1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individaully.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
137 <para> These two flags control how generalisation is done.
138 See <xref linkend="monomorphism"/>.
145 <option>-XExtendedDefaultRules</option>:
146 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
149 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
150 Independent of the <option>-fglasgow-exts</option>
157 <option>-XOverlappingInstances</option>
158 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
161 <option>-XUndecidableInstances</option>
162 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
165 <option>-XIncoherentInstances</option>
166 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
169 <option>-fcontext-stack=N</option>
170 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
173 <para> See <xref linkend="instance-decls"/>. Only relevant
174 if you also use <option>-fglasgow-exts</option>.</para>
180 <option>-finline-phase</option>
181 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
184 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
185 you also use <option>-fglasgow-exts</option>.</para>
191 <option>-XArrows</option>
192 <indexterm><primary><option>-XArrows</option></primary></indexterm>
195 <para>See <xref linkend="arrow-notation"/>. Independent of
196 <option>-fglasgow-exts</option>.</para>
198 <para>New reserved words/symbols: <literal>rec</literal>,
199 <literal>proc</literal>, <literal>-<</literal>,
200 <literal>>-</literal>, <literal>-<<</literal>,
201 <literal>>>-</literal>.</para>
203 <para>Other syntax stolen: <literal>(|</literal>,
204 <literal>|)</literal>.</para>
210 <option>-XGenerics</option>
211 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
214 <para>See <xref linkend="generic-classes"/>. Independent of
215 <option>-fglasgow-exts</option>.</para>
220 <term><option>-XNoImplicitPrelude</option></term>
222 <para><indexterm><primary>-XNoImplicitPrelude
223 option</primary></indexterm> GHC normally imports
224 <filename>Prelude.hi</filename> files for you. If you'd
225 rather it didn't, then give it a
226 <option>-XNoImplicitPrelude</option> option. The idea is
227 that you can then import a Prelude of your own. (But don't
228 call it <literal>Prelude</literal>; the Haskell module
229 namespace is flat, and you must not conflict with any
230 Prelude module.)</para>
232 <para>Even though you have not imported the Prelude, most of
233 the built-in syntax still refers to the built-in Haskell
234 Prelude types and values, as specified by the Haskell
235 Report. For example, the type <literal>[Int]</literal>
236 still means <literal>Prelude.[] Int</literal>; tuples
237 continue to refer to the standard Prelude tuples; the
238 translation for list comprehensions continues to use
239 <literal>Prelude.map</literal> etc.</para>
241 <para>However, <option>-XNoImplicitPrelude</option> does
242 change the handling of certain built-in syntax: see <xref
243 linkend="rebindable-syntax"/>.</para>
248 <term><option>-XImplicitParams</option></term>
250 <para>Enables implicit parameters (see <xref
251 linkend="implicit-parameters"/>). Currently also implied by
252 <option>-fglasgow-exts</option>.</para>
255 <literal>?<replaceable>varid</replaceable></literal>,
256 <literal>%<replaceable>varid</replaceable></literal>.</para>
261 <term><option>-XOverloadedStrings</option></term>
263 <para>Enables overloaded string literals (see <xref
264 linkend="overloaded-strings"/>).</para>
269 <term><option>-XScopedTypeVariables</option></term>
271 <para>Enables lexically-scoped type variables (see <xref
272 linkend="scoped-type-variables"/>). Implied by
273 <option>-fglasgow-exts</option>.</para>
278 <term><option>-XTemplateHaskell</option></term>
280 <para>Enables Template Haskell (see <xref
281 linkend="template-haskell"/>). This flag must
282 be given explicitly; it is no longer implied by
283 <option>-fglasgow-exts</option>.</para>
285 <para>Syntax stolen: <literal>[|</literal>,
286 <literal>[e|</literal>, <literal>[p|</literal>,
287 <literal>[d|</literal>, <literal>[t|</literal>,
288 <literal>$(</literal>,
289 <literal>$<replaceable>varid</replaceable></literal>.</para>
296 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
297 <sect1 id="primitives">
298 <title>Unboxed types and primitive operations</title>
300 <para>GHC is built on a raft of primitive data types and operations.
301 While you really can use this stuff to write fast code,
302 we generally find it a lot less painful, and more satisfying in the
303 long run, to use higher-level language features and libraries. With
304 any luck, the code you write will be optimised to the efficient
305 unboxed version in any case. And if it isn't, we'd like to know
308 <para>We do not currently have good, up-to-date documentation about the
309 primitives, perhaps because they are mainly intended for internal use.
310 There used to be a long section about them here in the User Guide, but it
311 became out of date, and wrong information is worse than none.</para>
313 <para>The Real Truth about what primitive types there are, and what operations
314 work over those types, is held in the file
315 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
316 This file is used directly to generate GHC's primitive-operation definitions, so
317 it is always correct! It is also intended for processing into text.</para>
320 the result of such processing is part of the description of the
322 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
323 Core language</ulink>.
324 So that document is a good place to look for a type-set version.
325 We would be very happy if someone wanted to volunteer to produce an SGML
326 back end to the program that processes <filename>primops.txt</filename> so that
327 we could include the results here in the User Guide.</para>
329 <para>What follows here is a brief summary of some main points.</para>
331 <sect2 id="glasgow-unboxed">
336 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
339 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
340 that values of that type are represented by a pointer to a heap
341 object. The representation of a Haskell <literal>Int</literal>, for
342 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
343 type, however, is represented by the value itself, no pointers or heap
344 allocation are involved.
348 Unboxed types correspond to the “raw machine” types you
349 would use in C: <literal>Int#</literal> (long int),
350 <literal>Double#</literal> (double), <literal>Addr#</literal>
351 (void *), etc. The <emphasis>primitive operations</emphasis>
352 (PrimOps) on these types are what you might expect; e.g.,
353 <literal>(+#)</literal> is addition on
354 <literal>Int#</literal>s, and is the machine-addition that we all
355 know and love—usually one instruction.
359 Primitive (unboxed) types cannot be defined in Haskell, and are
360 therefore built into the language and compiler. Primitive types are
361 always unlifted; that is, a value of a primitive type cannot be
362 bottom. We use the convention that primitive types, values, and
363 operations have a <literal>#</literal> suffix.
367 Primitive values are often represented by a simple bit-pattern, such
368 as <literal>Int#</literal>, <literal>Float#</literal>,
369 <literal>Double#</literal>. But this is not necessarily the case:
370 a primitive value might be represented by a pointer to a
371 heap-allocated object. Examples include
372 <literal>Array#</literal>, the type of primitive arrays. A
373 primitive array is heap-allocated because it is too big a value to fit
374 in a register, and would be too expensive to copy around; in a sense,
375 it is accidental that it is represented by a pointer. If a pointer
376 represents a primitive value, then it really does point to that value:
377 no unevaluated thunks, no indirections…nothing can be at the
378 other end of the pointer than the primitive value.
379 A numerically-intensive program using unboxed types can
380 go a <emphasis>lot</emphasis> faster than its “standard”
381 counterpart—we saw a threefold speedup on one example.
385 There are some restrictions on the use of primitive types:
387 <listitem><para>The main restriction
388 is that you can't pass a primitive value to a polymorphic
389 function or store one in a polymorphic data type. This rules out
390 things like <literal>[Int#]</literal> (i.e. lists of primitive
391 integers). The reason for this restriction is that polymorphic
392 arguments and constructor fields are assumed to be pointers: if an
393 unboxed integer is stored in one of these, the garbage collector would
394 attempt to follow it, leading to unpredictable space leaks. Or a
395 <function>seq</function> operation on the polymorphic component may
396 attempt to dereference the pointer, with disastrous results. Even
397 worse, the unboxed value might be larger than a pointer
398 (<literal>Double#</literal> for instance).
401 <listitem><para> You cannot define a newtype whose representation type
402 (the argument type of the data constructor) is an unboxed type. Thus,
408 <listitem><para> You cannot bind a variable with an unboxed type
409 in a <emphasis>top-level</emphasis> binding.
411 <listitem><para> You cannot bind a variable with an unboxed type
412 in a <emphasis>recursive</emphasis> binding.
414 <listitem><para> You may bind unboxed variables in a (non-recursive,
415 non-top-level) pattern binding, but any such variable causes the entire
417 to become strict. For example:
419 data Foo = Foo Int Int#
421 f x = let (Foo a b, w) = ..rhs.. in ..body..
423 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
425 is strict, and the program behaves as if you had written
427 data Foo = Foo Int Int#
429 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
438 <sect2 id="unboxed-tuples">
439 <title>Unboxed Tuples
443 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
444 they're available by default with <option>-fglasgow-exts</option>. An
445 unboxed tuple looks like this:
457 where <literal>e_1..e_n</literal> are expressions of any
458 type (primitive or non-primitive). The type of an unboxed tuple looks
463 Unboxed tuples are used for functions that need to return multiple
464 values, but they avoid the heap allocation normally associated with
465 using fully-fledged tuples. When an unboxed tuple is returned, the
466 components are put directly into registers or on the stack; the
467 unboxed tuple itself does not have a composite representation. Many
468 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
470 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
471 tuples to avoid unnecessary allocation during sequences of operations.
475 There are some pretty stringent restrictions on the use of unboxed tuples:
480 Values of unboxed tuple types are subject to the same restrictions as
481 other unboxed types; i.e. they may not be stored in polymorphic data
482 structures or passed to polymorphic functions.
489 No variable can have an unboxed tuple type, nor may a constructor or function
490 argument have an unboxed tuple type. The following are all illegal:
494 data Foo = Foo (# Int, Int #)
496 f :: (# Int, Int #) -> (# Int, Int #)
499 g :: (# Int, Int #) -> Int
502 h x = let y = (# x,x #) in ...
509 The typical use of unboxed tuples is simply to return multiple values,
510 binding those multiple results with a <literal>case</literal> expression, thus:
512 f x y = (# x+1, y-1 #)
513 g x = case f x x of { (# a, b #) -> a + b }
515 You can have an unboxed tuple in a pattern binding, thus
517 f x = let (# p,q #) = h x in ..body..
519 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
520 the resulting binding is lazy like any other Haskell pattern binding. The
521 above example desugars like this:
523 f x = let t = case h x o f{ (# p,q #) -> (p,q)
528 Indeed, the bindings can even be recursive.
535 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
537 <sect1 id="syntax-extns">
538 <title>Syntactic extensions</title>
540 <!-- ====================== HIERARCHICAL MODULES ======================= -->
542 <sect2 id="hierarchical-modules">
543 <title>Hierarchical Modules</title>
545 <para>GHC supports a small extension to the syntax of module
546 names: a module name is allowed to contain a dot
547 <literal>‘.’</literal>. This is also known as the
548 “hierarchical module namespace” extension, because
549 it extends the normally flat Haskell module namespace into a
550 more flexible hierarchy of modules.</para>
552 <para>This extension has very little impact on the language
553 itself; modules names are <emphasis>always</emphasis> fully
554 qualified, so you can just think of the fully qualified module
555 name as <quote>the module name</quote>. In particular, this
556 means that the full module name must be given after the
557 <literal>module</literal> keyword at the beginning of the
558 module; for example, the module <literal>A.B.C</literal> must
561 <programlisting>module A.B.C</programlisting>
564 <para>It is a common strategy to use the <literal>as</literal>
565 keyword to save some typing when using qualified names with
566 hierarchical modules. For example:</para>
569 import qualified Control.Monad.ST.Strict as ST
572 <para>For details on how GHC searches for source and interface
573 files in the presence of hierarchical modules, see <xref
574 linkend="search-path"/>.</para>
576 <para>GHC comes with a large collection of libraries arranged
577 hierarchically; see the accompanying <ulink
578 url="../libraries/index.html">library
579 documentation</ulink>. More libraries to install are available
581 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
584 <!-- ====================== PATTERN GUARDS ======================= -->
586 <sect2 id="pattern-guards">
587 <title>Pattern guards</title>
590 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
591 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.)
595 Suppose we have an abstract data type of finite maps, with a
599 lookup :: FiniteMap -> Int -> Maybe Int
602 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
603 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
607 clunky env var1 var2 | ok1 && ok2 = val1 + val2
608 | otherwise = var1 + var2
619 The auxiliary functions are
623 maybeToBool :: Maybe a -> Bool
624 maybeToBool (Just x) = True
625 maybeToBool Nothing = False
627 expectJust :: Maybe a -> a
628 expectJust (Just x) = x
629 expectJust Nothing = error "Unexpected Nothing"
633 What is <function>clunky</function> doing? The guard <literal>ok1 &&
634 ok2</literal> checks that both lookups succeed, using
635 <function>maybeToBool</function> to convert the <function>Maybe</function>
636 types to booleans. The (lazily evaluated) <function>expectJust</function>
637 calls extract the values from the results of the lookups, and binds the
638 returned values to <varname>val1</varname> and <varname>val2</varname>
639 respectively. If either lookup fails, then clunky takes the
640 <literal>otherwise</literal> case and returns the sum of its arguments.
644 This is certainly legal Haskell, but it is a tremendously verbose and
645 un-obvious way to achieve the desired effect. Arguably, a more direct way
646 to write clunky would be to use case expressions:
650 clunky env var1 var2 = case lookup env var1 of
652 Just val1 -> case lookup env var2 of
654 Just val2 -> val1 + val2
660 This is a bit shorter, but hardly better. Of course, we can rewrite any set
661 of pattern-matching, guarded equations as case expressions; that is
662 precisely what the compiler does when compiling equations! The reason that
663 Haskell provides guarded equations is because they allow us to write down
664 the cases we want to consider, one at a time, independently of each other.
665 This structure is hidden in the case version. Two of the right-hand sides
666 are really the same (<function>fail</function>), and the whole expression
667 tends to become more and more indented.
671 Here is how I would write clunky:
676 | Just val1 <- lookup env var1
677 , Just val2 <- lookup env var2
679 ...other equations for clunky...
683 The semantics should be clear enough. The qualifiers are matched in order.
684 For a <literal><-</literal> qualifier, which I call a pattern guard, the
685 right hand side is evaluated and matched against the pattern on the left.
686 If the match fails then the whole guard fails and the next equation is
687 tried. If it succeeds, then the appropriate binding takes place, and the
688 next qualifier is matched, in the augmented environment. Unlike list
689 comprehensions, however, the type of the expression to the right of the
690 <literal><-</literal> is the same as the type of the pattern to its
691 left. The bindings introduced by pattern guards scope over all the
692 remaining guard qualifiers, and over the right hand side of the equation.
696 Just as with list comprehensions, boolean expressions can be freely mixed
697 with among the pattern guards. For example:
708 Haskell's current guards therefore emerge as a special case, in which the
709 qualifier list has just one element, a boolean expression.
713 <!-- ===================== View patterns =================== -->
715 <sect2 id="view-patterns">
720 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
721 More information and examples of view patterns can be found on the
722 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
727 View patterns are somewhat like pattern guards that can be nested inside
728 of other patterns. They are a convenient way of pattern-matching
729 against values of abstract types. For example, in a programming language
730 implementation, we might represent the syntax of the types of the
739 view :: Type -> TypeView
741 -- additional operations for constructing Typ's ...
744 The representation of Typ is held abstract, permitting implementations
745 to use a fancy representation (e.g., hash-consing to managage sharing).
747 Without view patterns, using this signature a little inconvenient:
749 size :: Typ -> Integer
750 size t = case view t of
752 Arrow t1 t2 -> size t1 + size t2
755 It is necessary to iterate the case, rather than using an equational
756 function definition. And the situation is even worse when the matching
757 against <literal>t</literal> is buried deep inside another pattern.
761 View patterns permit calling the view function inside the pattern and
762 matching against the result:
764 size (view -> Unit) = 1
765 size (view -> Arrow t1 t2) = size t1 + size t2
768 That is, we add a new form of pattern, written
769 <replaceable>expression</replaceable> <literal>-></literal>
770 <replaceable>pattern</replaceable> that means "apply the expression to
771 whatever we're trying to match against, and then match the result of
772 that application against the pattern". The expression can be any Haskell
773 expression of function type, and view patterns can be used wherever
778 The semantics of a pattern <literal>(</literal>
779 <replaceable>exp</replaceable> <literal>-></literal>
780 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
786 <para>The variables bound by the view pattern are the variables bound by
787 <replaceable>pat</replaceable>.
791 Any variables in <replaceable>exp</replaceable> are bound occurrences,
792 but variables bound "to the left" in a pattern are in scope. This
793 feature permits, for example, one argument to a function to be used in
794 the view of another argument. For example, the function
795 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
796 written using view patterns as follows:
799 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
800 ...other equations for clunky...
805 More precisely, the scoping rules are:
809 In a single pattern, variables bound by patterns to the left of a view
810 pattern expression are in scope. For example:
812 example :: Maybe ((String -> Integer,Integer), String) -> Bool
813 example Just ((f,_), f -> 4) = True
816 Additionally, in function definitions, variables bound by matching earlier curried
817 arguments may be used in view pattern expressions in later arguments:
819 example :: (String -> Integer) -> String -> Bool
820 example f (f -> 4) = True
822 That is, the scoping is the same as it would be if the curried arguments
823 were collected into a tuple.
829 In mutually recursive bindings, such as <literal>let</literal>,
830 <literal>where</literal>, or the top level, view patterns in one
831 declaration may not mention variables bound by other declarations. That
832 is, each declaration must be self-contained. For example, the following
833 program is not allowed:
840 restriction in the future; the only cost is that type checking patterns
841 would get a little more complicated.)
851 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
852 <replaceable>T1</replaceable> <literal>-></literal>
853 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
854 a <replaceable>T2</replaceable>, then the whole view pattern matches a
855 <replaceable>T1</replaceable>.
858 <listitem><para> Matching: To the equations in Section 3.17.3 of the
859 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
860 Report</ulink>, add the following:
862 case v of { (e -> p) -> e1 ; _ -> e2 }
864 case (e v) of { p -> e1 ; _ -> e2 }
866 That is, to match a variable <replaceable>v</replaceable> against a pattern
867 <literal>(</literal> <replaceable>exp</replaceable>
868 <literal>-></literal> <replaceable>pat</replaceable>
869 <literal>)</literal>, evaluate <literal>(</literal>
870 <replaceable>exp</replaceable> <replaceable> v</replaceable>
871 <literal>)</literal> and match the result against
872 <replaceable>pat</replaceable>.
875 <listitem><para> Efficiency: When the same view function is applied in
876 multiple branches of a function definition or a case expression (e.g.,
877 in <literal>size</literal> above), GHC makes an attempt to collect these
878 applications into a single nested case expression, so that the view
879 function is only applied once. Pattern compilation in GHC follows the
880 matrix algorithm described in Chapter 4 of <ulink
881 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
882 Implementation of Functional Programming Languages</ulink>. When the
883 top rows of the first column of a matrix are all view patterns with the
884 "same" expression, these patterns are transformed into a single nested
885 case. This includes, for example, adjacent view patterns that line up
888 f ((view -> A, p1), p2) = e1
889 f ((view -> B, p3), p4) = e2
893 <para> The current notion of when two view pattern expressions are "the
894 same" is very restricted: it is not even full syntactic equality.
895 However, it does include variables, literals, applications, and tuples;
896 e.g., two instances of <literal>view ("hi", "there")</literal> will be
897 collected. However, the current implementation does not compare up to
898 alpha-equivalence, so two instances of <literal>(x, view x ->
899 y)</literal> will not be coalesced.
909 <!-- ===================== Recursive do-notation =================== -->
911 <sect2 id="mdo-notation">
912 <title>The recursive do-notation
915 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
916 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
917 by Levent Erkok, John Launchbury,
918 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
919 This paper is essential reading for anyone making non-trivial use of mdo-notation,
920 and we do not repeat it here.
923 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
924 that is, the variables bound in a do-expression are visible only in the textually following
925 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
926 group. It turns out that several applications can benefit from recursive bindings in
927 the do-notation, and this extension provides the necessary syntactic support.
930 Here is a simple (yet contrived) example:
933 import Control.Monad.Fix
935 justOnes = mdo xs <- Just (1:xs)
939 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
943 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
946 class Monad m => MonadFix m where
947 mfix :: (a -> m a) -> m a
950 The function <literal>mfix</literal>
951 dictates how the required recursion operation should be performed. For example,
952 <literal>justOnes</literal> desugars as follows:
954 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
956 For full details of the way in which mdo is typechecked and desugared, see
957 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
958 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
961 If recursive bindings are required for a monad,
962 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
963 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
964 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
965 for Haskell's internal state monad (strict and lazy, respectively).
968 Here are some important points in using the recursive-do notation:
971 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
972 than <literal>do</literal>).
976 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
977 <literal>-fglasgow-exts</literal>.
981 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
982 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
983 be distinct (Section 3.3 of the paper).
987 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
988 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
989 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
990 and improve termination (Section 3.2 of the paper).
996 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
997 contains up to date information on recursive monadic bindings.
1001 Historical note: The old implementation of the mdo-notation (and most
1002 of the existing documents) used the name
1003 <literal>MonadRec</literal> for the class and the corresponding library.
1004 This name is not supported by GHC.
1010 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1012 <sect2 id="parallel-list-comprehensions">
1013 <title>Parallel List Comprehensions</title>
1014 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1016 <indexterm><primary>parallel list comprehensions</primary>
1019 <para>Parallel list comprehensions are a natural extension to list
1020 comprehensions. List comprehensions can be thought of as a nice
1021 syntax for writing maps and filters. Parallel comprehensions
1022 extend this to include the zipWith family.</para>
1024 <para>A parallel list comprehension has multiple independent
1025 branches of qualifier lists, each separated by a `|' symbol. For
1026 example, the following zips together two lists:</para>
1029 [ (x, y) | x <- xs | y <- ys ]
1032 <para>The behavior of parallel list comprehensions follows that of
1033 zip, in that the resulting list will have the same length as the
1034 shortest branch.</para>
1036 <para>We can define parallel list comprehensions by translation to
1037 regular comprehensions. Here's the basic idea:</para>
1039 <para>Given a parallel comprehension of the form: </para>
1042 [ e | p1 <- e11, p2 <- e12, ...
1043 | q1 <- e21, q2 <- e22, ...
1048 <para>This will be translated to: </para>
1051 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1052 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1057 <para>where `zipN' is the appropriate zip for the given number of
1062 <!-- ===================== REBINDABLE SYNTAX =================== -->
1064 <sect2 id="rebindable-syntax">
1065 <title>Rebindable syntax</title>
1067 <para>GHC allows most kinds of built-in syntax to be rebound by
1068 the user, to facilitate replacing the <literal>Prelude</literal>
1069 with a home-grown version, for example.</para>
1071 <para>You may want to define your own numeric class
1072 hierarchy. It completely defeats that purpose if the
1073 literal "1" means "<literal>Prelude.fromInteger
1074 1</literal>", which is what the Haskell Report specifies.
1075 So the <option>-XNoImplicitPrelude</option> flag causes
1076 the following pieces of built-in syntax to refer to
1077 <emphasis>whatever is in scope</emphasis>, not the Prelude
1082 <para>An integer literal <literal>368</literal> means
1083 "<literal>fromInteger (368::Integer)</literal>", rather than
1084 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1087 <listitem><para>Fractional literals are handed in just the same way,
1088 except that the translation is
1089 <literal>fromRational (3.68::Rational)</literal>.
1092 <listitem><para>The equality test in an overloaded numeric pattern
1093 uses whatever <literal>(==)</literal> is in scope.
1096 <listitem><para>The subtraction operation, and the
1097 greater-than-or-equal test, in <literal>n+k</literal> patterns
1098 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1102 <para>Negation (e.g. "<literal>- (f x)</literal>")
1103 means "<literal>negate (f x)</literal>", both in numeric
1104 patterns, and expressions.
1108 <para>"Do" notation is translated using whatever
1109 functions <literal>(>>=)</literal>,
1110 <literal>(>>)</literal>, and <literal>fail</literal>,
1111 are in scope (not the Prelude
1112 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1113 comprehensions, are unaffected. </para></listitem>
1117 notation (see <xref linkend="arrow-notation"/>)
1118 uses whatever <literal>arr</literal>,
1119 <literal>(>>>)</literal>, <literal>first</literal>,
1120 <literal>app</literal>, <literal>(|||)</literal> and
1121 <literal>loop</literal> functions are in scope. But unlike the
1122 other constructs, the types of these functions must match the
1123 Prelude types very closely. Details are in flux; if you want
1127 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1128 even if that is a little unexpected. For emample, the
1129 static semantics of the literal <literal>368</literal>
1130 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1131 <literal>fromInteger</literal> to have any of the types:
1133 fromInteger :: Integer -> Integer
1134 fromInteger :: forall a. Foo a => Integer -> a
1135 fromInteger :: Num a => a -> Integer
1136 fromInteger :: Integer -> Bool -> Bool
1140 <para>Be warned: this is an experimental facility, with
1141 fewer checks than usual. Use <literal>-dcore-lint</literal>
1142 to typecheck the desugared program. If Core Lint is happy
1143 you should be all right.</para>
1147 <sect2 id="postfix-operators">
1148 <title>Postfix operators</title>
1151 GHC allows a small extension to the syntax of left operator sections, which
1152 allows you to define postfix operators. The extension is this: the left section
1156 is equivalent (from the point of view of both type checking and execution) to the expression
1160 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1161 The strict Haskell 98 interpretation is that the section is equivalent to
1165 That is, the operator must be a function of two arguments. GHC allows it to
1166 take only one argument, and that in turn allows you to write the function
1169 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1170 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1171 change their behaviour, of course.)
1173 <para>The extension does not extend to the left-hand side of function
1174 definitions; you must define such a function in prefix form.</para>
1178 <sect2 id="disambiguate-fields">
1179 <title>Record field disambiguation</title>
1181 In record construction and record pattern matching
1182 it is entirely unambiguous which field is referred to, even if there are two different
1183 data types in scope with a common field name. For example:
1186 data S = MkS { x :: Int, y :: Bool }
1191 data T = MkT { x :: Int }
1193 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1195 ok2 n = MkT { x = n+1 } -- Unambiguous
1197 bad1 k = k { x = 3 } -- Ambiguous
1198 bad2 k = x k -- Ambiguous
1200 Even though there are two <literal>x</literal>'s in scope,
1201 it is clear that the <literal>x</literal> in the pattern in the
1202 definition of <literal>ok1</literal> can only mean the field
1203 <literal>x</literal> from type <literal>S</literal>. Similarly for
1204 the function <literal>ok2</literal>. However, in the record update
1205 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1206 it is not clear which of the two types is intended.
1209 Haskell 98 regards all four as ambiguous, but with the
1210 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1211 the former two. The rules are precisely the same as those for instance
1212 declarations in Haskell 98, where the method names on the left-hand side
1213 of the method bindings in an instance declaration refer unambiguously
1214 to the method of that class (provided they are in scope at all), even
1215 if there are other variables in scope with the same name.
1216 This reduces the clutter of qualified names when you import two
1217 records from different modules that use the same field name.
1221 <!-- ===================== Record puns =================== -->
1223 <sect2 id="record-puns">
1228 Record puns are enabled by the flag <literal>-XRecordPuns</literal>.
1232 When using records, it is common to write a pattern that binds a
1233 variable with the same name as a record field, such as:
1236 data C = C {a :: Int}
1242 Record punning permits the variable name to be elided, so one can simply
1249 to mean the same pattern as above. That is, in a record pattern, the
1250 pattern <literal>a</literal> expands into the pattern <literal>a =
1251 a</literal> for the same name <literal>a</literal>.
1255 Note that puns and other patterns can be mixed in the same record:
1257 data C = C {a :: Int, b :: Int}
1258 f (C {a, b = 4}) = a
1260 and that puns can be used wherever record patterns occur (e.g. in
1261 <literal>let</literal> bindings or at the top-level).
1265 Record punning can also be used in an expression, writing, for example,
1271 let a = 1 in C {a = a}
1274 Note that this expansion is purely syntactic, so the record pun
1275 expression refers to the nearest enclosing variable that is spelled the
1276 same as the field name.
1281 <!-- ===================== Record wildcards =================== -->
1283 <sect2 id="record-wildcards">
1284 <title>Record wildcards
1288 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1292 For records with many fields, it can be tiresome to write out each field
1293 individually in a record pattern, as in
1295 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1296 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1301 Record wildcard syntax permits a (<literal>..</literal>) in a record
1302 pattern, where each elided field <literal>f</literal> is replaced by the
1303 pattern <literal>f = f</literal>. For example, the above pattern can be
1306 f (C {a = 1, ..}) = b + c + d
1311 Note that wildcards can be mixed with other patterns, including puns
1312 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1313 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1314 wherever record patterns occur, including in <literal>let</literal>
1315 bindings and at the top-level. For example, the top-level binding
1319 defines <literal>b</literal>, <literal>c</literal>, and
1320 <literal>d</literal>.
1324 Record wildcards can also be used in expressions, writing, for example,
1327 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1333 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1336 Note that this expansion is purely syntactic, so the record wildcard
1337 expression refers to the nearest enclosing variables that are spelled
1338 the same as the omitted field names.
1343 <!-- ===================== Local fixity declarations =================== -->
1345 <sect2 id="local-fixity-declarations">
1346 <title>Local Fixity Declarations
1349 <para>A careful reading of the Haskell 98 Report reveals that fixity
1350 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1351 <literal>infixr</literal>) are permitted to appear inside local bindings
1352 such those introduced by <literal>let</literal> and
1353 <literal>where</literal>. However, the Haskell Report does not specify
1354 the semantics of such bindings very precisely.
1357 <para>In GHC, a fixity declaration may accompany a local binding:
1364 and the fixity declaration applies wherever the binding is in scope.
1365 For example, in a <literal>let</literal>, it applies in the right-hand
1366 sides of other <literal>let</literal>-bindings and the body of the
1367 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1368 expressions (<xref linkend="mdo-notation"/>), the local fixity
1369 declarations of aA <literal>let</literal> statement scope over other
1370 statements in the group, just as the bound name does.
1373 Moreover, a local fixity declatation *must* accompany a local binding of
1374 that name: it is not possible to revise the fixity of name bound
1377 let infixr 9 $ in ...
1380 Because local fixity declarations are technically Haskell 98, no flag is
1381 necessary to enable them.
1387 <!-- TYPE SYSTEM EXTENSIONS -->
1388 <sect1 id="data-type-extensions">
1389 <title>Extensions to data types and type synonyms</title>
1391 <sect2 id="nullary-types">
1392 <title>Data types with no constructors</title>
1394 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1395 a data type with no constructors. For example:</para>
1399 data T a -- T :: * -> *
1402 <para>Syntactically, the declaration lacks the "= constrs" part. The
1403 type can be parameterised over types of any kind, but if the kind is
1404 not <literal>*</literal> then an explicit kind annotation must be used
1405 (see <xref linkend="kinding"/>).</para>
1407 <para>Such data types have only one value, namely bottom.
1408 Nevertheless, they can be useful when defining "phantom types".</para>
1411 <sect2 id="infix-tycons">
1412 <title>Infix type constructors, classes, and type variables</title>
1415 GHC allows type constructors, classes, and type variables to be operators, and
1416 to be written infix, very much like expressions. More specifically:
1419 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1420 The lexical syntax is the same as that for data constructors.
1423 Data type and type-synonym declarations can be written infix, parenthesised
1424 if you want further arguments. E.g.
1426 data a :*: b = Foo a b
1427 type a :+: b = Either a b
1428 class a :=: b where ...
1430 data (a :**: b) x = Baz a b x
1431 type (a :++: b) y = Either (a,b) y
1435 Types, and class constraints, can be written infix. For example
1438 f :: (a :=: b) => a -> b
1442 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1443 The lexical syntax is the same as that for variable operators, excluding "(.)",
1444 "(!)", and "(*)". In a binding position, the operator must be
1445 parenthesised. For example:
1447 type T (+) = Int + Int
1451 liftA2 :: Arrow (~>)
1452 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1458 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1459 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1462 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1463 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1464 sets the fixity for a data constructor and the corresponding type constructor. For example:
1468 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1469 and similarly for <literal>:*:</literal>.
1470 <literal>Int `a` Bool</literal>.
1473 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1480 <sect2 id="type-synonyms">
1481 <title>Liberalised type synonyms</title>
1484 Type synonyms are like macros at the type level, and
1485 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1486 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1488 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1489 in a type synonym, thus:
1491 type Discard a = forall b. Show b => a -> b -> (a, String)
1496 g :: Discard Int -> (Int,String) -- A rank-2 type
1503 You can write an unboxed tuple in a type synonym:
1505 type Pr = (# Int, Int #)
1513 You can apply a type synonym to a forall type:
1515 type Foo a = a -> a -> Bool
1517 f :: Foo (forall b. b->b)
1519 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1521 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1526 You can apply a type synonym to a partially applied type synonym:
1528 type Generic i o = forall x. i x -> o x
1531 foo :: Generic Id []
1533 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1535 foo :: forall x. x -> [x]
1543 GHC currently does kind checking before expanding synonyms (though even that
1547 After expanding type synonyms, GHC does validity checking on types, looking for
1548 the following mal-formedness which isn't detected simply by kind checking:
1551 Type constructor applied to a type involving for-alls.
1554 Unboxed tuple on left of an arrow.
1557 Partially-applied type synonym.
1561 this will be rejected:
1563 type Pr = (# Int, Int #)
1568 because GHC does not allow unboxed tuples on the left of a function arrow.
1573 <sect2 id="existential-quantification">
1574 <title>Existentially quantified data constructors
1578 The idea of using existential quantification in data type declarations
1579 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1580 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1581 London, 1991). It was later formalised by Laufer and Odersky
1582 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1583 TOPLAS, 16(5), pp1411-1430, 1994).
1584 It's been in Lennart
1585 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1586 proved very useful. Here's the idea. Consider the declaration:
1592 data Foo = forall a. MkFoo a (a -> Bool)
1599 The data type <literal>Foo</literal> has two constructors with types:
1605 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1612 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1613 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1614 For example, the following expression is fine:
1620 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1626 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1627 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1628 isUpper</function> packages a character with a compatible function. These
1629 two things are each of type <literal>Foo</literal> and can be put in a list.
1633 What can we do with a value of type <literal>Foo</literal>?. In particular,
1634 what happens when we pattern-match on <function>MkFoo</function>?
1640 f (MkFoo val fn) = ???
1646 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1647 are compatible, the only (useful) thing we can do with them is to
1648 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1655 f (MkFoo val fn) = fn val
1661 What this allows us to do is to package heterogenous values
1662 together with a bunch of functions that manipulate them, and then treat
1663 that collection of packages in a uniform manner. You can express
1664 quite a bit of object-oriented-like programming this way.
1667 <sect3 id="existential">
1668 <title>Why existential?
1672 What has this to do with <emphasis>existential</emphasis> quantification?
1673 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1679 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1685 But Haskell programmers can safely think of the ordinary
1686 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1687 adding a new existential quantification construct.
1693 <title>Type classes</title>
1696 An easy extension is to allow
1697 arbitrary contexts before the constructor. For example:
1703 data Baz = forall a. Eq a => Baz1 a a
1704 | forall b. Show b => Baz2 b (b -> b)
1710 The two constructors have the types you'd expect:
1716 Baz1 :: forall a. Eq a => a -> a -> Baz
1717 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1723 But when pattern matching on <function>Baz1</function> the matched values can be compared
1724 for equality, and when pattern matching on <function>Baz2</function> the first matched
1725 value can be converted to a string (as well as applying the function to it).
1726 So this program is legal:
1733 f (Baz1 p q) | p == q = "Yes"
1735 f (Baz2 v fn) = show (fn v)
1741 Operationally, in a dictionary-passing implementation, the
1742 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1743 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1744 extract it on pattern matching.
1748 Notice the way that the syntax fits smoothly with that used for
1749 universal quantification earlier.
1754 <sect3 id="existential-records">
1755 <title>Record Constructors</title>
1758 GHC allows existentials to be used with records syntax as well. For example:
1761 data Counter a = forall self. NewCounter
1763 , _inc :: self -> self
1764 , _display :: self -> IO ()
1768 Here <literal>tag</literal> is a public field, with a well-typed selector
1769 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1770 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1771 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1772 compile-time error. In other words, <emphasis>GHC defines a record selector function
1773 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1774 (This example used an underscore in the fields for which record selectors
1775 will not be defined, but that is only programming style; GHC ignores them.)
1779 To make use of these hidden fields, we need to create some helper functions:
1782 inc :: Counter a -> Counter a
1783 inc (NewCounter x i d t) = NewCounter
1784 { _this = i x, _inc = i, _display = d, tag = t }
1786 display :: Counter a -> IO ()
1787 display NewCounter{ _this = x, _display = d } = d x
1790 Now we can define counters with different underlying implementations:
1793 counterA :: Counter String
1794 counterA = NewCounter
1795 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1797 counterB :: Counter String
1798 counterB = NewCounter
1799 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1802 display (inc counterA) -- prints "1"
1803 display (inc (inc counterB)) -- prints "##"
1806 At the moment, record update syntax is only supported for Haskell 98 data types,
1807 so the following function does <emphasis>not</emphasis> work:
1810 -- This is invalid; use explicit NewCounter instead for now
1811 setTag :: Counter a -> a -> Counter a
1812 setTag obj t = obj{ tag = t }
1821 <title>Restrictions</title>
1824 There are several restrictions on the ways in which existentially-quantified
1825 constructors can be use.
1834 When pattern matching, each pattern match introduces a new,
1835 distinct, type for each existential type variable. These types cannot
1836 be unified with any other type, nor can they escape from the scope of
1837 the pattern match. For example, these fragments are incorrect:
1845 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1846 is the result of <function>f1</function>. One way to see why this is wrong is to
1847 ask what type <function>f1</function> has:
1851 f1 :: Foo -> a -- Weird!
1855 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1860 f1 :: forall a. Foo -> a -- Wrong!
1864 The original program is just plain wrong. Here's another sort of error
1868 f2 (Baz1 a b) (Baz1 p q) = a==q
1872 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1873 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1874 from the two <function>Baz1</function> constructors.
1882 You can't pattern-match on an existentially quantified
1883 constructor in a <literal>let</literal> or <literal>where</literal> group of
1884 bindings. So this is illegal:
1888 f3 x = a==b where { Baz1 a b = x }
1891 Instead, use a <literal>case</literal> expression:
1894 f3 x = case x of Baz1 a b -> a==b
1897 In general, you can only pattern-match
1898 on an existentially-quantified constructor in a <literal>case</literal> expression or
1899 in the patterns of a function definition.
1901 The reason for this restriction is really an implementation one.
1902 Type-checking binding groups is already a nightmare without
1903 existentials complicating the picture. Also an existential pattern
1904 binding at the top level of a module doesn't make sense, because it's
1905 not clear how to prevent the existentially-quantified type "escaping".
1906 So for now, there's a simple-to-state restriction. We'll see how
1914 You can't use existential quantification for <literal>newtype</literal>
1915 declarations. So this is illegal:
1919 newtype T = forall a. Ord a => MkT a
1923 Reason: a value of type <literal>T</literal> must be represented as a
1924 pair of a dictionary for <literal>Ord t</literal> and a value of type
1925 <literal>t</literal>. That contradicts the idea that
1926 <literal>newtype</literal> should have no concrete representation.
1927 You can get just the same efficiency and effect by using
1928 <literal>data</literal> instead of <literal>newtype</literal>. If
1929 there is no overloading involved, then there is more of a case for
1930 allowing an existentially-quantified <literal>newtype</literal>,
1931 because the <literal>data</literal> version does carry an
1932 implementation cost, but single-field existentially quantified
1933 constructors aren't much use. So the simple restriction (no
1934 existential stuff on <literal>newtype</literal>) stands, unless there
1935 are convincing reasons to change it.
1943 You can't use <literal>deriving</literal> to define instances of a
1944 data type with existentially quantified data constructors.
1946 Reason: in most cases it would not make sense. For example:;
1949 data T = forall a. MkT [a] deriving( Eq )
1952 To derive <literal>Eq</literal> in the standard way we would need to have equality
1953 between the single component of two <function>MkT</function> constructors:
1957 (MkT a) == (MkT b) = ???
1960 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1961 It's just about possible to imagine examples in which the derived instance
1962 would make sense, but it seems altogether simpler simply to prohibit such
1963 declarations. Define your own instances!
1974 <!-- ====================== Generalised algebraic data types ======================= -->
1976 <sect2 id="gadt-style">
1977 <title>Declaring data types with explicit constructor signatures</title>
1979 <para>GHC allows you to declare an algebraic data type by
1980 giving the type signatures of constructors explicitly. For example:
1984 Just :: a -> Maybe a
1986 The form is called a "GADT-style declaration"
1987 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1988 can only be declared using this form.</para>
1989 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1990 For example, these two declarations are equivalent:
1992 data Foo = forall a. MkFoo a (a -> Bool)
1993 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1996 <para>Any data type that can be declared in standard Haskell-98 syntax
1997 can also be declared using GADT-style syntax.
1998 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1999 they treat class constraints on the data constructors differently.
2000 Specifically, if the constructor is given a type-class context, that
2001 context is made available by pattern matching. For example:
2004 MkSet :: Eq a => [a] -> Set a
2006 makeSet :: Eq a => [a] -> Set a
2007 makeSet xs = MkSet (nub xs)
2009 insert :: a -> Set a -> Set a
2010 insert a (MkSet as) | a `elem` as = MkSet as
2011 | otherwise = MkSet (a:as)
2013 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2014 gives rise to a <literal>(Eq a)</literal>
2015 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2016 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2017 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2018 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2019 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2020 In the example, the equality dictionary is used to satisfy the equality constraint
2021 generated by the call to <literal>elem</literal>, so that the type of
2022 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2024 <para>This behaviour contrasts with Haskell 98's peculiar treament of
2025 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2026 In Haskell 98 the defintion
2028 data Eq a => Set' a = MkSet' [a]
2030 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2031 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2032 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2033 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2034 GHC's behaviour is much more useful, as well as much more intuitive.</para>
2036 For example, a possible application of GHC's behaviour is to reify dictionaries:
2038 data NumInst a where
2039 MkNumInst :: Num a => NumInst a
2041 intInst :: NumInst Int
2044 plus :: NumInst a -> a -> a -> a
2045 plus MkNumInst p q = p + q
2047 Here, a value of type <literal>NumInst a</literal> is equivalent
2048 to an explicit <literal>(Num a)</literal> dictionary.
2052 The rest of this section gives further details about GADT-style data
2057 The result type of each data constructor must begin with the type constructor being defined.
2058 If the result type of all constructors
2059 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2060 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2061 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2065 The type signature of
2066 each constructor is independent, and is implicitly universally quantified as usual.
2067 Different constructors may have different universally-quantified type variables
2068 and different type-class constraints.
2069 For example, this is fine:
2072 T1 :: Eq b => b -> T b
2073 T2 :: (Show c, Ix c) => c -> [c] -> T c
2078 Unlike a Haskell-98-style
2079 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2080 have no scope. Indeed, one can write a kind signature instead:
2082 data Set :: * -> * where ...
2084 or even a mixture of the two:
2086 data Foo a :: (* -> *) -> * where ...
2088 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2091 data Foo a (b :: * -> *) where ...
2097 You can use strictness annotations, in the obvious places
2098 in the constructor type:
2101 Lit :: !Int -> Term Int
2102 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2103 Pair :: Term a -> Term b -> Term (a,b)
2108 You can use a <literal>deriving</literal> clause on a GADT-style data type
2109 declaration. For example, these two declarations are equivalent
2111 data Maybe1 a where {
2112 Nothing1 :: Maybe1 a ;
2113 Just1 :: a -> Maybe1 a
2114 } deriving( Eq, Ord )
2116 data Maybe2 a = Nothing2 | Just2 a
2122 You can use record syntax on a GADT-style data type declaration:
2126 Adult { name :: String, children :: [Person] } :: Person
2127 Child { name :: String } :: Person
2129 As usual, for every constructor that has a field <literal>f</literal>, the type of
2130 field <literal>f</literal> must be the same (modulo alpha conversion).
2133 At the moment, record updates are not yet possible with GADT-style declarations,
2134 so support is limited to record construction, selection and pattern matching.
2137 aPerson = Adult { name = "Fred", children = [] }
2139 shortName :: Person -> Bool
2140 hasChildren (Adult { children = kids }) = not (null kids)
2141 hasChildren (Child {}) = False
2146 As in the case of existentials declared using the Haskell-98-like record syntax
2147 (<xref linkend="existential-records"/>),
2148 record-selector functions are generated only for those fields that have well-typed
2150 Here is the example of that section, in GADT-style syntax:
2152 data Counter a where
2153 NewCounter { _this :: self
2154 , _inc :: self -> self
2155 , _display :: self -> IO ()
2160 As before, only one selector function is generated here, that for <literal>tag</literal>.
2161 Nevertheless, you can still use all the field names in pattern matching and record construction.
2163 </itemizedlist></para>
2167 <title>Generalised Algebraic Data Types (GADTs)</title>
2169 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2170 by allowing constructors to have richer return types. Here is an example:
2173 Lit :: Int -> Term Int
2174 Succ :: Term Int -> Term Int
2175 IsZero :: Term Int -> Term Bool
2176 If :: Term Bool -> Term a -> Term a -> Term a
2177 Pair :: Term a -> Term b -> Term (a,b)
2179 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2180 case with ordinary data types. This generality allows us to
2181 write a well-typed <literal>eval</literal> function
2182 for these <literal>Terms</literal>:
2186 eval (Succ t) = 1 + eval t
2187 eval (IsZero t) = eval t == 0
2188 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2189 eval (Pair e1 e2) = (eval e1, eval e2)
2191 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2192 For example, in the right hand side of the equation
2197 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2198 A precise specification of the type rules is beyond what this user manual aspires to,
2199 but the design closely follows that described in
2201 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
2202 unification-based type inference for GADTs</ulink>,
2204 The general principle is this: <emphasis>type refinement is only carried out
2205 based on user-supplied type annotations</emphasis>.
2206 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2207 and lots of obscure error messages will
2208 occur. However, the refinement is quite general. For example, if we had:
2210 eval :: Term a -> a -> a
2211 eval (Lit i) j = i+j
2213 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2214 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2215 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2218 These and many other examples are given in papers by Hongwei Xi, and
2219 Tim Sheard. There is a longer introduction
2220 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2222 <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
2223 may use different notation to that implemented in GHC.
2226 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2227 <option>-XGADTs</option>.
2230 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2231 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2232 The result type of each constructor must begin with the type constructor being defined,
2233 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2234 For example, in the <literal>Term</literal> data
2235 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2236 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
2241 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2242 an ordianary data type.
2246 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2250 Lit { val :: Int } :: Term Int
2251 Succ { num :: Term Int } :: Term Int
2252 Pred { num :: Term Int } :: Term Int
2253 IsZero { arg :: Term Int } :: Term Bool
2254 Pair { arg1 :: Term a
2257 If { cnd :: Term Bool
2262 However, for GADTs there is the following additional constraint:
2263 every constructor that has a field <literal>f</literal> must have
2264 the same result type (modulo alpha conversion)
2265 Hence, in the above example, we cannot merge the <literal>num</literal>
2266 and <literal>arg</literal> fields above into a
2267 single name. Although their field types are both <literal>Term Int</literal>,
2268 their selector functions actually have different types:
2271 num :: Term Int -> Term Int
2272 arg :: Term Bool -> Term Int
2282 <!-- ====================== End of Generalised algebraic data types ======================= -->
2284 <sect1 id="deriving">
2285 <title>Extensions to the "deriving" mechanism</title>
2287 <sect2 id="deriving-inferred">
2288 <title>Inferred context for deriving clauses</title>
2291 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2294 data T0 f a = MkT0 a deriving( Eq )
2295 data T1 f a = MkT1 (f a) deriving( Eq )
2296 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2298 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2300 instance Eq a => Eq (T0 f a) where ...
2301 instance Eq (f a) => Eq (T1 f a) where ...
2302 instance Eq (f (f a)) => Eq (T2 f a) where ...
2304 The first of these is obviously fine. The second is still fine, although less obviously.
2305 The third is not Haskell 98, and risks losing termination of instances.
2308 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2309 each constraint in the inferred instance context must consist only of type variables,
2310 with no repititions.
2313 This rule is applied regardless of flags. If you want a more exotic context, you can write
2314 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2318 <sect2 id="stand-alone-deriving">
2319 <title>Stand-alone deriving declarations</title>
2322 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2324 data Foo a = Bar a | Baz String
2326 deriving instance Eq a => Eq (Foo a)
2328 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2329 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2330 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2331 exactly as you would in an ordinary instance declaration.
2332 (In contrast the context is inferred in a <literal>deriving</literal> clause
2333 attached to a data type declaration.) These <literal>deriving instance</literal>
2334 rules obey the same rules concerning form and termination as ordinary instance declarations,
2335 controlled by the same flags; see <xref linkend="instance-decls"/>. </para>
2337 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2338 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2341 newtype Foo a = MkFoo (State Int a)
2343 deriving instance MonadState Int Foo
2345 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2346 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2352 <sect2 id="deriving-typeable">
2353 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2356 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2357 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2358 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2359 classes <literal>Eq</literal>, <literal>Ord</literal>,
2360 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2363 GHC extends this list with two more classes that may be automatically derived
2364 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2365 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2366 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2367 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2369 <para>An instance of <literal>Typeable</literal> can only be derived if the
2370 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2371 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2373 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2374 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2376 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2377 are used, and only <literal>Typeable1</literal> up to
2378 <literal>Typeable7</literal> are provided in the library.)
2379 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2380 class, whose kind suits that of the data type constructor, and
2381 then writing the data type instance by hand.
2385 <sect2 id="newtype-deriving">
2386 <title>Generalised derived instances for newtypes</title>
2389 When you define an abstract type using <literal>newtype</literal>, you may want
2390 the new type to inherit some instances from its representation. In
2391 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2392 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2393 other classes you have to write an explicit instance declaration. For
2394 example, if you define
2397 newtype Dollars = Dollars Int
2400 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2401 explicitly define an instance of <literal>Num</literal>:
2404 instance Num Dollars where
2405 Dollars a + Dollars b = Dollars (a+b)
2408 All the instance does is apply and remove the <literal>newtype</literal>
2409 constructor. It is particularly galling that, since the constructor
2410 doesn't appear at run-time, this instance declaration defines a
2411 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2412 dictionary, only slower!
2416 <sect3> <title> Generalising the deriving clause </title>
2418 GHC now permits such instances to be derived instead,
2419 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2422 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2425 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2426 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2427 derives an instance declaration of the form
2430 instance Num Int => Num Dollars
2433 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2437 We can also derive instances of constructor classes in a similar
2438 way. For example, suppose we have implemented state and failure monad
2439 transformers, such that
2442 instance Monad m => Monad (State s m)
2443 instance Monad m => Monad (Failure m)
2445 In Haskell 98, we can define a parsing monad by
2447 type Parser tok m a = State [tok] (Failure m) a
2450 which is automatically a monad thanks to the instance declarations
2451 above. With the extension, we can make the parser type abstract,
2452 without needing to write an instance of class <literal>Monad</literal>, via
2455 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2458 In this case the derived instance declaration is of the form
2460 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2463 Notice that, since <literal>Monad</literal> is a constructor class, the
2464 instance is a <emphasis>partial application</emphasis> of the new type, not the
2465 entire left hand side. We can imagine that the type declaration is
2466 "eta-converted" to generate the context of the instance
2471 We can even derive instances of multi-parameter classes, provided the
2472 newtype is the last class parameter. In this case, a ``partial
2473 application'' of the class appears in the <literal>deriving</literal>
2474 clause. For example, given the class
2477 class StateMonad s m | m -> s where ...
2478 instance Monad m => StateMonad s (State s m) where ...
2480 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2482 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2483 deriving (Monad, StateMonad [tok])
2486 The derived instance is obtained by completing the application of the
2487 class to the new type:
2490 instance StateMonad [tok] (State [tok] (Failure m)) =>
2491 StateMonad [tok] (Parser tok m)
2496 As a result of this extension, all derived instances in newtype
2497 declarations are treated uniformly (and implemented just by reusing
2498 the dictionary for the representation type), <emphasis>except</emphasis>
2499 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2500 the newtype and its representation.
2504 <sect3> <title> A more precise specification </title>
2506 Derived instance declarations are constructed as follows. Consider the
2507 declaration (after expansion of any type synonyms)
2510 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2516 The <literal>ci</literal> are partial applications of
2517 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2518 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2521 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2524 The type <literal>t</literal> is an arbitrary type.
2527 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2528 nor in the <literal>ci</literal>, and
2531 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2532 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2533 should not "look through" the type or its constructor. You can still
2534 derive these classes for a newtype, but it happens in the usual way, not
2535 via this new mechanism.
2538 Then, for each <literal>ci</literal>, the derived instance
2541 instance ci t => ci (T v1...vk)
2543 As an example which does <emphasis>not</emphasis> work, consider
2545 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2547 Here we cannot derive the instance
2549 instance Monad (State s m) => Monad (NonMonad m)
2552 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2553 and so cannot be "eta-converted" away. It is a good thing that this
2554 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2555 not, in fact, a monad --- for the same reason. Try defining
2556 <literal>>>=</literal> with the correct type: you won't be able to.
2560 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2561 important, since we can only derive instances for the last one. If the
2562 <literal>StateMonad</literal> class above were instead defined as
2565 class StateMonad m s | m -> s where ...
2568 then we would not have been able to derive an instance for the
2569 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2570 classes usually have one "main" parameter for which deriving new
2571 instances is most interesting.
2573 <para>Lastly, all of this applies only for classes other than
2574 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2575 and <literal>Data</literal>, for which the built-in derivation applies (section
2576 4.3.3. of the Haskell Report).
2577 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2578 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2579 the standard method is used or the one described here.)
2586 <!-- TYPE SYSTEM EXTENSIONS -->
2587 <sect1 id="type-class-extensions">
2588 <title>Class and instances declarations</title>
2590 <sect2 id="multi-param-type-classes">
2591 <title>Class declarations</title>
2594 This section, and the next one, documents GHC's type-class extensions.
2595 There's lots of background in the paper <ulink
2596 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2597 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2598 Jones, Erik Meijer).
2601 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2605 <title>Multi-parameter type classes</title>
2607 Multi-parameter type classes are permitted. For example:
2611 class Collection c a where
2612 union :: c a -> c a -> c a
2620 <title>The superclasses of a class declaration</title>
2623 There are no restrictions on the context in a class declaration
2624 (which introduces superclasses), except that the class hierarchy must
2625 be acyclic. So these class declarations are OK:
2629 class Functor (m k) => FiniteMap m k where
2632 class (Monad m, Monad (t m)) => Transform t m where
2633 lift :: m a -> (t m) a
2639 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2640 of "acyclic" involves only the superclass relationships. For example,
2646 op :: D b => a -> b -> b
2649 class C a => D a where { ... }
2653 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2654 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2655 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2662 <sect3 id="class-method-types">
2663 <title>Class method types</title>
2666 Haskell 98 prohibits class method types to mention constraints on the
2667 class type variable, thus:
2670 fromList :: [a] -> s a
2671 elem :: Eq a => a -> s a -> Bool
2673 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2674 contains the constraint <literal>Eq a</literal>, constrains only the
2675 class type variable (in this case <literal>a</literal>).
2676 GHC lifts this restriction.
2683 <sect2 id="functional-dependencies">
2684 <title>Functional dependencies
2687 <para> Functional dependencies are implemented as described by Mark Jones
2688 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2689 In Proceedings of the 9th European Symposium on Programming,
2690 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2694 Functional dependencies are introduced by a vertical bar in the syntax of a
2695 class declaration; e.g.
2697 class (Monad m) => MonadState s m | m -> s where ...
2699 class Foo a b c | a b -> c where ...
2701 There should be more documentation, but there isn't (yet). Yell if you need it.
2704 <sect3><title>Rules for functional dependencies </title>
2706 In a class declaration, all of the class type variables must be reachable (in the sense
2707 mentioned in <xref linkend="type-restrictions"/>)
2708 from the free variables of each method type.
2712 class Coll s a where
2714 insert :: s -> a -> s
2717 is not OK, because the type of <literal>empty</literal> doesn't mention
2718 <literal>a</literal>. Functional dependencies can make the type variable
2721 class Coll s a | s -> a where
2723 insert :: s -> a -> s
2726 Alternatively <literal>Coll</literal> might be rewritten
2729 class Coll s a where
2731 insert :: s a -> a -> s a
2735 which makes the connection between the type of a collection of
2736 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2737 Occasionally this really doesn't work, in which case you can split the
2745 class CollE s => Coll s a where
2746 insert :: s -> a -> s
2753 <title>Background on functional dependencies</title>
2755 <para>The following description of the motivation and use of functional dependencies is taken
2756 from the Hugs user manual, reproduced here (with minor changes) by kind
2757 permission of Mark Jones.
2760 Consider the following class, intended as part of a
2761 library for collection types:
2763 class Collects e ce where
2765 insert :: e -> ce -> ce
2766 member :: e -> ce -> Bool
2768 The type variable e used here represents the element type, while ce is the type
2769 of the container itself. Within this framework, we might want to define
2770 instances of this class for lists or characteristic functions (both of which
2771 can be used to represent collections of any equality type), bit sets (which can
2772 be used to represent collections of characters), or hash tables (which can be
2773 used to represent any collection whose elements have a hash function). Omitting
2774 standard implementation details, this would lead to the following declarations:
2776 instance Eq e => Collects e [e] where ...
2777 instance Eq e => Collects e (e -> Bool) where ...
2778 instance Collects Char BitSet where ...
2779 instance (Hashable e, Collects a ce)
2780 => Collects e (Array Int ce) where ...
2782 All this looks quite promising; we have a class and a range of interesting
2783 implementations. Unfortunately, there are some serious problems with the class
2784 declaration. First, the empty function has an ambiguous type:
2786 empty :: Collects e ce => ce
2788 By "ambiguous" we mean that there is a type variable e that appears on the left
2789 of the <literal>=></literal> symbol, but not on the right. The problem with
2790 this is that, according to the theoretical foundations of Haskell overloading,
2791 we cannot guarantee a well-defined semantics for any term with an ambiguous
2795 We can sidestep this specific problem by removing the empty member from the
2796 class declaration. However, although the remaining members, insert and member,
2797 do not have ambiguous types, we still run into problems when we try to use
2798 them. For example, consider the following two functions:
2800 f x y = insert x . insert y
2803 for which GHC infers the following types:
2805 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2806 g :: (Collects Bool c, Collects Char c) => c -> c
2808 Notice that the type for f allows the two parameters x and y to be assigned
2809 different types, even though it attempts to insert each of the two values, one
2810 after the other, into the same collection. If we're trying to model collections
2811 that contain only one type of value, then this is clearly an inaccurate
2812 type. Worse still, the definition for g is accepted, without causing a type
2813 error. As a result, the error in this code will not be flagged at the point
2814 where it appears. Instead, it will show up only when we try to use g, which
2815 might even be in a different module.
2818 <sect4><title>An attempt to use constructor classes</title>
2821 Faced with the problems described above, some Haskell programmers might be
2822 tempted to use something like the following version of the class declaration:
2824 class Collects e c where
2826 insert :: e -> c e -> c e
2827 member :: e -> c e -> Bool
2829 The key difference here is that we abstract over the type constructor c that is
2830 used to form the collection type c e, and not over that collection type itself,
2831 represented by ce in the original class declaration. This avoids the immediate
2832 problems that we mentioned above: empty has type <literal>Collects e c => c
2833 e</literal>, which is not ambiguous.
2836 The function f from the previous section has a more accurate type:
2838 f :: (Collects e c) => e -> e -> c e -> c e
2840 The function g from the previous section is now rejected with a type error as
2841 we would hope because the type of f does not allow the two arguments to have
2843 This, then, is an example of a multiple parameter class that does actually work
2844 quite well in practice, without ambiguity problems.
2845 There is, however, a catch. This version of the Collects class is nowhere near
2846 as general as the original class seemed to be: only one of the four instances
2847 for <literal>Collects</literal>
2848 given above can be used with this version of Collects because only one of
2849 them---the instance for lists---has a collection type that can be written in
2850 the form c e, for some type constructor c, and element type e.
2854 <sect4><title>Adding functional dependencies</title>
2857 To get a more useful version of the Collects class, Hugs provides a mechanism
2858 that allows programmers to specify dependencies between the parameters of a
2859 multiple parameter class (For readers with an interest in theoretical
2860 foundations and previous work: The use of dependency information can be seen
2861 both as a generalization of the proposal for `parametric type classes' that was
2862 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2863 later framework for "improvement" of qualified types. The
2864 underlying ideas are also discussed in a more theoretical and abstract setting
2865 in a manuscript [implparam], where they are identified as one point in a
2866 general design space for systems of implicit parameterization.).
2868 To start with an abstract example, consider a declaration such as:
2870 class C a b where ...
2872 which tells us simply that C can be thought of as a binary relation on types
2873 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2874 included in the definition of classes to add information about dependencies
2875 between parameters, as in the following examples:
2877 class D a b | a -> b where ...
2878 class E a b | a -> b, b -> a where ...
2880 The notation <literal>a -> b</literal> used here between the | and where
2881 symbols --- not to be
2882 confused with a function type --- indicates that the a parameter uniquely
2883 determines the b parameter, and might be read as "a determines b." Thus D is
2884 not just a relation, but actually a (partial) function. Similarly, from the two
2885 dependencies that are included in the definition of E, we can see that E
2886 represents a (partial) one-one mapping between types.
2889 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2890 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2891 m>=0, meaning that the y parameters are uniquely determined by the x
2892 parameters. Spaces can be used as separators if more than one variable appears
2893 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2894 annotated with multiple dependencies using commas as separators, as in the
2895 definition of E above. Some dependencies that we can write in this notation are
2896 redundant, and will be rejected because they don't serve any useful
2897 purpose, and may instead indicate an error in the program. Examples of
2898 dependencies like this include <literal>a -> a </literal>,
2899 <literal>a -> a a </literal>,
2900 <literal>a -> </literal>, etc. There can also be
2901 some redundancy if multiple dependencies are given, as in
2902 <literal>a->b</literal>,
2903 <literal>b->c </literal>, <literal>a->c </literal>, and
2904 in which some subset implies the remaining dependencies. Examples like this are
2905 not treated as errors. Note that dependencies appear only in class
2906 declarations, and not in any other part of the language. In particular, the
2907 syntax for instance declarations, class constraints, and types is completely
2911 By including dependencies in a class declaration, we provide a mechanism for
2912 the programmer to specify each multiple parameter class more precisely. The
2913 compiler, on the other hand, is responsible for ensuring that the set of
2914 instances that are in scope at any given point in the program is consistent
2915 with any declared dependencies. For example, the following pair of instance
2916 declarations cannot appear together in the same scope because they violate the
2917 dependency for D, even though either one on its own would be acceptable:
2919 instance D Bool Int where ...
2920 instance D Bool Char where ...
2922 Note also that the following declaration is not allowed, even by itself:
2924 instance D [a] b where ...
2926 The problem here is that this instance would allow one particular choice of [a]
2927 to be associated with more than one choice for b, which contradicts the
2928 dependency specified in the definition of D. More generally, this means that,
2929 in any instance of the form:
2931 instance D t s where ...
2933 for some particular types t and s, the only variables that can appear in s are
2934 the ones that appear in t, and hence, if the type t is known, then s will be
2935 uniquely determined.
2938 The benefit of including dependency information is that it allows us to define
2939 more general multiple parameter classes, without ambiguity problems, and with
2940 the benefit of more accurate types. To illustrate this, we return to the
2941 collection class example, and annotate the original definition of <literal>Collects</literal>
2942 with a simple dependency:
2944 class Collects e ce | ce -> e where
2946 insert :: e -> ce -> ce
2947 member :: e -> ce -> Bool
2949 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2950 determined by the type of the collection ce. Note that both parameters of
2951 Collects are of kind *; there are no constructor classes here. Note too that
2952 all of the instances of Collects that we gave earlier can be used
2953 together with this new definition.
2956 What about the ambiguity problems that we encountered with the original
2957 definition? The empty function still has type Collects e ce => ce, but it is no
2958 longer necessary to regard that as an ambiguous type: Although the variable e
2959 does not appear on the right of the => symbol, the dependency for class
2960 Collects tells us that it is uniquely determined by ce, which does appear on
2961 the right of the => symbol. Hence the context in which empty is used can still
2962 give enough information to determine types for both ce and e, without
2963 ambiguity. More generally, we need only regard a type as ambiguous if it
2964 contains a variable on the left of the => that is not uniquely determined
2965 (either directly or indirectly) by the variables on the right.
2968 Dependencies also help to produce more accurate types for user defined
2969 functions, and hence to provide earlier detection of errors, and less cluttered
2970 types for programmers to work with. Recall the previous definition for a
2973 f x y = insert x y = insert x . insert y
2975 for which we originally obtained a type:
2977 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2979 Given the dependency information that we have for Collects, however, we can
2980 deduce that a and b must be equal because they both appear as the second
2981 parameter in a Collects constraint with the same first parameter c. Hence we
2982 can infer a shorter and more accurate type for f:
2984 f :: (Collects a c) => a -> a -> c -> c
2986 In a similar way, the earlier definition of g will now be flagged as a type error.
2989 Although we have given only a few examples here, it should be clear that the
2990 addition of dependency information can help to make multiple parameter classes
2991 more useful in practice, avoiding ambiguity problems, and allowing more general
2992 sets of instance declarations.
2998 <sect2 id="instance-decls">
2999 <title>Instance declarations</title>
3001 <sect3 id="instance-rules">
3002 <title>Relaxed rules for instance declarations</title>
3004 <para>An instance declaration has the form
3006 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 ...
3008 The part before the "<literal>=></literal>" is the
3009 <emphasis>context</emphasis>, while the part after the
3010 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3014 In Haskell 98 the head of an instance declaration
3015 must be of the form <literal>C (T a1 ... an)</literal>, where
3016 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3017 and the <literal>a1 ... an</literal> are distinct type variables.
3018 Furthermore, the assertions in the context of the instance declaration
3019 must be of the form <literal>C a</literal> where <literal>a</literal>
3020 is a type variable that occurs in the head.
3023 The <option>-fglasgow-exts</option> flag loosens these restrictions
3024 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3025 the context and head of the instance declaration can each consist of arbitrary
3026 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3030 The Paterson Conditions: for each assertion in the context
3032 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3033 <listitem><para>The assertion has fewer constructors and variables (taken together
3034 and counting repetitions) than the head</para></listitem>
3038 <listitem><para>The Coverage Condition. For each functional dependency,
3039 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3040 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3041 every type variable in
3042 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3043 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3044 substitution mapping each type variable in the class declaration to the
3045 corresponding type in the instance declaration.
3048 These restrictions ensure that context reduction terminates: each reduction
3049 step makes the problem smaller by at least one
3050 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3051 if you give the <option>-fallow-undecidable-instances</option>
3052 flag (<xref linkend="undecidable-instances"/>).
3053 You can find lots of background material about the reason for these
3054 restrictions in the paper <ulink
3055 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3056 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3059 For example, these are OK:
3061 instance C Int [a] -- Multiple parameters
3062 instance Eq (S [a]) -- Structured type in head
3064 -- Repeated type variable in head
3065 instance C4 a a => C4 [a] [a]
3066 instance Stateful (ST s) (MutVar s)
3068 -- Head can consist of type variables only
3070 instance (Eq a, Show b) => C2 a b
3072 -- Non-type variables in context
3073 instance Show (s a) => Show (Sized s a)
3074 instance C2 Int a => C3 Bool [a]
3075 instance C2 Int a => C3 [a] b
3079 -- Context assertion no smaller than head
3080 instance C a => C a where ...
3081 -- (C b b) has more more occurrences of b than the head
3082 instance C b b => Foo [b] where ...
3087 The same restrictions apply to instances generated by
3088 <literal>deriving</literal> clauses. Thus the following is accepted:
3090 data MinHeap h a = H a (h a)
3093 because the derived instance
3095 instance (Show a, Show (h a)) => Show (MinHeap h a)
3097 conforms to the above rules.
3101 A useful idiom permitted by the above rules is as follows.
3102 If one allows overlapping instance declarations then it's quite
3103 convenient to have a "default instance" declaration that applies if
3104 something more specific does not:
3112 <sect3 id="undecidable-instances">
3113 <title>Undecidable instances</title>
3116 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3117 For example, sometimes you might want to use the following to get the
3118 effect of a "class synonym":
3120 class (C1 a, C2 a, C3 a) => C a where { }
3122 instance (C1 a, C2 a, C3 a) => C a where { }
3124 This allows you to write shorter signatures:
3130 f :: (C1 a, C2 a, C3 a) => ...
3132 The restrictions on functional dependencies (<xref
3133 linkend="functional-dependencies"/>) are particularly troublesome.
3134 It is tempting to introduce type variables in the context that do not appear in
3135 the head, something that is excluded by the normal rules. For example:
3137 class HasConverter a b | a -> b where
3140 data Foo a = MkFoo a
3142 instance (HasConverter a b,Show b) => Show (Foo a) where
3143 show (MkFoo value) = show (convert value)
3145 This is dangerous territory, however. Here, for example, is a program that would make the
3150 instance F [a] [[a]]
3151 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3153 Similarly, it can be tempting to lift the coverage condition:
3155 class Mul a b c | a b -> c where
3156 (.*.) :: a -> b -> c
3158 instance Mul Int Int Int where (.*.) = (*)
3159 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3160 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3162 The third instance declaration does not obey the coverage condition;
3163 and indeed the (somewhat strange) definition:
3165 f = \ b x y -> if b then x .*. [y] else y
3167 makes instance inference go into a loop, because it requires the constraint
3168 <literal>(Mul a [b] b)</literal>.
3171 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3172 the experimental flag <option>-XUndecidableInstances</option>
3173 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3174 both the Paterson Conditions and the Coverage Condition
3175 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3176 fixed-depth recursion stack. If you exceed the stack depth you get a
3177 sort of backtrace, and the opportunity to increase the stack depth
3178 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3184 <sect3 id="instance-overlap">
3185 <title>Overlapping instances</title>
3187 In general, <emphasis>GHC requires that that it be unambiguous which instance
3189 should be used to resolve a type-class constraint</emphasis>. This behaviour
3190 can be modified by two flags: <option>-XOverlappingInstances</option>
3191 <indexterm><primary>-XOverlappingInstances
3192 </primary></indexterm>
3193 and <option>-XIncoherentInstances</option>
3194 <indexterm><primary>-XIncoherentInstances
3195 </primary></indexterm>, as this section discusses. Both these
3196 flags are dynamic flags, and can be set on a per-module basis, using
3197 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3199 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3200 it tries to match every instance declaration against the
3202 by instantiating the head of the instance declaration. For example, consider
3205 instance context1 => C Int a where ... -- (A)
3206 instance context2 => C a Bool where ... -- (B)
3207 instance context3 => C Int [a] where ... -- (C)
3208 instance context4 => C Int [Int] where ... -- (D)
3210 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3211 but (C) and (D) do not. When matching, GHC takes
3212 no account of the context of the instance declaration
3213 (<literal>context1</literal> etc).
3214 GHC's default behaviour is that <emphasis>exactly one instance must match the
3215 constraint it is trying to resolve</emphasis>.
3216 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3217 including both declarations (A) and (B), say); an error is only reported if a
3218 particular constraint matches more than one.
3222 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3223 more than one instance to match, provided there is a most specific one. For
3224 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3225 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3226 most-specific match, the program is rejected.
3229 However, GHC is conservative about committing to an overlapping instance. For example:
3234 Suppose that from the RHS of <literal>f</literal> we get the constraint
3235 <literal>C Int [b]</literal>. But
3236 GHC does not commit to instance (C), because in a particular
3237 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3238 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3239 So GHC rejects the program.
3240 (If you add the flag <option>-XIncoherentInstances</option>,
3241 GHC will instead pick (C), without complaining about
3242 the problem of subsequent instantiations.)
3245 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3246 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3247 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3248 it instead. In this case, GHC will refrain from
3249 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3250 as before) but, rather than rejecting the program, it will infer the type
3252 f :: C Int b => [b] -> [b]
3254 That postpones the question of which instance to pick to the
3255 call site for <literal>f</literal>
3256 by which time more is known about the type <literal>b</literal>.
3259 The willingness to be overlapped or incoherent is a property of
3260 the <emphasis>instance declaration</emphasis> itself, controlled by the
3261 presence or otherwise of the <option>-XOverlappingInstances</option>
3262 and <option>-XIncoherentInstances</option> flags when that mdodule is
3263 being defined. Neither flag is required in a module that imports and uses the
3264 instance declaration. Specifically, during the lookup process:
3267 An instance declaration is ignored during the lookup process if (a) a more specific
3268 match is found, and (b) the instance declaration was compiled with
3269 <option>-XOverlappingInstances</option>. The flag setting for the
3270 more-specific instance does not matter.
3273 Suppose an instance declaration does not match the constraint being looked up, but
3274 does unify with it, so that it might match when the constraint is further
3275 instantiated. Usually GHC will regard this as a reason for not committing to
3276 some other constraint. But if the instance declaration was compiled with
3277 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3278 check for that declaration.
3281 These rules make it possible for a library author to design a library that relies on
3282 overlapping instances without the library client having to know.
3285 If an instance declaration is compiled without
3286 <option>-XOverlappingInstances</option>,
3287 then that instance can never be overlapped. This could perhaps be
3288 inconvenient. Perhaps the rule should instead say that the
3289 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3290 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3291 at a usage site should be permitted regardless of how the instance declarations
3292 are compiled, if the <option>-XOverlappingInstances</option> flag is
3293 used at the usage site. (Mind you, the exact usage site can occasionally be
3294 hard to pin down.) We are interested to receive feedback on these points.
3296 <para>The <option>-XIncoherentInstances</option> flag implies the
3297 <option>-XOverlappingInstances</option> flag, but not vice versa.
3302 <title>Type synonyms in the instance head</title>
3305 <emphasis>Unlike Haskell 98, instance heads may use type
3306 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3307 As always, using a type synonym is just shorthand for
3308 writing the RHS of the type synonym definition. For example:
3312 type Point = (Int,Int)
3313 instance C Point where ...
3314 instance C [Point] where ...
3318 is legal. However, if you added
3322 instance C (Int,Int) where ...
3326 as well, then the compiler will complain about the overlapping
3327 (actually, identical) instance declarations. As always, type synonyms
3328 must be fully applied. You cannot, for example, write:
3333 instance Monad P where ...
3337 This design decision is independent of all the others, and easily
3338 reversed, but it makes sense to me.
3346 <sect2 id="overloaded-strings">
3347 <title>Overloaded string literals
3351 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3352 string literal has type <literal>String</literal>, but with overloaded string
3353 literals enabled (with <literal>-XOverloadedStrings</literal>)
3354 a string literal has type <literal>(IsString a) => a</literal>.
3357 This means that the usual string syntax can be used, e.g., for packed strings
3358 and other variations of string like types. String literals behave very much
3359 like integer literals, i.e., they can be used in both expressions and patterns.
3360 If used in a pattern the literal with be replaced by an equality test, in the same
3361 way as an integer literal is.
3364 The class <literal>IsString</literal> is defined as:
3366 class IsString a where
3367 fromString :: String -> a
3369 The only predefined instance is the obvious one to make strings work as usual:
3371 instance IsString [Char] where
3374 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3375 it explicitly (for exmaple, to give an instance declaration for it), you can import it
3376 from module <literal>GHC.Exts</literal>.
3379 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3383 Each type in a default declaration must be an
3384 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3388 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3389 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3390 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3391 <emphasis>or</emphasis> <literal>IsString</literal>.
3400 import GHC.Exts( IsString(..) )
3402 newtype MyString = MyString String deriving (Eq, Show)
3403 instance IsString MyString where
3404 fromString = MyString
3406 greet :: MyString -> MyString
3407 greet "hello" = "world"
3411 print $ greet "hello"
3412 print $ greet "fool"
3416 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3417 to work since it gets translated into an equality comparison.
3423 <sect1 id="other-type-extensions">
3424 <title>Other type system extensions</title>
3426 <sect2 id="type-restrictions">
3427 <title>Type signatures</title>
3429 <sect3><title>The context of a type signature</title>
3431 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3432 the form <emphasis>(class type-variable)</emphasis> or
3433 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3434 these type signatures are perfectly OK
3437 g :: Ord (T a ()) => ...
3441 GHC imposes the following restrictions on the constraints in a type signature.
3445 forall tv1..tvn (c1, ...,cn) => type
3448 (Here, we write the "foralls" explicitly, although the Haskell source
3449 language omits them; in Haskell 98, all the free type variables of an
3450 explicit source-language type signature are universally quantified,
3451 except for the class type variables in a class declaration. However,
3452 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3461 <emphasis>Each universally quantified type variable
3462 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3464 A type variable <literal>a</literal> is "reachable" if it it appears
3465 in the same constraint as either a type variable free in in
3466 <literal>type</literal>, or another reachable type variable.
3467 A value with a type that does not obey
3468 this reachability restriction cannot be used without introducing
3469 ambiguity; that is why the type is rejected.
3470 Here, for example, is an illegal type:
3474 forall a. Eq a => Int
3478 When a value with this type was used, the constraint <literal>Eq tv</literal>
3479 would be introduced where <literal>tv</literal> is a fresh type variable, and
3480 (in the dictionary-translation implementation) the value would be
3481 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3482 can never know which instance of <literal>Eq</literal> to use because we never
3483 get any more information about <literal>tv</literal>.
3487 that the reachability condition is weaker than saying that <literal>a</literal> is
3488 functionally dependent on a type variable free in
3489 <literal>type</literal> (see <xref
3490 linkend="functional-dependencies"/>). The reason for this is there
3491 might be a "hidden" dependency, in a superclass perhaps. So
3492 "reachable" is a conservative approximation to "functionally dependent".
3493 For example, consider:
3495 class C a b | a -> b where ...
3496 class C a b => D a b where ...
3497 f :: forall a b. D a b => a -> a
3499 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3500 but that is not immediately apparent from <literal>f</literal>'s type.
3506 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3507 universally quantified type variables <literal>tvi</literal></emphasis>.
3509 For example, this type is OK because <literal>C a b</literal> mentions the
3510 universally quantified type variable <literal>b</literal>:
3514 forall a. C a b => burble
3518 The next type is illegal because the constraint <literal>Eq b</literal> does not
3519 mention <literal>a</literal>:
3523 forall a. Eq b => burble
3527 The reason for this restriction is milder than the other one. The
3528 excluded types are never useful or necessary (because the offending
3529 context doesn't need to be witnessed at this point; it can be floated
3530 out). Furthermore, floating them out increases sharing. Lastly,
3531 excluding them is a conservative choice; it leaves a patch of
3532 territory free in case we need it later.
3546 <sect2 id="implicit-parameters">
3547 <title>Implicit parameters</title>
3549 <para> Implicit parameters are implemented as described in
3550 "Implicit parameters: dynamic scoping with static types",
3551 J Lewis, MB Shields, E Meijer, J Launchbury,
3552 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3556 <para>(Most of the following, stil rather incomplete, documentation is
3557 due to Jeff Lewis.)</para>
3559 <para>Implicit parameter support is enabled with the option
3560 <option>-XImplicitParams</option>.</para>
3563 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3564 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3565 context. In Haskell, all variables are statically bound. Dynamic
3566 binding of variables is a notion that goes back to Lisp, but was later
3567 discarded in more modern incarnations, such as Scheme. Dynamic binding
3568 can be very confusing in an untyped language, and unfortunately, typed
3569 languages, in particular Hindley-Milner typed languages like Haskell,
3570 only support static scoping of variables.
3573 However, by a simple extension to the type class system of Haskell, we
3574 can support dynamic binding. Basically, we express the use of a
3575 dynamically bound variable as a constraint on the type. These
3576 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3577 function uses a dynamically-bound variable <literal>?x</literal>
3578 of type <literal>t'</literal>". For
3579 example, the following expresses the type of a sort function,
3580 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3582 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3584 The dynamic binding constraints are just a new form of predicate in the type class system.
3587 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3588 where <literal>x</literal> is
3589 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3590 Use of this construct also introduces a new
3591 dynamic-binding constraint in the type of the expression.
3592 For example, the following definition
3593 shows how we can define an implicitly parameterized sort function in
3594 terms of an explicitly parameterized <literal>sortBy</literal> function:
3596 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3598 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3604 <title>Implicit-parameter type constraints</title>
3606 Dynamic binding constraints behave just like other type class
3607 constraints in that they are automatically propagated. Thus, when a
3608 function is used, its implicit parameters are inherited by the
3609 function that called it. For example, our <literal>sort</literal> function might be used
3610 to pick out the least value in a list:
3612 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3613 least xs = head (sort xs)
3615 Without lifting a finger, the <literal>?cmp</literal> parameter is
3616 propagated to become a parameter of <literal>least</literal> as well. With explicit
3617 parameters, the default is that parameters must always be explicit
3618 propagated. With implicit parameters, the default is to always
3622 An implicit-parameter type constraint differs from other type class constraints in the
3623 following way: All uses of a particular implicit parameter must have
3624 the same type. This means that the type of <literal>(?x, ?x)</literal>
3625 is <literal>(?x::a) => (a,a)</literal>, and not
3626 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3630 <para> You can't have an implicit parameter in the context of a class or instance
3631 declaration. For example, both these declarations are illegal:
3633 class (?x::Int) => C a where ...
3634 instance (?x::a) => Foo [a] where ...
3636 Reason: exactly which implicit parameter you pick up depends on exactly where
3637 you invoke a function. But the ``invocation'' of instance declarations is done
3638 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3639 Easiest thing is to outlaw the offending types.</para>
3641 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3643 f :: (?x :: [a]) => Int -> Int
3646 g :: (Read a, Show a) => String -> String
3649 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3650 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3651 quite unambiguous, and fixes the type <literal>a</literal>.
3656 <title>Implicit-parameter bindings</title>
3659 An implicit parameter is <emphasis>bound</emphasis> using the standard
3660 <literal>let</literal> or <literal>where</literal> binding forms.
3661 For example, we define the <literal>min</literal> function by binding
3662 <literal>cmp</literal>.
3665 min = let ?cmp = (<=) in least
3669 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3670 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3671 (including in a list comprehension, or do-notation, or pattern guards),
3672 or a <literal>where</literal> clause.
3673 Note the following points:
3676 An implicit-parameter binding group must be a
3677 collection of simple bindings to implicit-style variables (no
3678 function-style bindings, and no type signatures); these bindings are
3679 neither polymorphic or recursive.
3682 You may not mix implicit-parameter bindings with ordinary bindings in a
3683 single <literal>let</literal>
3684 expression; use two nested <literal>let</literal>s instead.
3685 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3689 You may put multiple implicit-parameter bindings in a
3690 single binding group; but they are <emphasis>not</emphasis> treated
3691 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3692 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3693 parameter. The bindings are not nested, and may be re-ordered without changing
3694 the meaning of the program.
3695 For example, consider:
3697 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3699 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3700 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3702 f :: (?x::Int) => Int -> Int
3710 <sect3><title>Implicit parameters and polymorphic recursion</title>
3713 Consider these two definitions:
3716 len1 xs = let ?acc = 0 in len_acc1 xs
3719 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3724 len2 xs = let ?acc = 0 in len_acc2 xs
3726 len_acc2 :: (?acc :: Int) => [a] -> Int
3728 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3730 The only difference between the two groups is that in the second group
3731 <literal>len_acc</literal> is given a type signature.
3732 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3733 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3734 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3735 has a type signature, the recursive call is made to the
3736 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3737 as an implicit parameter. So we get the following results in GHCi:
3744 Adding a type signature dramatically changes the result! This is a rather
3745 counter-intuitive phenomenon, worth watching out for.
3749 <sect3><title>Implicit parameters and monomorphism</title>
3751 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3752 Haskell Report) to implicit parameters. For example, consider:
3760 Since the binding for <literal>y</literal> falls under the Monomorphism
3761 Restriction it is not generalised, so the type of <literal>y</literal> is
3762 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3763 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3764 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3765 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3766 <literal>y</literal> in the body of the <literal>let</literal> will see the
3767 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3768 <literal>14</literal>.
3773 <!-- ======================= COMMENTED OUT ========================
3775 We intend to remove linear implicit parameters, so I'm at least removing
3776 them from the 6.6 user manual
3778 <sect2 id="linear-implicit-parameters">
3779 <title>Linear implicit parameters</title>
3781 Linear implicit parameters are an idea developed by Koen Claessen,
3782 Mark Shields, and Simon PJ. They address the long-standing
3783 problem that monads seem over-kill for certain sorts of problem, notably:
3786 <listitem> <para> distributing a supply of unique names </para> </listitem>
3787 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3788 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3792 Linear implicit parameters are just like ordinary implicit parameters,
3793 except that they are "linear"; that is, they cannot be copied, and
3794 must be explicitly "split" instead. Linear implicit parameters are
3795 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3796 (The '/' in the '%' suggests the split!)
3801 import GHC.Exts( Splittable )
3803 data NameSupply = ...
3805 splitNS :: NameSupply -> (NameSupply, NameSupply)
3806 newName :: NameSupply -> Name
3808 instance Splittable NameSupply where
3812 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3813 f env (Lam x e) = Lam x' (f env e)
3816 env' = extend env x x'
3817 ...more equations for f...
3819 Notice that the implicit parameter %ns is consumed
3821 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3822 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3826 So the translation done by the type checker makes
3827 the parameter explicit:
3829 f :: NameSupply -> Env -> Expr -> Expr
3830 f ns env (Lam x e) = Lam x' (f ns1 env e)
3832 (ns1,ns2) = splitNS ns
3834 env = extend env x x'
3836 Notice the call to 'split' introduced by the type checker.
3837 How did it know to use 'splitNS'? Because what it really did
3838 was to introduce a call to the overloaded function 'split',
3839 defined by the class <literal>Splittable</literal>:
3841 class Splittable a where
3844 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3845 split for name supplies. But we can simply write
3851 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3853 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3854 <literal>GHC.Exts</literal>.
3859 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3860 are entirely distinct implicit parameters: you
3861 can use them together and they won't intefere with each other. </para>
3864 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3866 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3867 in the context of a class or instance declaration. </para></listitem>
3871 <sect3><title>Warnings</title>
3874 The monomorphism restriction is even more important than usual.
3875 Consider the example above:
3877 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3878 f env (Lam x e) = Lam x' (f env e)
3881 env' = extend env x x'
3883 If we replaced the two occurrences of x' by (newName %ns), which is
3884 usually a harmless thing to do, we get:
3886 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3887 f env (Lam x e) = Lam (newName %ns) (f env e)
3889 env' = extend env x (newName %ns)
3891 But now the name supply is consumed in <emphasis>three</emphasis> places
3892 (the two calls to newName,and the recursive call to f), so
3893 the result is utterly different. Urk! We don't even have
3897 Well, this is an experimental change. With implicit
3898 parameters we have already lost beta reduction anyway, and
3899 (as John Launchbury puts it) we can't sensibly reason about
3900 Haskell programs without knowing their typing.
3905 <sect3><title>Recursive functions</title>
3906 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3909 foo :: %x::T => Int -> [Int]
3911 foo n = %x : foo (n-1)
3913 where T is some type in class Splittable.</para>
3915 Do you get a list of all the same T's or all different T's
3916 (assuming that split gives two distinct T's back)?
3918 If you supply the type signature, taking advantage of polymorphic
3919 recursion, you get what you'd probably expect. Here's the
3920 translated term, where the implicit param is made explicit:
3923 foo x n = let (x1,x2) = split x
3924 in x1 : foo x2 (n-1)
3926 But if you don't supply a type signature, GHC uses the Hindley
3927 Milner trick of using a single monomorphic instance of the function
3928 for the recursive calls. That is what makes Hindley Milner type inference
3929 work. So the translation becomes
3933 foom n = x : foom (n-1)
3937 Result: 'x' is not split, and you get a list of identical T's. So the
3938 semantics of the program depends on whether or not foo has a type signature.
3941 You may say that this is a good reason to dislike linear implicit parameters
3942 and you'd be right. That is why they are an experimental feature.
3948 ================ END OF Linear Implicit Parameters commented out -->
3950 <sect2 id="kinding">
3951 <title>Explicitly-kinded quantification</title>
3954 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3955 to give the kind explicitly as (machine-checked) documentation,
3956 just as it is nice to give a type signature for a function. On some occasions,
3957 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3958 John Hughes had to define the data type:
3960 data Set cxt a = Set [a]
3961 | Unused (cxt a -> ())
3963 The only use for the <literal>Unused</literal> constructor was to force the correct
3964 kind for the type variable <literal>cxt</literal>.
3967 GHC now instead allows you to specify the kind of a type variable directly, wherever
3968 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
3971 This flag enables kind signatures in the following places:
3973 <listitem><para><literal>data</literal> declarations:
3975 data Set (cxt :: * -> *) a = Set [a]
3976 </screen></para></listitem>
3977 <listitem><para><literal>type</literal> declarations:
3979 type T (f :: * -> *) = f Int
3980 </screen></para></listitem>
3981 <listitem><para><literal>class</literal> declarations:
3983 class (Eq a) => C (f :: * -> *) a where ...
3984 </screen></para></listitem>
3985 <listitem><para><literal>forall</literal>'s in type signatures:
3987 f :: forall (cxt :: * -> *). Set cxt Int
3988 </screen></para></listitem>
3993 The parentheses are required. Some of the spaces are required too, to
3994 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3995 will get a parse error, because "<literal>::*->*</literal>" is a
3996 single lexeme in Haskell.
4000 As part of the same extension, you can put kind annotations in types
4003 f :: (Int :: *) -> Int
4004 g :: forall a. a -> (a :: *)
4008 atype ::= '(' ctype '::' kind ')
4010 The parentheses are required.
4015 <sect2 id="universal-quantification">
4016 <title>Arbitrary-rank polymorphism
4020 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4021 allows us to say exactly what this means. For example:
4029 g :: forall b. (b -> b)
4031 The two are treated identically.
4035 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4036 explicit universal quantification in
4038 For example, all the following types are legal:
4040 f1 :: forall a b. a -> b -> a
4041 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4043 f2 :: (forall a. a->a) -> Int -> Int
4044 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4046 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4048 f4 :: Int -> (forall a. a -> a)
4050 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4051 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4052 The <literal>forall</literal> makes explicit the universal quantification that
4053 is implicitly added by Haskell.
4056 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4057 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4058 shows, the polymorphic type on the left of the function arrow can be overloaded.
4061 The function <literal>f3</literal> has a rank-3 type;
4062 it has rank-2 types on the left of a function arrow.
4065 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
4066 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
4067 that restriction has now been lifted.)
4068 In particular, a forall-type (also called a "type scheme"),
4069 including an operational type class context, is legal:
4071 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4072 of a function arrow </para> </listitem>
4073 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4074 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4075 field type signatures.</para> </listitem>
4076 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4077 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4079 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4080 a type variable any more!
4089 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4090 the types of the constructor arguments. Here are several examples:
4096 data T a = T1 (forall b. b -> b -> b) a
4098 data MonadT m = MkMonad { return :: forall a. a -> m a,
4099 bind :: forall a b. m a -> (a -> m b) -> m b
4102 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4108 The constructors have rank-2 types:
4114 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4115 MkMonad :: forall m. (forall a. a -> m a)
4116 -> (forall a b. m a -> (a -> m b) -> m b)
4118 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4124 Notice that you don't need to use a <literal>forall</literal> if there's an
4125 explicit context. For example in the first argument of the
4126 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4127 prefixed to the argument type. The implicit <literal>forall</literal>
4128 quantifies all type variables that are not already in scope, and are
4129 mentioned in the type quantified over.
4133 As for type signatures, implicit quantification happens for non-overloaded
4134 types too. So if you write this:
4137 data T a = MkT (Either a b) (b -> b)
4140 it's just as if you had written this:
4143 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4146 That is, since the type variable <literal>b</literal> isn't in scope, it's
4147 implicitly universally quantified. (Arguably, it would be better
4148 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4149 where that is what is wanted. Feedback welcomed.)
4153 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4154 the constructor to suitable values, just as usual. For example,
4165 a3 = MkSwizzle reverse
4168 a4 = let r x = Just x
4175 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4176 mkTs f x y = [T1 f x, T1 f y]
4182 The type of the argument can, as usual, be more general than the type
4183 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4184 does not need the <literal>Ord</literal> constraint.)
4188 When you use pattern matching, the bound variables may now have
4189 polymorphic types. For example:
4195 f :: T a -> a -> (a, Char)
4196 f (T1 w k) x = (w k x, w 'c' 'd')
4198 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4199 g (MkSwizzle s) xs f = s (map f (s xs))
4201 h :: MonadT m -> [m a] -> m [a]
4202 h m [] = return m []
4203 h m (x:xs) = bind m x $ \y ->
4204 bind m (h m xs) $ \ys ->
4211 In the function <function>h</function> we use the record selectors <literal>return</literal>
4212 and <literal>bind</literal> to extract the polymorphic bind and return functions
4213 from the <literal>MonadT</literal> data structure, rather than using pattern
4219 <title>Type inference</title>
4222 In general, type inference for arbitrary-rank types is undecidable.
4223 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4224 to get a decidable algorithm by requiring some help from the programmer.
4225 We do not yet have a formal specification of "some help" but the rule is this:
4228 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4229 provides an explicit polymorphic type for x, or GHC's type inference will assume
4230 that x's type has no foralls in it</emphasis>.
4233 What does it mean to "provide" an explicit type for x? You can do that by
4234 giving a type signature for x directly, using a pattern type signature
4235 (<xref linkend="scoped-type-variables"/>), thus:
4237 \ f :: (forall a. a->a) -> (f True, f 'c')
4239 Alternatively, you can give a type signature to the enclosing
4240 context, which GHC can "push down" to find the type for the variable:
4242 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4244 Here the type signature on the expression can be pushed inwards
4245 to give a type signature for f. Similarly, and more commonly,
4246 one can give a type signature for the function itself:
4248 h :: (forall a. a->a) -> (Bool,Char)
4249 h f = (f True, f 'c')
4251 You don't need to give a type signature if the lambda bound variable
4252 is a constructor argument. Here is an example we saw earlier:
4254 f :: T a -> a -> (a, Char)
4255 f (T1 w k) x = (w k x, w 'c' 'd')
4257 Here we do not need to give a type signature to <literal>w</literal>, because
4258 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4265 <sect3 id="implicit-quant">
4266 <title>Implicit quantification</title>
4269 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4270 user-written types, if and only if there is no explicit <literal>forall</literal>,
4271 GHC finds all the type variables mentioned in the type that are not already
4272 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4276 f :: forall a. a -> a
4283 h :: forall b. a -> b -> b
4289 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4292 f :: (a -> a) -> Int
4294 f :: forall a. (a -> a) -> Int
4296 f :: (forall a. a -> a) -> Int
4299 g :: (Ord a => a -> a) -> Int
4300 -- MEANS the illegal type
4301 g :: forall a. (Ord a => a -> a) -> Int
4303 g :: (forall a. Ord a => a -> a) -> Int
4305 The latter produces an illegal type, which you might think is silly,
4306 but at least the rule is simple. If you want the latter type, you
4307 can write your for-alls explicitly. Indeed, doing so is strongly advised
4314 <sect2 id="impredicative-polymorphism">
4315 <title>Impredicative polymorphism
4317 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
4318 that you can call a polymorphic function at a polymorphic type, and
4319 parameterise data structures over polymorphic types. For example:
4321 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4322 f (Just g) = Just (g [3], g "hello")
4325 Notice here that the <literal>Maybe</literal> type is parameterised by the
4326 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4329 <para>The technical details of this extension are described in the paper
4330 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
4331 type inference for higher-rank types and impredicativity</ulink>,
4332 which appeared at ICFP 2006.
4336 <sect2 id="scoped-type-variables">
4337 <title>Lexically scoped type variables
4341 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4342 which some type signatures are simply impossible to write. For example:
4344 f :: forall a. [a] -> [a]
4350 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4351 the entire definition of <literal>f</literal>.
4352 In particular, it is in scope at the type signature for <varname>ys</varname>.
4353 In Haskell 98 it is not possible to declare
4354 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4355 it becomes possible to do so.
4357 <para>Lexically-scoped type variables are enabled by
4358 <option>-fglasgow-exts</option>.
4360 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4361 variables work, compared to earlier releases. Read this section
4365 <title>Overview</title>
4367 <para>The design follows the following principles
4369 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4370 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4371 design.)</para></listitem>
4372 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4373 type variables. This means that every programmer-written type signature
4374 (includin one that contains free scoped type variables) denotes a
4375 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4376 checker, and no inference is involved.</para></listitem>
4377 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4378 changing the program.</para></listitem>
4382 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4384 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4385 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4386 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4387 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4391 In Haskell, a programmer-written type signature is implicitly quantifed over
4392 its free type variables (<ulink
4393 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
4395 of the Haskel Report).
4396 Lexically scoped type variables affect this implicit quantification rules
4397 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4398 quantified. For example, if type variable <literal>a</literal> is in scope,
4401 (e :: a -> a) means (e :: a -> a)
4402 (e :: b -> b) means (e :: forall b. b->b)
4403 (e :: a -> b) means (e :: forall b. a->b)
4411 <sect3 id="decl-type-sigs">
4412 <title>Declaration type signatures</title>
4413 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4414 quantification (using <literal>forall</literal>) brings into scope the
4415 explicitly-quantified
4416 type variables, in the definition of the named function(s). For example:
4418 f :: forall a. [a] -> [a]
4419 f (x:xs) = xs ++ [ x :: a ]
4421 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4422 the definition of "<literal>f</literal>".
4424 <para>This only happens if the quantification in <literal>f</literal>'s type
4425 signature is explicit. For example:
4428 g (x:xs) = xs ++ [ x :: a ]
4430 This program will be rejected, because "<literal>a</literal>" does not scope
4431 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4432 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4433 quantification rules.
4437 <sect3 id="exp-type-sigs">
4438 <title>Expression type signatures</title>
4440 <para>An expression type signature that has <emphasis>explicit</emphasis>
4441 quantification (using <literal>forall</literal>) brings into scope the
4442 explicitly-quantified
4443 type variables, in the annotated expression. For example:
4445 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4447 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4448 type variable <literal>s</literal> into scope, in the annotated expression
4449 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4454 <sect3 id="pattern-type-sigs">
4455 <title>Pattern type signatures</title>
4457 A type signature may occur in any pattern; this is a <emphasis>pattern type
4458 signature</emphasis>.
4461 -- f and g assume that 'a' is already in scope
4462 f = \(x::Int, y::a) -> x
4464 h ((x,y) :: (Int,Bool)) = (y,x)
4466 In the case where all the type variables in the pattern type sigature are
4467 already in scope (i.e. bound by the enclosing context), matters are simple: the
4468 signature simply constrains the type of the pattern in the obvious way.
4471 There is only one situation in which you can write a pattern type signature that
4472 mentions a type variable that is not already in scope, namely in pattern match
4473 of an existential data constructor. For example:
4475 data T = forall a. MkT [a]
4478 k (MkT [t::a]) = MkT t3
4482 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4483 variable that is not already in scope. Indeed, it cannot already be in scope,
4484 because it is bound by the pattern match. GHC's rule is that in this situation
4485 (and only then), a pattern type signature can mention a type variable that is
4486 not already in scope; the effect is to bring it into scope, standing for the
4487 existentially-bound type variable.
4490 If this seems a little odd, we think so too. But we must have
4491 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4492 could not name existentially-bound type variables in subequent type signatures.
4495 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4496 signature is allowed to mention a lexical variable that is not already in
4498 For example, both <literal>f</literal> and <literal>g</literal> would be
4499 illegal if <literal>a</literal> was not already in scope.
4505 <!-- ==================== Commented out part about result type signatures
4507 <sect3 id="result-type-sigs">
4508 <title>Result type signatures</title>
4511 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4514 {- f assumes that 'a' is already in scope -}
4515 f x y :: [a] = [x,y,x]
4517 g = \ x :: [Int] -> [3,4]
4519 h :: forall a. [a] -> a
4523 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4524 the result of the function. Similarly, the body of the lambda in the RHS of
4525 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4526 alternative in <literal>h</literal> is <literal>a</literal>.
4528 <para> A result type signature never brings new type variables into scope.</para>
4530 There are a couple of syntactic wrinkles. First, notice that all three
4531 examples would parse quite differently with parentheses:
4533 {- f assumes that 'a' is already in scope -}
4534 f x (y :: [a]) = [x,y,x]
4536 g = \ (x :: [Int]) -> [3,4]
4538 h :: forall a. [a] -> a
4542 Now the signature is on the <emphasis>pattern</emphasis>; and
4543 <literal>h</literal> would certainly be ill-typed (since the pattern
4544 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4546 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4547 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4548 token or a parenthesised type of some sort). To see why,
4549 consider how one would parse this:
4558 <sect3 id="cls-inst-scoped-tyvars">
4559 <title>Class and instance declarations</title>
4562 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4563 scope over the methods defined in the <literal>where</literal> part. For example:
4581 <sect2 id="typing-binds">
4582 <title>Generalised typing of mutually recursive bindings</title>
4585 The Haskell Report specifies that a group of bindings (at top level, or in a
4586 <literal>let</literal> or <literal>where</literal>) should be sorted into
4587 strongly-connected components, and then type-checked in dependency order
4588 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4589 Report, Section 4.5.1</ulink>).
4590 As each group is type-checked, any binders of the group that
4592 an explicit type signature are put in the type environment with the specified
4594 and all others are monomorphic until the group is generalised
4595 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4598 <para>Following a suggestion of Mark Jones, in his paper
4599 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4601 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4603 <emphasis>the dependency analysis ignores references to variables that have an explicit
4604 type signature</emphasis>.
4605 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4606 typecheck. For example, consider:
4608 f :: Eq a => a -> Bool
4609 f x = (x == x) || g True || g "Yes"
4611 g y = (y <= y) || f True
4613 This is rejected by Haskell 98, but under Jones's scheme the definition for
4614 <literal>g</literal> is typechecked first, separately from that for
4615 <literal>f</literal>,
4616 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4617 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4618 type is generalised, to get
4620 g :: Ord a => a -> Bool
4622 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4623 <literal>g</literal> in the type environment.
4627 The same refined dependency analysis also allows the type signatures of
4628 mutually-recursive functions to have different contexts, something that is illegal in
4629 Haskell 98 (Section 4.5.2, last sentence). With
4630 <option>-XRelaxedPolyRec</option>
4631 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4632 type signatures; in practice this means that only variables bound by the same
4633 pattern binding must have the same context. For example, this is fine:
4635 f :: Eq a => a -> Bool
4636 f x = (x == x) || g True
4638 g :: Ord a => a -> Bool
4639 g y = (y <= y) || f True
4644 <sect2 id="type-families">
4645 <title>Type families
4649 GHC supports the definition of type families indexed by types. They may be
4650 seen as an extension of Haskell 98's class-based overloading of values to
4651 types. When type families are declared in classes, they are also known as
4655 There are two forms of type families: data families and type synonym families.
4656 Currently, only the former are fully implemented, while we are still working
4657 on the latter. As a result, the specification of the language extension is
4658 also still to some degree in flux. Hence, a more detailed description of
4659 the language extension and its use is currently available
4660 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4661 wiki page on type families</ulink>. The material will be moved to this user's
4662 guide when it has stabilised.
4665 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4672 <!-- ==================== End of type system extensions ================= -->
4674 <!-- ====================== TEMPLATE HASKELL ======================= -->
4676 <sect1 id="template-haskell">
4677 <title>Template Haskell</title>
4679 <para>Template Haskell allows you to do compile-time meta-programming in
4682 the main technical innovations is discussed in "<ulink
4683 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4684 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4687 There is a Wiki page about
4688 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4689 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4693 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4694 Haskell library reference material</ulink>
4695 (look for module <literal>Language.Haskell.TH</literal>).
4696 Many changes to the original design are described in
4697 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4698 Notes on Template Haskell version 2</ulink>.
4699 Not all of these changes are in GHC, however.
4702 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4703 as a worked example to help get you started.
4707 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4708 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4713 <title>Syntax</title>
4715 <para> Template Haskell has the following new syntactic
4716 constructions. You need to use the flag
4717 <option>-XTemplateHaskell</option>
4718 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4719 </indexterm>to switch these syntactic extensions on
4720 (<option>-XTemplateHaskell</option> is no longer implied by
4721 <option>-fglasgow-exts</option>).</para>
4725 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4726 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4727 There must be no space between the "$" and the identifier or parenthesis. This use
4728 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4729 of "." as an infix operator. If you want the infix operator, put spaces around it.
4731 <para> A splice can occur in place of
4733 <listitem><para> an expression; the spliced expression must
4734 have type <literal>Q Exp</literal></para></listitem>
4735 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4738 Inside a splice you can can only call functions defined in imported modules,
4739 not functions defined elsewhere in the same module.</listitem>
4743 A expression quotation is written in Oxford brackets, thus:
4745 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4746 the quotation has type <literal>Q Exp</literal>.</para></listitem>
4747 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4748 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4749 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4750 the quotation has type <literal>Q Typ</literal>.</para></listitem>
4751 </itemizedlist></para></listitem>
4754 A name can be quoted with either one or two prefix single quotes:
4756 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
4757 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
4758 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
4760 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
4761 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
4764 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, delarations etc. They
4765 may also be given as an argument to the <literal>reify</literal> function.
4771 (Compared to the original paper, there are many differnces of detail.
4772 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
4773 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
4774 Type splices are not implemented, and neither are pattern splices or quotations.
4778 <sect2> <title> Using Template Haskell </title>
4782 The data types and monadic constructor functions for Template Haskell are in the library
4783 <literal>Language.Haskell.THSyntax</literal>.
4787 You can only run a function at compile time if it is imported from another module. That is,
4788 you can't define a function in a module, and call it from within a splice in the same module.
4789 (It would make sense to do so, but it's hard to implement.)
4793 Furthermore, you can only run a function at compile time if it is imported
4794 from another module <emphasis>that is not part of a mutually-recursive group of modules
4795 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4796 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4797 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4801 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4804 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4805 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4806 compiles and runs a program, and then looks at the result. So it's important that
4807 the program it compiles produces results whose representations are identical to
4808 those of the compiler itself.
4812 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4813 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4818 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
4819 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4820 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4827 -- Import our template "pr"
4828 import Printf ( pr )
4830 -- The splice operator $ takes the Haskell source code
4831 -- generated at compile time by "pr" and splices it into
4832 -- the argument of "putStrLn".
4833 main = putStrLn ( $(pr "Hello") )
4839 -- Skeletal printf from the paper.
4840 -- It needs to be in a separate module to the one where
4841 -- you intend to use it.
4843 -- Import some Template Haskell syntax
4844 import Language.Haskell.TH
4846 -- Describe a format string
4847 data Format = D | S | L String
4849 -- Parse a format string. This is left largely to you
4850 -- as we are here interested in building our first ever
4851 -- Template Haskell program and not in building printf.
4852 parse :: String -> [Format]
4855 -- Generate Haskell source code from a parsed representation
4856 -- of the format string. This code will be spliced into
4857 -- the module which calls "pr", at compile time.
4858 gen :: [Format] -> Q Exp
4859 gen [D] = [| \n -> show n |]
4860 gen [S] = [| \s -> s |]
4861 gen [L s] = stringE s
4863 -- Here we generate the Haskell code for the splice
4864 -- from an input format string.
4865 pr :: String -> Q Exp
4866 pr s = gen (parse s)
4869 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4872 $ ghc --make -XTemplateHaskell main.hs -o main.exe
4875 <para>Run "main.exe" and here is your output:</para>
4885 <title>Using Template Haskell with Profiling</title>
4886 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4888 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4889 interpreter to run the splice expressions. The bytecode interpreter
4890 runs the compiled expression on top of the same runtime on which GHC
4891 itself is running; this means that the compiled code referred to by
4892 the interpreted expression must be compatible with this runtime, and
4893 in particular this means that object code that is compiled for
4894 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4895 expression, because profiled object code is only compatible with the
4896 profiling version of the runtime.</para>
4898 <para>This causes difficulties if you have a multi-module program
4899 containing Template Haskell code and you need to compile it for
4900 profiling, because GHC cannot load the profiled object code and use it
4901 when executing the splices. Fortunately GHC provides a workaround.
4902 The basic idea is to compile the program twice:</para>
4906 <para>Compile the program or library first the normal way, without
4907 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4910 <para>Then compile it again with <option>-prof</option>, and
4911 additionally use <option>-osuf
4912 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4913 to name the object files differentliy (you can choose any suffix
4914 that isn't the normal object suffix here). GHC will automatically
4915 load the object files built in the first step when executing splice
4916 expressions. If you omit the <option>-osuf</option> flag when
4917 building with <option>-prof</option> and Template Haskell is used,
4918 GHC will emit an error message. </para>
4925 <!-- ===================== Arrow notation =================== -->
4927 <sect1 id="arrow-notation">
4928 <title>Arrow notation
4931 <para>Arrows are a generalization of monads introduced by John Hughes.
4932 For more details, see
4937 “Generalising Monads to Arrows”,
4938 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4939 pp67–111, May 2000.
4945 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4946 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4952 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4953 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4959 and the arrows web page at
4960 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4961 With the <option>-XArrows</option> flag, GHC supports the arrow
4962 notation described in the second of these papers.
4963 What follows is a brief introduction to the notation;
4964 it won't make much sense unless you've read Hughes's paper.
4965 This notation is translated to ordinary Haskell,
4966 using combinators from the
4967 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4971 <para>The extension adds a new kind of expression for defining arrows:
4973 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4974 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4976 where <literal>proc</literal> is a new keyword.
4977 The variables of the pattern are bound in the body of the
4978 <literal>proc</literal>-expression,
4979 which is a new sort of thing called a <firstterm>command</firstterm>.
4980 The syntax of commands is as follows:
4982 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4983 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4984 | <replaceable>cmd</replaceable><superscript>0</superscript>
4986 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4987 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4988 infix operators as for expressions, and
4990 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4991 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4992 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4993 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4994 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4995 | <replaceable>fcmd</replaceable>
4997 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4998 | ( <replaceable>cmd</replaceable> )
4999 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5001 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5002 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5003 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5004 | <replaceable>cmd</replaceable>
5006 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5007 except that the bodies are commands instead of expressions.
5011 Commands produce values, but (like monadic computations)
5012 may yield more than one value,
5013 or none, and may do other things as well.
5014 For the most part, familiarity with monadic notation is a good guide to
5016 However the values of expressions, even monadic ones,
5017 are determined by the values of the variables they contain;
5018 this is not necessarily the case for commands.
5022 A simple example of the new notation is the expression
5024 proc x -> f -< x+1
5026 We call this a <firstterm>procedure</firstterm> or
5027 <firstterm>arrow abstraction</firstterm>.
5028 As with a lambda expression, the variable <literal>x</literal>
5029 is a new variable bound within the <literal>proc</literal>-expression.
5030 It refers to the input to the arrow.
5031 In the above example, <literal>-<</literal> is not an identifier but an
5032 new reserved symbol used for building commands from an expression of arrow
5033 type and an expression to be fed as input to that arrow.
5034 (The weird look will make more sense later.)
5035 It may be read as analogue of application for arrows.
5036 The above example is equivalent to the Haskell expression
5038 arr (\ x -> x+1) >>> f
5040 That would make no sense if the expression to the left of
5041 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5042 More generally, the expression to the left of <literal>-<</literal>
5043 may not involve any <firstterm>local variable</firstterm>,
5044 i.e. a variable bound in the current arrow abstraction.
5045 For such a situation there is a variant <literal>-<<</literal>, as in
5047 proc x -> f x -<< x+1
5049 which is equivalent to
5051 arr (\ x -> (f x, x+1)) >>> app
5053 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5055 Such an arrow is equivalent to a monad, so if you're using this form
5056 you may find a monadic formulation more convenient.
5060 <title>do-notation for commands</title>
5063 Another form of command is a form of <literal>do</literal>-notation.
5064 For example, you can write
5073 You can read this much like ordinary <literal>do</literal>-notation,
5074 but with commands in place of monadic expressions.
5075 The first line sends the value of <literal>x+1</literal> as an input to
5076 the arrow <literal>f</literal>, and matches its output against
5077 <literal>y</literal>.
5078 In the next line, the output is discarded.
5079 The arrow <function>returnA</function> is defined in the
5080 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5081 module as <literal>arr id</literal>.
5082 The above example is treated as an abbreviation for
5084 arr (\ x -> (x, x)) >>>
5085 first (arr (\ x -> x+1) >>> f) >>>
5086 arr (\ (y, x) -> (y, (x, y))) >>>
5087 first (arr (\ y -> 2*y) >>> g) >>>
5089 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5090 first (arr (\ (x, z) -> x*z) >>> h) >>>
5091 arr (\ (t, z) -> t+z) >>>
5094 Note that variables not used later in the composition are projected out.
5095 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5097 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5098 module, this reduces to
5100 arr (\ x -> (x+1, x)) >>>
5102 arr (\ (y, x) -> (2*y, (x, y))) >>>
5104 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5106 arr (\ (t, z) -> t+z)
5108 which is what you might have written by hand.
5109 With arrow notation, GHC keeps track of all those tuples of variables for you.
5113 Note that although the above translation suggests that
5114 <literal>let</literal>-bound variables like <literal>z</literal> must be
5115 monomorphic, the actual translation produces Core,
5116 so polymorphic variables are allowed.
5120 It's also possible to have mutually recursive bindings,
5121 using the new <literal>rec</literal> keyword, as in the following example:
5123 counter :: ArrowCircuit a => a Bool Int
5124 counter = proc reset -> do
5125 rec output <- returnA -< if reset then 0 else next
5126 next <- delay 0 -< output+1
5127 returnA -< output
5129 The translation of such forms uses the <function>loop</function> combinator,
5130 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5136 <title>Conditional commands</title>
5139 In the previous example, we used a conditional expression to construct the
5141 Sometimes we want to conditionally execute different commands, as in
5148 which is translated to
5150 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5151 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5153 Since the translation uses <function>|||</function>,
5154 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5158 There are also <literal>case</literal> commands, like
5164 y <- h -< (x1, x2)
5168 The syntax is the same as for <literal>case</literal> expressions,
5169 except that the bodies of the alternatives are commands rather than expressions.
5170 The translation is similar to that of <literal>if</literal> commands.
5176 <title>Defining your own control structures</title>
5179 As we're seen, arrow notation provides constructs,
5180 modelled on those for expressions,
5181 for sequencing, value recursion and conditionals.
5182 But suitable combinators,
5183 which you can define in ordinary Haskell,
5184 may also be used to build new commands out of existing ones.
5185 The basic idea is that a command defines an arrow from environments to values.
5186 These environments assign values to the free local variables of the command.
5187 Thus combinators that produce arrows from arrows
5188 may also be used to build commands from commands.
5189 For example, the <literal>ArrowChoice</literal> class includes a combinator
5191 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5193 so we can use it to build commands:
5195 expr' = proc x -> do
5198 symbol Plus -< ()
5199 y <- term -< ()
5202 symbol Minus -< ()
5203 y <- term -< ()
5206 (The <literal>do</literal> on the first line is needed to prevent the first
5207 <literal><+> ...</literal> from being interpreted as part of the
5208 expression on the previous line.)
5209 This is equivalent to
5211 expr' = (proc x -> returnA -< x)
5212 <+> (proc x -> do
5213 symbol Plus -< ()
5214 y <- term -< ()
5216 <+> (proc x -> do
5217 symbol Minus -< ()
5218 y <- term -< ()
5221 It is essential that this operator be polymorphic in <literal>e</literal>
5222 (representing the environment input to the command
5223 and thence to its subcommands)
5224 and satisfy the corresponding naturality property
5226 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5228 at least for strict <literal>k</literal>.
5229 (This should be automatic if you're not using <function>seq</function>.)
5230 This ensures that environments seen by the subcommands are environments
5231 of the whole command,
5232 and also allows the translation to safely trim these environments.
5233 The operator must also not use any variable defined within the current
5238 We could define our own operator
5240 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5241 untilA body cond = proc x ->
5242 if cond x then returnA -< ()
5245 untilA body cond -< x
5247 and use it in the same way.
5248 Of course this infix syntax only makes sense for binary operators;
5249 there is also a more general syntax involving special brackets:
5253 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5260 <title>Primitive constructs</title>
5263 Some operators will need to pass additional inputs to their subcommands.
5264 For example, in an arrow type supporting exceptions,
5265 the operator that attaches an exception handler will wish to pass the
5266 exception that occurred to the handler.
5267 Such an operator might have a type
5269 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5271 where <literal>Ex</literal> is the type of exceptions handled.
5272 You could then use this with arrow notation by writing a command
5274 body `handleA` \ ex -> handler
5276 so that if an exception is raised in the command <literal>body</literal>,
5277 the variable <literal>ex</literal> is bound to the value of the exception
5278 and the command <literal>handler</literal>,
5279 which typically refers to <literal>ex</literal>, is entered.
5280 Though the syntax here looks like a functional lambda,
5281 we are talking about commands, and something different is going on.
5282 The input to the arrow represented by a command consists of values for
5283 the free local variables in the command, plus a stack of anonymous values.
5284 In all the prior examples, this stack was empty.
5285 In the second argument to <function>handleA</function>,
5286 this stack consists of one value, the value of the exception.
5287 The command form of lambda merely gives this value a name.
5292 the values on the stack are paired to the right of the environment.
5293 So operators like <function>handleA</function> that pass
5294 extra inputs to their subcommands can be designed for use with the notation
5295 by pairing the values with the environment in this way.
5296 More precisely, the type of each argument of the operator (and its result)
5297 should have the form
5299 a (...(e,t1), ... tn) t
5301 where <replaceable>e</replaceable> is a polymorphic variable
5302 (representing the environment)
5303 and <replaceable>ti</replaceable> are the types of the values on the stack,
5304 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5305 The polymorphic variable <replaceable>e</replaceable> must not occur in
5306 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5307 <replaceable>t</replaceable>.
5308 However the arrows involved need not be the same.
5309 Here are some more examples of suitable operators:
5311 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5312 runReader :: ... => a e c -> a' (e,State) c
5313 runState :: ... => a e c -> a' (e,State) (c,State)
5315 We can supply the extra input required by commands built with the last two
5316 by applying them to ordinary expressions, as in
5320 (|runReader (do { ... })|) s
5322 which adds <literal>s</literal> to the stack of inputs to the command
5323 built using <function>runReader</function>.
5327 The command versions of lambda abstraction and application are analogous to
5328 the expression versions.
5329 In particular, the beta and eta rules describe equivalences of commands.
5330 These three features (operators, lambda abstraction and application)
5331 are the core of the notation; everything else can be built using them,
5332 though the results would be somewhat clumsy.
5333 For example, we could simulate <literal>do</literal>-notation by defining
5335 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5336 u `bind` f = returnA &&& u >>> f
5338 bind_ :: Arrow a => a e b -> a e c -> a e c
5339 u `bind_` f = u `bind` (arr fst >>> f)
5341 We could simulate <literal>if</literal> by defining
5343 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5344 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5351 <title>Differences with the paper</title>
5356 <para>Instead of a single form of arrow application (arrow tail) with two
5357 translations, the implementation provides two forms
5358 <quote><literal>-<</literal></quote> (first-order)
5359 and <quote><literal>-<<</literal></quote> (higher-order).
5364 <para>User-defined operators are flagged with banana brackets instead of
5365 a new <literal>form</literal> keyword.
5374 <title>Portability</title>
5377 Although only GHC implements arrow notation directly,
5378 there is also a preprocessor
5380 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5381 that translates arrow notation into Haskell 98
5382 for use with other Haskell systems.
5383 You would still want to check arrow programs with GHC;
5384 tracing type errors in the preprocessor output is not easy.
5385 Modules intended for both GHC and the preprocessor must observe some
5386 additional restrictions:
5391 The module must import
5392 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5398 The preprocessor cannot cope with other Haskell extensions.
5399 These would have to go in separate modules.
5405 Because the preprocessor targets Haskell (rather than Core),
5406 <literal>let</literal>-bound variables are monomorphic.
5417 <!-- ==================== BANG PATTERNS ================= -->
5419 <sect1 id="bang-patterns">
5420 <title>Bang patterns
5421 <indexterm><primary>Bang patterns</primary></indexterm>
5423 <para>GHC supports an extension of pattern matching called <emphasis>bang
5424 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5426 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5427 prime feature description</ulink> contains more discussion and examples
5428 than the material below.
5431 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5434 <sect2 id="bang-patterns-informal">
5435 <title>Informal description of bang patterns
5438 The main idea is to add a single new production to the syntax of patterns:
5442 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5443 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5448 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5449 whereas without the bang it would be lazy.
5450 Bang patterns can be nested of course:
5454 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5455 <literal>y</literal>.
5456 A bang only really has an effect if it precedes a variable or wild-card pattern:
5461 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5462 forces evaluation anyway does nothing.
5464 Bang patterns work in <literal>case</literal> expressions too, of course:
5466 g5 x = let y = f x in body
5467 g6 x = case f x of { y -> body }
5468 g7 x = case f x of { !y -> body }
5470 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5471 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
5472 result, and then evaluates <literal>body</literal>.
5474 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5475 definitions too. For example:
5479 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5480 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5481 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5482 in a function argument <literal>![x,y]</literal> means the
5483 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5484 is part of the syntax of <literal>let</literal> bindings.
5489 <sect2 id="bang-patterns-sem">
5490 <title>Syntax and semantics
5494 We add a single new production to the syntax of patterns:
5498 There is one problem with syntactic ambiguity. Consider:
5502 Is this a definition of the infix function "<literal>(!)</literal>",
5503 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5504 ambiguity in favour of the latter. If you want to define
5505 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5510 The semantics of Haskell pattern matching is described in <ulink
5511 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5512 Section 3.17.2</ulink> of the Haskell Report. To this description add
5513 one extra item 10, saying:
5514 <itemizedlist><listitem><para>Matching
5515 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5516 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5517 <listitem><para>otherwise, <literal>pat</literal> is matched against
5518 <literal>v</literal></para></listitem>
5520 </para></listitem></itemizedlist>
5521 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5522 Section 3.17.3</ulink>, add a new case (t):
5524 case v of { !pat -> e; _ -> e' }
5525 = v `seq` case v of { pat -> e; _ -> e' }
5528 That leaves let expressions, whose translation is given in
5529 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5531 of the Haskell Report.
5532 In the translation box, first apply
5533 the following transformation: for each pattern <literal>pi</literal> that is of
5534 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5535 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5536 have a bang at the top, apply the rules in the existing box.
5538 <para>The effect of the let rule is to force complete matching of the pattern
5539 <literal>qi</literal> before evaluation of the body is begun. The bang is
5540 retained in the translated form in case <literal>qi</literal> is a variable,
5548 The let-binding can be recursive. However, it is much more common for
5549 the let-binding to be non-recursive, in which case the following law holds:
5550 <literal>(let !p = rhs in body)</literal>
5552 <literal>(case rhs of !p -> body)</literal>
5555 A pattern with a bang at the outermost level is not allowed at the top level of
5561 <!-- ==================== ASSERTIONS ================= -->
5563 <sect1 id="assertions">
5565 <indexterm><primary>Assertions</primary></indexterm>
5569 If you want to make use of assertions in your standard Haskell code, you
5570 could define a function like the following:
5576 assert :: Bool -> a -> a
5577 assert False x = error "assertion failed!"
5584 which works, but gives you back a less than useful error message --
5585 an assertion failed, but which and where?
5589 One way out is to define an extended <function>assert</function> function which also
5590 takes a descriptive string to include in the error message and
5591 perhaps combine this with the use of a pre-processor which inserts
5592 the source location where <function>assert</function> was used.
5596 Ghc offers a helping hand here, doing all of this for you. For every
5597 use of <function>assert</function> in the user's source:
5603 kelvinToC :: Double -> Double
5604 kelvinToC k = assert (k >= 0.0) (k+273.15)
5610 Ghc will rewrite this to also include the source location where the
5617 assert pred val ==> assertError "Main.hs|15" pred val
5623 The rewrite is only performed by the compiler when it spots
5624 applications of <function>Control.Exception.assert</function>, so you
5625 can still define and use your own versions of
5626 <function>assert</function>, should you so wish. If not, import
5627 <literal>Control.Exception</literal> to make use
5628 <function>assert</function> in your code.
5632 GHC ignores assertions when optimisation is turned on with the
5633 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5634 <literal>assert pred e</literal> will be rewritten to
5635 <literal>e</literal>. You can also disable assertions using the
5636 <option>-fignore-asserts</option>
5637 option<indexterm><primary><option>-fignore-asserts</option></primary>
5638 </indexterm>.</para>
5641 Assertion failures can be caught, see the documentation for the
5642 <literal>Control.Exception</literal> library for the details.
5648 <!-- =============================== PRAGMAS =========================== -->
5650 <sect1 id="pragmas">
5651 <title>Pragmas</title>
5653 <indexterm><primary>pragma</primary></indexterm>
5655 <para>GHC supports several pragmas, or instructions to the
5656 compiler placed in the source code. Pragmas don't normally affect
5657 the meaning of the program, but they might affect the efficiency
5658 of the generated code.</para>
5660 <para>Pragmas all take the form
5662 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5664 where <replaceable>word</replaceable> indicates the type of
5665 pragma, and is followed optionally by information specific to that
5666 type of pragma. Case is ignored in
5667 <replaceable>word</replaceable>. The various values for
5668 <replaceable>word</replaceable> that GHC understands are described
5669 in the following sections; any pragma encountered with an
5670 unrecognised <replaceable>word</replaceable> is (silently)
5673 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
5674 pragma must precede the <literal>module</literal> keyword in the file.
5675 There can be as many file-header pragmas as you please, and they can be
5676 preceded or followed by comments.</para>
5678 <sect2 id="language-pragma">
5679 <title>LANGUAGE pragma</title>
5681 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5682 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5684 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
5686 It is the intention that all Haskell compilers support the
5687 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5688 all extensions are supported by all compilers, of
5689 course. The <literal>LANGUAGE</literal> pragma should be used instead
5690 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5692 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5694 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5696 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5698 <para>Every language extension can also be turned into a command-line flag
5699 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
5700 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
5703 <para>A list of all supported language extensions can be obtained by invoking
5704 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
5706 <para>Any extension from the <literal>Extension</literal> type defined in
5708 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
5709 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
5713 <sect2 id="options-pragma">
5714 <title>OPTIONS_GHC pragma</title>
5715 <indexterm><primary>OPTIONS_GHC</primary>
5717 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5720 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5721 additional options that are given to the compiler when compiling
5722 this source file. See <xref linkend="source-file-options"/> for
5725 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5726 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5729 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5731 <sect2 id="include-pragma">
5732 <title>INCLUDE pragma</title>
5734 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5735 of C header files that should be <literal>#include</literal>'d into
5736 the C source code generated by the compiler for the current module (if
5737 compiling via C). For example:</para>
5740 {-# INCLUDE "foo.h" #-}
5741 {-# INCLUDE <stdio.h> #-}</programlisting>
5743 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5745 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5746 to the <option>-#include</option> option (<xref
5747 linkend="options-C-compiler" />), because the
5748 <literal>INCLUDE</literal> pragma is understood by other
5749 compilers. Yet another alternative is to add the include file to each
5750 <literal>foreign import</literal> declaration in your code, but we
5751 don't recommend using this approach with GHC.</para>
5754 <sect2 id="deprecated-pragma">
5755 <title>DEPRECATED pragma</title>
5756 <indexterm><primary>DEPRECATED</primary>
5759 <para>The DEPRECATED pragma lets you specify that a particular
5760 function, class, or type, is deprecated. There are two
5765 <para>You can deprecate an entire module thus:</para>
5767 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5770 <para>When you compile any module that import
5771 <literal>Wibble</literal>, GHC will print the specified
5776 <para>You can deprecate a function, class, type, or data constructor, with the
5777 following top-level declaration:</para>
5779 {-# DEPRECATED f, C, T "Don't use these" #-}
5781 <para>When you compile any module that imports and uses any
5782 of the specified entities, GHC will print the specified
5784 <para> You can only depecate entities declared at top level in the module
5785 being compiled, and you can only use unqualified names in the list of
5786 entities being deprecated. A capitalised name, such as <literal>T</literal>
5787 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5788 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5789 both are in scope. If both are in scope, there is currently no way to deprecate
5790 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5793 Any use of the deprecated item, or of anything from a deprecated
5794 module, will be flagged with an appropriate message. However,
5795 deprecations are not reported for
5796 (a) uses of a deprecated function within its defining module, and
5797 (b) uses of a deprecated function in an export list.
5798 The latter reduces spurious complaints within a library
5799 in which one module gathers together and re-exports
5800 the exports of several others.
5802 <para>You can suppress the warnings with the flag
5803 <option>-fno-warn-deprecations</option>.</para>
5806 <sect2 id="inline-noinline-pragma">
5807 <title>INLINE and NOINLINE pragmas</title>
5809 <para>These pragmas control the inlining of function
5812 <sect3 id="inline-pragma">
5813 <title>INLINE pragma</title>
5814 <indexterm><primary>INLINE</primary></indexterm>
5816 <para>GHC (with <option>-O</option>, as always) tries to
5817 inline (or “unfold”) functions/values that are
5818 “small enough,” thus avoiding the call overhead
5819 and possibly exposing other more-wonderful optimisations.
5820 Normally, if GHC decides a function is “too
5821 expensive” to inline, it will not do so, nor will it
5822 export that unfolding for other modules to use.</para>
5824 <para>The sledgehammer you can bring to bear is the
5825 <literal>INLINE</literal><indexterm><primary>INLINE
5826 pragma</primary></indexterm> pragma, used thusly:</para>
5829 key_function :: Int -> String -> (Bool, Double)
5831 #ifdef __GLASGOW_HASKELL__
5832 {-# INLINE key_function #-}
5836 <para>(You don't need to do the C pre-processor carry-on
5837 unless you're going to stick the code through HBC—it
5838 doesn't like <literal>INLINE</literal> pragmas.)</para>
5840 <para>The major effect of an <literal>INLINE</literal> pragma
5841 is to declare a function's “cost” to be very low.
5842 The normal unfolding machinery will then be very keen to
5845 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5846 function can be put anywhere its type signature could be
5849 <para><literal>INLINE</literal> pragmas are a particularly
5851 <literal>then</literal>/<literal>return</literal> (or
5852 <literal>bind</literal>/<literal>unit</literal>) functions in
5853 a monad. For example, in GHC's own
5854 <literal>UniqueSupply</literal> monad code, we have:</para>
5857 #ifdef __GLASGOW_HASKELL__
5858 {-# INLINE thenUs #-}
5859 {-# INLINE returnUs #-}
5863 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5864 linkend="noinline-pragma"/>).</para>
5867 <sect3 id="noinline-pragma">
5868 <title>NOINLINE pragma</title>
5870 <indexterm><primary>NOINLINE</primary></indexterm>
5871 <indexterm><primary>NOTINLINE</primary></indexterm>
5873 <para>The <literal>NOINLINE</literal> pragma does exactly what
5874 you'd expect: it stops the named function from being inlined
5875 by the compiler. You shouldn't ever need to do this, unless
5876 you're very cautious about code size.</para>
5878 <para><literal>NOTINLINE</literal> is a synonym for
5879 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5880 specified by Haskell 98 as the standard way to disable
5881 inlining, so it should be used if you want your code to be
5885 <sect3 id="phase-control">
5886 <title>Phase control</title>
5888 <para> Sometimes you want to control exactly when in GHC's
5889 pipeline the INLINE pragma is switched on. Inlining happens
5890 only during runs of the <emphasis>simplifier</emphasis>. Each
5891 run of the simplifier has a different <emphasis>phase
5892 number</emphasis>; the phase number decreases towards zero.
5893 If you use <option>-dverbose-core2core</option> you'll see the
5894 sequence of phase numbers for successive runs of the
5895 simplifier. In an INLINE pragma you can optionally specify a
5899 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5900 <literal>f</literal>
5901 until phase <literal>k</literal>, but from phase
5902 <literal>k</literal> onwards be very keen to inline it.
5905 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5906 <literal>f</literal>
5907 until phase <literal>k</literal>, but from phase
5908 <literal>k</literal> onwards do not inline it.
5911 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5912 <literal>f</literal>
5913 until phase <literal>k</literal>, but from phase
5914 <literal>k</literal> onwards be willing to inline it (as if
5915 there was no pragma).
5918 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5919 <literal>f</literal>
5920 until phase <literal>k</literal>, but from phase
5921 <literal>k</literal> onwards do not inline it.
5924 The same information is summarised here:
5926 -- Before phase 2 Phase 2 and later
5927 {-# INLINE [2] f #-} -- No Yes
5928 {-# INLINE [~2] f #-} -- Yes No
5929 {-# NOINLINE [2] f #-} -- No Maybe
5930 {-# NOINLINE [~2] f #-} -- Maybe No
5932 {-# INLINE f #-} -- Yes Yes
5933 {-# NOINLINE f #-} -- No No
5935 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5936 function body is small, or it is applied to interesting-looking arguments etc).
5937 Another way to understand the semantics is this:
5939 <listitem><para>For both INLINE and NOINLINE, the phase number says
5940 when inlining is allowed at all.</para></listitem>
5941 <listitem><para>The INLINE pragma has the additional effect of making the
5942 function body look small, so that when inlining is allowed it is very likely to
5947 <para>The same phase-numbering control is available for RULES
5948 (<xref linkend="rewrite-rules"/>).</para>
5952 <sect2 id="line-pragma">
5953 <title>LINE pragma</title>
5955 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5956 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5957 <para>This pragma is similar to C's <literal>#line</literal>
5958 pragma, and is mainly for use in automatically generated Haskell
5959 code. It lets you specify the line number and filename of the
5960 original code; for example</para>
5962 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5964 <para>if you'd generated the current file from something called
5965 <filename>Foo.vhs</filename> and this line corresponds to line
5966 42 in the original. GHC will adjust its error messages to refer
5967 to the line/file named in the <literal>LINE</literal>
5972 <title>RULES pragma</title>
5974 <para>The RULES pragma lets you specify rewrite rules. It is
5975 described in <xref linkend="rewrite-rules"/>.</para>
5978 <sect2 id="specialize-pragma">
5979 <title>SPECIALIZE pragma</title>
5981 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5982 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5983 <indexterm><primary>overloading, death to</primary></indexterm>
5985 <para>(UK spelling also accepted.) For key overloaded
5986 functions, you can create extra versions (NB: more code space)
5987 specialised to particular types. Thus, if you have an
5988 overloaded function:</para>
5991 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5994 <para>If it is heavily used on lists with
5995 <literal>Widget</literal> keys, you could specialise it as
5999 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6002 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6003 be put anywhere its type signature could be put.</para>
6005 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6006 (a) a specialised version of the function and (b) a rewrite rule
6007 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6008 un-specialised function into a call to the specialised one.</para>
6010 <para>The type in a SPECIALIZE pragma can be any type that is less
6011 polymorphic than the type of the original function. In concrete terms,
6012 if the original function is <literal>f</literal> then the pragma
6014 {-# SPECIALIZE f :: <type> #-}
6016 is valid if and only if the defintion
6018 f_spec :: <type>
6021 is valid. Here are some examples (where we only give the type signature
6022 for the original function, not its code):
6024 f :: Eq a => a -> b -> b
6025 {-# SPECIALISE f :: Int -> b -> b #-}
6027 g :: (Eq a, Ix b) => a -> b -> b
6028 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6030 h :: Eq a => a -> a -> a
6031 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6033 The last of these examples will generate a
6034 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6035 well. If you use this kind of specialisation, let us know how well it works.
6038 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6039 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6040 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6041 The <literal>INLINE</literal> pragma affects the specialised verison of the
6042 function (only), and applies even if the function is recursive. The motivating
6045 -- A GADT for arrays with type-indexed representation
6047 ArrInt :: !Int -> ByteArray# -> Arr Int
6048 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6050 (!:) :: Arr e -> Int -> e
6051 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6052 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6053 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6054 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6056 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6057 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6058 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6059 the specialised function will be inlined. It has two calls to
6060 <literal>(!:)</literal>,
6061 both at type <literal>Int</literal>. Both these calls fire the first
6062 specialisation, whose body is also inlined. The result is a type-based
6063 unrolling of the indexing function.</para>
6064 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6065 on an ordinarily-recursive function.</para>
6067 <para>Note: In earlier versions of GHC, it was possible to provide your own
6068 specialised function for a given type:
6071 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6074 This feature has been removed, as it is now subsumed by the
6075 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6079 <sect2 id="specialize-instance-pragma">
6080 <title>SPECIALIZE instance pragma
6084 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6085 <indexterm><primary>overloading, death to</primary></indexterm>
6086 Same idea, except for instance declarations. For example:
6089 instance (Eq a) => Eq (Foo a) where {
6090 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6094 The pragma must occur inside the <literal>where</literal> part
6095 of the instance declaration.
6098 Compatible with HBC, by the way, except perhaps in the placement
6104 <sect2 id="unpack-pragma">
6105 <title>UNPACK pragma</title>
6107 <indexterm><primary>UNPACK</primary></indexterm>
6109 <para>The <literal>UNPACK</literal> indicates to the compiler
6110 that it should unpack the contents of a constructor field into
6111 the constructor itself, removing a level of indirection. For
6115 data T = T {-# UNPACK #-} !Float
6116 {-# UNPACK #-} !Float
6119 <para>will create a constructor <literal>T</literal> containing
6120 two unboxed floats. This may not always be an optimisation: if
6121 the <function>T</function> constructor is scrutinised and the
6122 floats passed to a non-strict function for example, they will
6123 have to be reboxed (this is done automatically by the
6126 <para>Unpacking constructor fields should only be used in
6127 conjunction with <option>-O</option>, in order to expose
6128 unfoldings to the compiler so the reboxing can be removed as
6129 often as possible. For example:</para>
6133 f (T f1 f2) = f1 + f2
6136 <para>The compiler will avoid reboxing <function>f1</function>
6137 and <function>f2</function> by inlining <function>+</function>
6138 on floats, but only when <option>-O</option> is on.</para>
6140 <para>Any single-constructor data is eligible for unpacking; for
6144 data T = T {-# UNPACK #-} !(Int,Int)
6147 <para>will store the two <literal>Int</literal>s directly in the
6148 <function>T</function> constructor, by flattening the pair.
6149 Multi-level unpacking is also supported:</para>
6152 data T = T {-# UNPACK #-} !S
6153 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6156 <para>will store two unboxed <literal>Int#</literal>s
6157 directly in the <function>T</function> constructor. The
6158 unpacker can see through newtypes, too.</para>
6160 <para>If a field cannot be unpacked, you will not get a warning,
6161 so it might be an idea to check the generated code with
6162 <option>-ddump-simpl</option>.</para>
6164 <para>See also the <option>-funbox-strict-fields</option> flag,
6165 which essentially has the effect of adding
6166 <literal>{-# UNPACK #-}</literal> to every strict
6167 constructor field.</para>
6172 <!-- ======================= REWRITE RULES ======================== -->
6174 <sect1 id="rewrite-rules">
6175 <title>Rewrite rules
6177 <indexterm><primary>RULES pragma</primary></indexterm>
6178 <indexterm><primary>pragma, RULES</primary></indexterm>
6179 <indexterm><primary>rewrite rules</primary></indexterm></title>
6182 The programmer can specify rewrite rules as part of the source program
6183 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6184 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6185 and (b) the <option>-frules-off</option> flag
6186 (<xref linkend="options-f"/>) is not specified, and (c) the
6187 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6196 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6203 <title>Syntax</title>
6206 From a syntactic point of view:
6212 There may be zero or more rules in a <literal>RULES</literal> pragma.
6219 Each rule has a name, enclosed in double quotes. The name itself has
6220 no significance at all. It is only used when reporting how many times the rule fired.
6226 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6227 immediately after the name of the rule. Thus:
6230 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6233 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6234 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6243 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
6244 is set, so you must lay out your rules starting in the same column as the
6245 enclosing definitions.
6252 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6253 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6254 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6255 by spaces, just like in a type <literal>forall</literal>.
6261 A pattern variable may optionally have a type signature.
6262 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6263 For example, here is the <literal>foldr/build</literal> rule:
6266 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6267 foldr k z (build g) = g k z
6270 Since <function>g</function> has a polymorphic type, it must have a type signature.
6277 The left hand side of a rule must consist of a top-level variable applied
6278 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6281 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6282 "wrong2" forall f. f True = True
6285 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6292 A rule does not need to be in the same module as (any of) the
6293 variables it mentions, though of course they need to be in scope.
6299 Rules are automatically exported from a module, just as instance declarations are.
6310 <title>Semantics</title>
6313 From a semantic point of view:
6319 Rules are only applied if you use the <option>-O</option> flag.
6325 Rules are regarded as left-to-right rewrite rules.
6326 When GHC finds an expression that is a substitution instance of the LHS
6327 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6328 By "a substitution instance" we mean that the LHS can be made equal to the
6329 expression by substituting for the pattern variables.
6336 The LHS and RHS of a rule are typechecked, and must have the
6344 GHC makes absolutely no attempt to verify that the LHS and RHS
6345 of a rule have the same meaning. That is undecidable in general, and
6346 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6353 GHC makes no attempt to make sure that the rules are confluent or
6354 terminating. For example:
6357 "loop" forall x,y. f x y = f y x
6360 This rule will cause the compiler to go into an infinite loop.
6367 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6373 GHC currently uses a very simple, syntactic, matching algorithm
6374 for matching a rule LHS with an expression. It seeks a substitution
6375 which makes the LHS and expression syntactically equal modulo alpha
6376 conversion. The pattern (rule), but not the expression, is eta-expanded if
6377 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6378 But not beta conversion (that's called higher-order matching).
6382 Matching is carried out on GHC's intermediate language, which includes
6383 type abstractions and applications. So a rule only matches if the
6384 types match too. See <xref linkend="rule-spec"/> below.
6390 GHC keeps trying to apply the rules as it optimises the program.
6391 For example, consider:
6400 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6401 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6402 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6403 not be substituted, and the rule would not fire.
6410 In the earlier phases of compilation, GHC inlines <emphasis>nothing
6411 that appears on the LHS of a rule</emphasis>, because once you have substituted
6412 for something you can't match against it (given the simple minded
6413 matching). So if you write the rule
6416 "map/map" forall f,g. map f . map g = map (f.g)
6419 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
6420 It will only match something written with explicit use of ".".
6421 Well, not quite. It <emphasis>will</emphasis> match the expression
6427 where <function>wibble</function> is defined:
6430 wibble f g = map f . map g
6433 because <function>wibble</function> will be inlined (it's small).
6435 Later on in compilation, GHC starts inlining even things on the
6436 LHS of rules, but still leaves the rules enabled. This inlining
6437 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
6444 All rules are implicitly exported from the module, and are therefore
6445 in force in any module that imports the module that defined the rule, directly
6446 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6447 in force when compiling A.) The situation is very similar to that for instance
6459 <title>List fusion</title>
6462 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6463 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6464 intermediate list should be eliminated entirely.
6468 The following are good producers:
6480 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6486 Explicit lists (e.g. <literal>[True, False]</literal>)
6492 The cons constructor (e.g <literal>3:4:[]</literal>)
6498 <function>++</function>
6504 <function>map</function>
6510 <function>take</function>, <function>filter</function>
6516 <function>iterate</function>, <function>repeat</function>
6522 <function>zip</function>, <function>zipWith</function>
6531 The following are good consumers:
6543 <function>array</function> (on its second argument)
6549 <function>++</function> (on its first argument)
6555 <function>foldr</function>
6561 <function>map</function>
6567 <function>take</function>, <function>filter</function>
6573 <function>concat</function>
6579 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6585 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6586 will fuse with one but not the other)
6592 <function>partition</function>
6598 <function>head</function>
6604 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6610 <function>sequence_</function>
6616 <function>msum</function>
6622 <function>sortBy</function>
6631 So, for example, the following should generate no intermediate lists:
6634 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6640 This list could readily be extended; if there are Prelude functions that you use
6641 a lot which are not included, please tell us.
6645 If you want to write your own good consumers or producers, look at the
6646 Prelude definitions of the above functions to see how to do so.
6651 <sect2 id="rule-spec">
6652 <title>Specialisation
6656 Rewrite rules can be used to get the same effect as a feature
6657 present in earlier versions of GHC.
6658 For example, suppose that:
6661 genericLookup :: Ord a => Table a b -> a -> b
6662 intLookup :: Table Int b -> Int -> b
6665 where <function>intLookup</function> is an implementation of
6666 <function>genericLookup</function> that works very fast for
6667 keys of type <literal>Int</literal>. You might wish
6668 to tell GHC to use <function>intLookup</function> instead of
6669 <function>genericLookup</function> whenever the latter was called with
6670 type <literal>Table Int b -> Int -> b</literal>.
6671 It used to be possible to write
6674 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6677 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6680 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6683 This slightly odd-looking rule instructs GHC to replace
6684 <function>genericLookup</function> by <function>intLookup</function>
6685 <emphasis>whenever the types match</emphasis>.
6686 What is more, this rule does not need to be in the same
6687 file as <function>genericLookup</function>, unlike the
6688 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6689 have an original definition available to specialise).
6692 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6693 <function>intLookup</function> really behaves as a specialised version
6694 of <function>genericLookup</function>!!!</para>
6696 <para>An example in which using <literal>RULES</literal> for
6697 specialisation will Win Big:
6700 toDouble :: Real a => a -> Double
6701 toDouble = fromRational . toRational
6703 {-# RULES "toDouble/Int" toDouble = i2d #-}
6704 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6707 The <function>i2d</function> function is virtually one machine
6708 instruction; the default conversion—via an intermediate
6709 <literal>Rational</literal>—is obscenely expensive by
6716 <title>Controlling what's going on</title>
6724 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6730 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6731 If you add <option>-dppr-debug</option> you get a more detailed listing.
6737 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6740 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6741 {-# INLINE build #-}
6745 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6746 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6747 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6748 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6755 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6756 see how to write rules that will do fusion and yet give an efficient
6757 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6767 <sect2 id="core-pragma">
6768 <title>CORE pragma</title>
6770 <indexterm><primary>CORE pragma</primary></indexterm>
6771 <indexterm><primary>pragma, CORE</primary></indexterm>
6772 <indexterm><primary>core, annotation</primary></indexterm>
6775 The external core format supports <quote>Note</quote> annotations;
6776 the <literal>CORE</literal> pragma gives a way to specify what these
6777 should be in your Haskell source code. Syntactically, core
6778 annotations are attached to expressions and take a Haskell string
6779 literal as an argument. The following function definition shows an
6783 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6786 Semantically, this is equivalent to:
6794 However, when external for is generated (via
6795 <option>-fext-core</option>), there will be Notes attached to the
6796 expressions <function>show</function> and <varname>x</varname>.
6797 The core function declaration for <function>f</function> is:
6801 f :: %forall a . GHCziShow.ZCTShow a ->
6802 a -> GHCziBase.ZMZN GHCziBase.Char =
6803 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6805 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6807 (tpl1::GHCziBase.Int ->
6809 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6811 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6812 (tpl3::GHCziBase.ZMZN a ->
6813 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6821 Here, we can see that the function <function>show</function> (which
6822 has been expanded out to a case expression over the Show dictionary)
6823 has a <literal>%note</literal> attached to it, as does the
6824 expression <varname>eta</varname> (which used to be called
6825 <varname>x</varname>).
6832 <sect1 id="special-ids">
6833 <title>Special built-in functions</title>
6834 <para>GHC has a few built-in funcions with special behaviour. These
6835 are now described in the module <ulink
6836 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
6837 in the library documentation.</para>
6841 <sect1 id="generic-classes">
6842 <title>Generic classes</title>
6845 The ideas behind this extension are described in detail in "Derivable type classes",
6846 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6847 An example will give the idea:
6855 fromBin :: [Int] -> (a, [Int])
6857 toBin {| Unit |} Unit = []
6858 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6859 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6860 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6862 fromBin {| Unit |} bs = (Unit, bs)
6863 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6864 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6865 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6866 (y,bs'') = fromBin bs'
6869 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6870 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6871 which are defined thus in the library module <literal>Generics</literal>:
6875 data a :+: b = Inl a | Inr b
6876 data a :*: b = a :*: b
6879 Now you can make a data type into an instance of Bin like this:
6881 instance (Bin a, Bin b) => Bin (a,b)
6882 instance Bin a => Bin [a]
6884 That is, just leave off the "where" clause. Of course, you can put in the
6885 where clause and over-ride whichever methods you please.
6889 <title> Using generics </title>
6890 <para>To use generics you need to</para>
6893 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6894 <option>-XGenerics</option> (to generate extra per-data-type code),
6895 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6899 <para>Import the module <literal>Generics</literal> from the
6900 <literal>lang</literal> package. This import brings into
6901 scope the data types <literal>Unit</literal>,
6902 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6903 don't need this import if you don't mention these types
6904 explicitly; for example, if you are simply giving instance
6905 declarations.)</para>
6910 <sect2> <title> Changes wrt the paper </title>
6912 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6913 can be written infix (indeed, you can now use
6914 any operator starting in a colon as an infix type constructor). Also note that
6915 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6916 Finally, note that the syntax of the type patterns in the class declaration
6917 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6918 alone would ambiguous when they appear on right hand sides (an extension we
6919 anticipate wanting).
6923 <sect2> <title>Terminology and restrictions</title>
6925 Terminology. A "generic default method" in a class declaration
6926 is one that is defined using type patterns as above.
6927 A "polymorphic default method" is a default method defined as in Haskell 98.
6928 A "generic class declaration" is a class declaration with at least one
6929 generic default method.
6937 Alas, we do not yet implement the stuff about constructor names and
6944 A generic class can have only one parameter; you can't have a generic
6945 multi-parameter class.
6951 A default method must be defined entirely using type patterns, or entirely
6952 without. So this is illegal:
6955 op :: a -> (a, Bool)
6956 op {| Unit |} Unit = (Unit, True)
6959 However it is perfectly OK for some methods of a generic class to have
6960 generic default methods and others to have polymorphic default methods.
6966 The type variable(s) in the type pattern for a generic method declaration
6967 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:
6971 op {| p :*: q |} (x :*: y) = op (x :: p)
6979 The type patterns in a generic default method must take one of the forms:
6985 where "a" and "b" are type variables. Furthermore, all the type patterns for
6986 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6987 must use the same type variables. So this is illegal:
6991 op {| a :+: b |} (Inl x) = True
6992 op {| p :+: q |} (Inr y) = False
6994 The type patterns must be identical, even in equations for different methods of the class.
6995 So this too is illegal:
6999 op1 {| a :*: b |} (x :*: y) = True
7002 op2 {| p :*: q |} (x :*: y) = False
7004 (The reason for this restriction is that we gather all the equations for a particular type consructor
7005 into a single generic instance declaration.)
7011 A generic method declaration must give a case for each of the three type constructors.
7017 The type for a generic method can be built only from:
7019 <listitem> <para> Function arrows </para> </listitem>
7020 <listitem> <para> Type variables </para> </listitem>
7021 <listitem> <para> Tuples </para> </listitem>
7022 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7024 Here are some example type signatures for generic methods:
7027 op2 :: Bool -> (a,Bool)
7028 op3 :: [Int] -> a -> a
7031 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7035 This restriction is an implementation restriction: we just havn't got around to
7036 implementing the necessary bidirectional maps over arbitrary type constructors.
7037 It would be relatively easy to add specific type constructors, such as Maybe and list,
7038 to the ones that are allowed.</para>
7043 In an instance declaration for a generic class, the idea is that the compiler
7044 will fill in the methods for you, based on the generic templates. However it can only
7049 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7054 No constructor of the instance type has unboxed fields.
7058 (Of course, these things can only arise if you are already using GHC extensions.)
7059 However, you can still give an instance declarations for types which break these rules,
7060 provided you give explicit code to override any generic default methods.
7068 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7069 what the compiler does with generic declarations.
7074 <sect2> <title> Another example </title>
7076 Just to finish with, here's another example I rather like:
7080 nCons {| Unit |} _ = 1
7081 nCons {| a :*: b |} _ = 1
7082 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7085 tag {| Unit |} _ = 1
7086 tag {| a :*: b |} _ = 1
7087 tag {| a :+: b |} (Inl x) = tag x
7088 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7094 <sect1 id="monomorphism">
7095 <title>Control over monomorphism</title>
7097 <para>GHC supports two flags that control the way in which generalisation is
7098 carried out at let and where bindings.
7102 <title>Switching off the dreaded Monomorphism Restriction</title>
7103 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7105 <para>Haskell's monomorphism restriction (see
7106 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
7108 of the Haskell Report)
7109 can be completely switched off by
7110 <option>-XNoMonomorphismRestriction</option>.
7115 <title>Monomorphic pattern bindings</title>
7116 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7117 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7119 <para> As an experimental change, we are exploring the possibility of
7120 making pattern bindings monomorphic; that is, not generalised at all.
7121 A pattern binding is a binding whose LHS has no function arguments,
7122 and is not a simple variable. For example:
7124 f x = x -- Not a pattern binding
7125 f = \x -> x -- Not a pattern binding
7126 f :: Int -> Int = \x -> x -- Not a pattern binding
7128 (g,h) = e -- A pattern binding
7129 (f) = e -- A pattern binding
7130 [x] = e -- A pattern binding
7132 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7133 default</emphasis>. Use <option>-XMonoPatBinds</option> to recover the
7142 ;;; Local Variables: ***
7144 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
projects / ghc-hetmet.git / blob