule must consist of a top-level variable applied
6742 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6745 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6746 "wrong2" forall f. f True = True
6749 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6756 A rule does not need to be in the same module as (any of) the
6757 variables it mentions, though of course they need to be in scope.
6763 Rules are automatically exported from a module, just as instance declarations are.
6774 <title>Semantics</title>
6777 From a semantic point of view:
6783 Rules are only applied if you use the <option>-O</option> flag.
6789 Rules are regarded as left-to-right rewrite rules.
6790 When GHC finds an expression that is a substitution instance of the LHS
6791 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6792 By "a substitution instance" we mean that the LHS can be made equal to the
6793 expression by substituting for the pattern variables.
6800 The LHS and RHS of a rule are typechecked, and must have the
6808 GHC makes absolutely no attempt to verify that the LHS and RHS
6809 of a rule have the same meaning. That is undecidable in general, and
6810 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6817 GHC makes no attempt to make sure that the rules are confluent or
6818 terminating. For example:
6821 "loop" forall x y. f x y = f y x
6824 This rule will cause the compiler to go into an infinite loop.
6831 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6837 GHC currently uses a very simple, syntactic, matching algorithm
6838 for matching a rule LHS with an expression. It seeks a substitution
6839 which makes the LHS and expression syntactically equal modulo alpha
6840 conversion. The pattern (rule), but not the expression, is eta-expanded if
6841 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6842 But not beta conversion (that's called higher-order matching).
6846 Matching is carried out on GHC's intermediate language, which includes
6847 type abstractions and applications. So a rule only matches if the
6848 types match too. See <xref linkend="rule-spec"/> below.
6854 GHC keeps trying to apply the rules as it optimises the program.
6855 For example, consider:
6864 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6865 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6866 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6867 not be substituted, and the rule would not fire.
6874 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6875 results. Consider this (artificial) example
6878 {-# RULES "f" f True = False #-}
6884 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
6889 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
6891 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
6892 would have been a better chance that <literal>f</literal>'s RULE might fire.
6895 The way to get predictable behaviour is to use a NOINLINE
6896 pragma on <literal>f</literal>, to ensure
6897 that it is not inlined until its RULEs have had a chance to fire.
6903 All rules are implicitly exported from the module, and are therefore
6904 in force in any module that imports the module that defined the rule, directly
6905 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6906 in force when compiling A.) The situation is very similar to that for instance
6918 <title>List fusion</title>
6921 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6922 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6923 intermediate list should be eliminated entirely.
6927 The following are good producers:
6939 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6945 Explicit lists (e.g. <literal>[True, False]</literal>)
6951 The cons constructor (e.g <literal>3:4:[]</literal>)
6957 <function>++</function>
6963 <function>map</function>
6969 <function>take</function>, <function>filter</function>
6975 <function>iterate</function>, <function>repeat</function>
6981 <function>zip</function>, <function>zipWith</function>
6990 The following are good consumers:
7002 <function>array</function> (on its second argument)
7008 <function>++</function> (on its first argument)
7014 <function>foldr</function>
7020 <function>map</function>
7026 <function>take</function>, <function>filter</function>
7032 <function>concat</function>
7038 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7044 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7045 will fuse with one but not the other)
7051 <function>partition</function>
7057 <function>head</function>
7063 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7069 <function>sequence_</function>
7075 <function>msum</function>
7081 <function>sortBy</function>
7090 So, for example, the following should generate no intermediate lists:
7093 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7099 This list could readily be extended; if there are Prelude functions that you use
7100 a lot which are not included, please tell us.
7104 If you want to write your own good consumers or producers, look at the
7105 Prelude definitions of the above functions to see how to do so.
7110 <sect2 id="rule-spec">
7111 <title>Specialisation
7115 Rewrite rules can be used to get the same effect as a feature
7116 present in earlier versions of GHC.
7117 For example, suppose that:
7120 genericLookup :: Ord a => Table a b -> a -> b
7121 intLookup :: Table Int b -> Int -> b
7124 where <function>intLookup</function> is an implementation of
7125 <function>genericLookup</function> that works very fast for
7126 keys of type <literal>Int</literal>. You might wish
7127 to tell GHC to use <function>intLookup</function> instead of
7128 <function>genericLookup</function> whenever the latter was called with
7129 type <literal>Table Int b -> Int -> b</literal>.
7130 It used to be possible to write
7133 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7136 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7139 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7142 This slightly odd-looking rule instructs GHC to replace
7143 <function>genericLookup</function> by <function>intLookup</function>
7144 <emphasis>whenever the types match</emphasis>.
7145 What is more, this rule does not need to be in the same
7146 file as <function>genericLookup</function>, unlike the
7147 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7148 have an original definition available to specialise).
7151 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7152 <function>intLookup</function> really behaves as a specialised version
7153 of <function>genericLookup</function>!!!</para>
7155 <para>An example in which using <literal>RULES</literal> for
7156 specialisation will Win Big:
7159 toDouble :: Real a => a -> Double
7160 toDouble = fromRational . toRational
7162 {-# RULES "toDouble/Int" toDouble = i2d #-}
7163 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7166 The <function>i2d</function> function is virtually one machine
7167 instruction; the default conversion—via an intermediate
7168 <literal>Rational</literal>—is obscenely expensive by
7175 <title>Controlling what's going on</title>
7183 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7189 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7190 If you add <option>-dppr-debug</option> you get a more detailed listing.
7196 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7199 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7200 {-# INLINE build #-}
7204 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7205 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7206 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7207 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7214 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7215 see how to write rules that will do fusion and yet give an efficient
7216 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7226 <sect2 id="core-pragma">
7227 <title>CORE pragma</title>
7229 <indexterm><primary>CORE pragma</primary></indexterm>
7230 <indexterm><primary>pragma, CORE</primary></indexterm>
7231 <indexterm><primary>core, annotation</primary></indexterm>
7234 The external core format supports <quote>Note</quote> annotations;
7235 the <literal>CORE</literal> pragma gives a way to specify what these
7236 should be in your Haskell source code. Syntactically, core
7237 annotations are attached to expressions and take a Haskell string
7238 literal as an argument. The following function definition shows an
7242 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7245 Semantically, this is equivalent to:
7253 However, when external core is generated (via
7254 <option>-fext-core</option>), there will be Notes attached to the
7255 expressions <function>show</function> and <varname>x</varname>.
7256 The core function declaration for <function>f</function> is:
7260 f :: %forall a . GHCziShow.ZCTShow a ->
7261 a -> GHCziBase.ZMZN GHCziBase.Char =
7262 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7264 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7266 (tpl1::GHCziBase.Int ->
7268 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7270 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7271 (tpl3::GHCziBase.ZMZN a ->
7272 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7280 Here, we can see that the function <function>show</function> (which
7281 has been expanded out to a case expression over the Show dictionary)
7282 has a <literal>%note</literal> attached to it, as does the
7283 expression <varname>eta</varname> (which used to be called
7284 <varname>x</varname>).
7291 <sect1 id="special-ids">
7292 <title>Special built-in functions</title>
7293 <para>GHC has a few built-in functions with special behaviour. These
7294 are now described in the module <ulink
7295 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7296 in the library documentation.</para>
7300 <sect1 id="generic-classes">
7301 <title>Generic classes</title>
7304 The ideas behind this extension are described in detail in "Derivable type classes",
7305 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7306 An example will give the idea:
7314 fromBin :: [Int] -> (a, [Int])
7316 toBin {| Unit |} Unit = []
7317 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7318 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7319 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7321 fromBin {| Unit |} bs = (Unit, bs)
7322 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7323 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7324 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7325 (y,bs'') = fromBin bs'
7328 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7329 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7330 which are defined thus in the library module <literal>Generics</literal>:
7334 data a :+: b = Inl a | Inr b
7335 data a :*: b = a :*: b
7338 Now you can make a data type into an instance of Bin like this:
7340 instance (Bin a, Bin b) => Bin (a,b)
7341 instance Bin a => Bin [a]
7343 That is, just leave off the "where" clause. Of course, you can put in the
7344 where clause and over-ride whichever methods you please.
7348 <title> Using generics </title>
7349 <para>To use generics you need to</para>
7352 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7353 <option>-XGenerics</option> (to generate extra per-data-type code),
7354 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7358 <para>Import the module <literal>Generics</literal> from the
7359 <literal>lang</literal> package. This import brings into
7360 scope the data types <literal>Unit</literal>,
7361 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7362 don't need this import if you don't mention these types
7363 explicitly; for example, if you are simply giving instance
7364 declarations.)</para>
7369 <sect2> <title> Changes wrt the paper </title>
7371 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7372 can be written infix (indeed, you can now use
7373 any operator starting in a colon as an infix type constructor). Also note that
7374 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7375 Finally, note that the syntax of the type patterns in the class declaration
7376 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7377 alone would ambiguous when they appear on right hand sides (an extension we
7378 anticipate wanting).
7382 <sect2> <title>Terminology and restrictions</title>
7384 Terminology. A "generic default method" in a class declaration
7385 is one that is defined using type patterns as above.
7386 A "polymorphic default method" is a default method defined as in Haskell 98.
7387 A "generic class declaration" is a class declaration with at least one
7388 generic default method.
7396 Alas, we do not yet implement the stuff about constructor names and
7403 A generic class can have only one parameter; you can't have a generic
7404 multi-parameter class.
7410 A default method must be defined entirely using type patterns, or entirely
7411 without. So this is illegal:
7414 op :: a -> (a, Bool)
7415 op {| Unit |} Unit = (Unit, True)
7418 However it is perfectly OK for some methods of a generic class to have
7419 generic default methods and others to have polymorphic default methods.
7425 The type variable(s) in the type pattern for a generic method declaration
7426 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:
7430 op {| p :*: q |} (x :*: y) = op (x :: p)
7438 The type patterns in a generic default method must take one of the forms:
7444 where "a" and "b" are type variables. Furthermore, all the type patterns for
7445 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7446 must use the same type variables. So this is illegal:
7450 op {| a :+: b |} (Inl x) = True
7451 op {| p :+: q |} (Inr y) = False
7453 The type patterns must be identical, even in equations for different methods of the class.
7454 So this too is illegal:
7458 op1 {| a :*: b |} (x :*: y) = True
7461 op2 {| p :*: q |} (x :*: y) = False
7463 (The reason for this restriction is that we gather all the equations for a particular type constructor
7464 into a single generic instance declaration.)
7470 A generic method declaration must give a case for each of the three type constructors.
7476 The type for a generic method can be built only from:
7478 <listitem> <para> Function arrows </para> </listitem>
7479 <listitem> <para> Type variables </para> </listitem>
7480 <listitem> <para> Tuples </para> </listitem>
7481 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7483 Here are some example type signatures for generic methods:
7486 op2 :: Bool -> (a,Bool)
7487 op3 :: [Int] -> a -> a
7490 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7494 This restriction is an implementation restriction: we just haven't got around to
7495 implementing the necessary bidirectional maps over arbitrary type constructors.
7496 It would be relatively easy to add specific type constructors, such as Maybe and list,
7497 to the ones that are allowed.</para>
7502 In an instance declaration for a generic class, the idea is that the compiler
7503 will fill in the methods for you, based on the generic templates. However it can only
7508 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7513 No constructor of the instance type has unboxed fields.
7517 (Of course, these things can only arise if you are already using GHC extensions.)
7518 However, you can still give an instance declarations for types which break these rules,
7519 provided you give explicit code to override any generic default methods.
7527 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7528 what the compiler does with generic declarations.
7533 <sect2> <title> Another example </title>
7535 Just to finish with, here's another example I rather like:
7539 nCons {| Unit |} _ = 1
7540 nCons {| a :*: b |} _ = 1
7541 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7544 tag {| Unit |} _ = 1
7545 tag {| a :*: b |} _ = 1
7546 tag {| a :+: b |} (Inl x) = tag x
7547 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7553 <sect1 id="monomorphism">
7554 <title>Control over monomorphism</title>
7556 <para>GHC supports two flags that control the way in which generalisation is
7557 carried out at let and where bindings.
7561 <title>Switching off the dreaded Monomorphism Restriction</title>
7562 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7564 <para>Haskell's monomorphism restriction (see
7565 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7567 of the Haskell Report)
7568 can be completely switched off by
7569 <option>-XNoMonomorphismRestriction</option>.
7574 <title>Monomorphic pattern bindings</title>
7575 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7576 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7578 <para> As an experimental change, we are exploring the possibility of
7579 making pattern bindings monomorphic; that is, not generalised at all.
7580 A pattern binding is a binding whose LHS has no function arguments,
7581 and is not a simple variable. For example:
7583 f x = x -- Not a pattern binding
7584 f = \x -> x -- Not a pattern binding
7585 f :: Int -> Int = \x -> x -- Not a pattern binding
7587 (g,h) = e -- A pattern binding
7588 (f) = e -- A pattern binding
7589 [x] = e -- A pattern binding
7591 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7592 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7601 ;;; Local Variables: ***
7603 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7604 ;;; ispell-local-dictionary: "british" ***
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