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.
1749 <sect3 id="existential-records">
1750 <title>Record Constructors</title>
1753 GHC allows existentials to be used with records syntax as well. For example:
1756 data Counter a = forall self. NewCounter
1758 , _inc :: self -> self
1759 , _display :: self -> IO ()
1763 Here <literal>tag</literal> is a public field, with a well-typed selector
1764 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1765 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1766 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1767 compile-time error. In other words, <emphasis>GHC defines a record selector function
1768 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1769 (This example used an underscore in the fields for which record selectors
1770 will not be defined, but that is only programming style; GHC ignores them.)
1774 To make use of these hidden fields, we need to create some helper functions:
1777 inc :: Counter a -> Counter a
1778 inc (NewCounter x i d t) = NewCounter
1779 { _this = i x, _inc = i, _display = d, tag = t }
1781 display :: Counter a -> IO ()
1782 display NewCounter{ _this = x, _display = d } = d x
1785 Now we can define counters with different underlying implementations:
1788 counterA :: Counter String
1789 counterA = NewCounter
1790 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1792 counterB :: Counter String
1793 counterB = NewCounter
1794 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1797 display (inc counterA) -- prints "1"
1798 display (inc (inc counterB)) -- prints "##"
1801 At the moment, record update syntax is only supported for Haskell 98 data types,
1802 so the following function does <emphasis>not</emphasis> work:
1805 -- This is invalid; use explicit NewCounter instead for now
1806 setTag :: Counter a -> a -> Counter a
1807 setTag obj t = obj{ tag = t }
1816 <title>Restrictions</title>
1819 There are several restrictions on the ways in which existentially-quantified
1820 constructors can be use.
1829 When pattern matching, each pattern match introduces a new,
1830 distinct, type for each existential type variable. These types cannot
1831 be unified with any other type, nor can they escape from the scope of
1832 the pattern match. For example, these fragments are incorrect:
1840 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1841 is the result of <function>f1</function>. One way to see why this is wrong is to
1842 ask what type <function>f1</function> has:
1846 f1 :: Foo -> a -- Weird!
1850 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1855 f1 :: forall a. Foo -> a -- Wrong!
1859 The original program is just plain wrong. Here's another sort of error
1863 f2 (Baz1 a b) (Baz1 p q) = a==q
1867 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1868 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1869 from the two <function>Baz1</function> constructors.
1877 You can't pattern-match on an existentially quantified
1878 constructor in a <literal>let</literal> or <literal>where</literal> group of
1879 bindings. So this is illegal:
1883 f3 x = a==b where { Baz1 a b = x }
1886 Instead, use a <literal>case</literal> expression:
1889 f3 x = case x of Baz1 a b -> a==b
1892 In general, you can only pattern-match
1893 on an existentially-quantified constructor in a <literal>case</literal> expression or
1894 in the patterns of a function definition.
1896 The reason for this restriction is really an implementation one.
1897 Type-checking binding groups is already a nightmare without
1898 existentials complicating the picture. Also an existential pattern
1899 binding at the top level of a module doesn't make sense, because it's
1900 not clear how to prevent the existentially-quantified type "escaping".
1901 So for now, there's a simple-to-state restriction. We'll see how
1909 You can't use existential quantification for <literal>newtype</literal>
1910 declarations. So this is illegal:
1914 newtype T = forall a. Ord a => MkT a
1918 Reason: a value of type <literal>T</literal> must be represented as a
1919 pair of a dictionary for <literal>Ord t</literal> and a value of type
1920 <literal>t</literal>. That contradicts the idea that
1921 <literal>newtype</literal> should have no concrete representation.
1922 You can get just the same efficiency and effect by using
1923 <literal>data</literal> instead of <literal>newtype</literal>. If
1924 there is no overloading involved, then there is more of a case for
1925 allowing an existentially-quantified <literal>newtype</literal>,
1926 because the <literal>data</literal> version does carry an
1927 implementation cost, but single-field existentially quantified
1928 constructors aren't much use. So the simple restriction (no
1929 existential stuff on <literal>newtype</literal>) stands, unless there
1930 are convincing reasons to change it.
1938 You can't use <literal>deriving</literal> to define instances of a
1939 data type with existentially quantified data constructors.
1941 Reason: in most cases it would not make sense. For example:;
1944 data T = forall a. MkT [a] deriving( Eq )
1947 To derive <literal>Eq</literal> in the standard way we would need to have equality
1948 between the single component of two <function>MkT</function> constructors:
1952 (MkT a) == (MkT b) = ???
1955 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1956 It's just about possible to imagine examples in which the derived instance
1957 would make sense, but it seems altogether simpler simply to prohibit such
1958 declarations. Define your own instances!
1969 <!-- ====================== Generalised algebraic data types ======================= -->
1971 <sect2 id="gadt-style">
1972 <title>Declaring data types with explicit constructor signatures</title>
1974 <para>GHC allows you to declare an algebraic data type by
1975 giving the type signatures of constructors explicitly. For example:
1979 Just :: a -> Maybe a
1981 The form is called a "GADT-style declaration"
1982 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1983 can only be declared using this form.</para>
1984 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1985 For example, these two declarations are equivalent:
1987 data Foo = forall a. MkFoo a (a -> Bool)
1988 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1991 <para>Any data type that can be declared in standard Haskell-98 syntax
1992 can also be declared using GADT-style syntax.
1993 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1994 they treat class constraints on the data constructors differently.
1995 Specifically, if the constructor is given a type-class context, that
1996 context is made available by pattern matching. For example:
1999 MkSet :: Eq a => [a] -> Set a
2001 makeSet :: Eq a => [a] -> Set a
2002 makeSet xs = MkSet (nub xs)
2004 insert :: a -> Set a -> Set a
2005 insert a (MkSet as) | a `elem` as = MkSet as
2006 | otherwise = MkSet (a:as)
2008 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2009 gives rise to a <literal>(Eq a)</literal>
2010 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2011 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2012 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2013 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2014 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2015 In the example, the equality dictionary is used to satisfy the equality constraint
2016 generated by the call to <literal>elem</literal>, so that the type of
2017 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2019 <para>This behaviour contrasts with Haskell 98's peculiar treatment of
2020 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2021 In Haskell 98 the definition
2023 data Eq a => Set' a = MkSet' [a]
2025 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2026 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2027 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2028 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2029 GHC's behaviour is much more useful, as well as much more intuitive.</para>
2031 For example, a possible application of GHC's behaviour is to reify dictionaries:
2033 data NumInst a where
2034 MkNumInst :: Num a => NumInst a
2036 intInst :: NumInst Int
2039 plus :: NumInst a -> a -> a -> a
2040 plus MkNumInst p q = p + q
2042 Here, a value of type <literal>NumInst a</literal> is equivalent
2043 to an explicit <literal>(Num a)</literal> dictionary.
2047 The rest of this section gives further details about GADT-style data
2052 The result type of each data constructor must begin with the type constructor being defined.
2053 If the result type of all constructors
2054 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2055 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2056 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2060 The type signature of
2061 each constructor is independent, and is implicitly universally quantified as usual.
2062 Different constructors may have different universally-quantified type variables
2063 and different type-class constraints.
2064 For example, this is fine:
2067 T1 :: Eq b => b -> T b
2068 T2 :: (Show c, Ix c) => c -> [c] -> T c
2073 Unlike a Haskell-98-style
2074 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2075 have no scope. Indeed, one can write a kind signature instead:
2077 data Set :: * -> * where ...
2079 or even a mixture of the two:
2081 data Foo a :: (* -> *) -> * where ...
2083 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2086 data Foo a (b :: * -> *) where ...
2092 You can use strictness annotations, in the obvious places
2093 in the constructor type:
2096 Lit :: !Int -> Term Int
2097 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2098 Pair :: Term a -> Term b -> Term (a,b)
2103 You can use a <literal>deriving</literal> clause on a GADT-style data type
2104 declaration. For example, these two declarations are equivalent
2106 data Maybe1 a where {
2107 Nothing1 :: Maybe1 a ;
2108 Just1 :: a -> Maybe1 a
2109 } deriving( Eq, Ord )
2111 data Maybe2 a = Nothing2 | Just2 a
2117 You can use record syntax on a GADT-style data type declaration:
2121 Adult { name :: String, children :: [Person] } :: Person
2122 Child { name :: String } :: Person
2124 As usual, for every constructor that has a field <literal>f</literal>, the type of
2125 field <literal>f</literal> must be the same (modulo alpha conversion).
2128 At the moment, record updates are not yet possible with GADT-style declarations,
2129 so support is limited to record construction, selection and pattern matching.
2132 aPerson = Adult { name = "Fred", children = [] }
2134 shortName :: Person -> Bool
2135 hasChildren (Adult { children = kids }) = not (null kids)
2136 hasChildren (Child {}) = False
2141 As in the case of existentials declared using the Haskell-98-like record syntax
2142 (<xref linkend="existential-records"/>),
2143 record-selector functions are generated only for those fields that have well-typed
2145 Here is the example of that section, in GADT-style syntax:
2147 data Counter a where
2148 NewCounter { _this :: self
2149 , _inc :: self -> self
2150 , _display :: self -> IO ()
2155 As before, only one selector function is generated here, that for <literal>tag</literal>.
2156 Nevertheless, you can still use all the field names in pattern matching and record construction.
2158 </itemizedlist></para>
2162 <title>Generalised Algebraic Data Types (GADTs)</title>
2164 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2165 by allowing constructors to have richer return types. Here is an example:
2168 Lit :: Int -> Term Int
2169 Succ :: Term Int -> Term Int
2170 IsZero :: Term Int -> Term Bool
2171 If :: Term Bool -> Term a -> Term a -> Term a
2172 Pair :: Term a -> Term b -> Term (a,b)
2174 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2175 case with ordinary data types. This generality allows us to
2176 write a well-typed <literal>eval</literal> function
2177 for these <literal>Terms</literal>:
2181 eval (Succ t) = 1 + eval t
2182 eval (IsZero t) = eval t == 0
2183 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2184 eval (Pair e1 e2) = (eval e1, eval e2)
2186 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2187 For example, in the right hand side of the equation
2192 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2193 A precise specification of the type rules is beyond what this user manual aspires to,
2194 but the design closely follows that described in
2196 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
2197 unification-based type inference for GADTs</ulink>,
2199 The general principle is this: <emphasis>type refinement is only carried out
2200 based on user-supplied type annotations</emphasis>.
2201 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2202 and lots of obscure error messages will
2203 occur. However, the refinement is quite general. For example, if we had:
2205 eval :: Term a -> a -> a
2206 eval (Lit i) j = i+j
2208 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2209 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2210 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2213 These and many other examples are given in papers by Hongwei Xi, and
2214 Tim Sheard. There is a longer introduction
2215 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2217 <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
2218 may use different notation to that implemented in GHC.
2221 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2222 <option>-XGADTs</option>.
2225 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2226 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2227 The result type of each constructor must begin with the type constructor being defined,
2228 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2229 For example, in the <literal>Term</literal> data
2230 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2231 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
2236 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2237 an ordinary data type.
2241 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2245 Lit { val :: Int } :: Term Int
2246 Succ { num :: Term Int } :: Term Int
2247 Pred { num :: Term Int } :: Term Int
2248 IsZero { arg :: Term Int } :: Term Bool
2249 Pair { arg1 :: Term a
2252 If { cnd :: Term Bool
2257 However, for GADTs there is the following additional constraint:
2258 every constructor that has a field <literal>f</literal> must have
2259 the same result type (modulo alpha conversion)
2260 Hence, in the above example, we cannot merge the <literal>num</literal>
2261 and <literal>arg</literal> fields above into a
2262 single name. Although their field types are both <literal>Term Int</literal>,
2263 their selector functions actually have different types:
2266 num :: Term Int -> Term Int
2267 arg :: Term Bool -> Term Int
2277 <!-- ====================== End of Generalised algebraic data types ======================= -->
2279 <sect1 id="deriving">
2280 <title>Extensions to the "deriving" mechanism</title>
2282 <sect2 id="deriving-inferred">
2283 <title>Inferred context for deriving clauses</title>
2286 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2289 data T0 f a = MkT0 a deriving( Eq )
2290 data T1 f a = MkT1 (f a) deriving( Eq )
2291 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2293 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2295 instance Eq a => Eq (T0 f a) where ...
2296 instance Eq (f a) => Eq (T1 f a) where ...
2297 instance Eq (f (f a)) => Eq (T2 f a) where ...
2299 The first of these is obviously fine. The second is still fine, although less obviously.
2300 The third is not Haskell 98, and risks losing termination of instances.
2303 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2304 each constraint in the inferred instance context must consist only of type variables,
2305 with no repetitions.
2308 This rule is applied regardless of flags. If you want a more exotic context, you can write
2309 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2313 <sect2 id="stand-alone-deriving">
2314 <title>Stand-alone deriving declarations</title>
2317 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2319 data Foo a = Bar a | Baz String
2321 deriving instance Eq a => Eq (Foo a)
2323 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2324 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2325 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2326 exactly as you would in an ordinary instance declaration.
2327 (In contrast the context is inferred in a <literal>deriving</literal> clause
2328 attached to a data type declaration.) These <literal>deriving instance</literal>
2329 rules obey the same rules concerning form and termination as ordinary instance declarations,
2330 controlled by the same flags; see <xref linkend="instance-decls"/>. </para>
2332 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2333 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2336 newtype Foo a = MkFoo (State Int a)
2338 deriving instance MonadState Int Foo
2340 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2341 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2347 <sect2 id="deriving-typeable">
2348 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2351 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2352 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2353 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2354 classes <literal>Eq</literal>, <literal>Ord</literal>,
2355 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2358 GHC extends this list with two more classes that may be automatically derived
2359 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2360 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2361 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2362 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2364 <para>An instance of <literal>Typeable</literal> can only be derived if the
2365 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2366 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2368 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2369 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2371 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2372 are used, and only <literal>Typeable1</literal> up to
2373 <literal>Typeable7</literal> are provided in the library.)
2374 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2375 class, whose kind suits that of the data type constructor, and
2376 then writing the data type instance by hand.
2380 <sect2 id="newtype-deriving">
2381 <title>Generalised derived instances for newtypes</title>
2384 When you define an abstract type using <literal>newtype</literal>, you may want
2385 the new type to inherit some instances from its representation. In
2386 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2387 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2388 other classes you have to write an explicit instance declaration. For
2389 example, if you define
2392 newtype Dollars = Dollars Int
2395 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2396 explicitly define an instance of <literal>Num</literal>:
2399 instance Num Dollars where
2400 Dollars a + Dollars b = Dollars (a+b)
2403 All the instance does is apply and remove the <literal>newtype</literal>
2404 constructor. It is particularly galling that, since the constructor
2405 doesn't appear at run-time, this instance declaration defines a
2406 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2407 dictionary, only slower!
2411 <sect3> <title> Generalising the deriving clause </title>
2413 GHC now permits such instances to be derived instead,
2414 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2417 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2420 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2421 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2422 derives an instance declaration of the form
2425 instance Num Int => Num Dollars
2428 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2432 We can also derive instances of constructor classes in a similar
2433 way. For example, suppose we have implemented state and failure monad
2434 transformers, such that
2437 instance Monad m => Monad (State s m)
2438 instance Monad m => Monad (Failure m)
2440 In Haskell 98, we can define a parsing monad by
2442 type Parser tok m a = State [tok] (Failure m) a
2445 which is automatically a monad thanks to the instance declarations
2446 above. With the extension, we can make the parser type abstract,
2447 without needing to write an instance of class <literal>Monad</literal>, via
2450 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2453 In this case the derived instance declaration is of the form
2455 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2458 Notice that, since <literal>Monad</literal> is a constructor class, the
2459 instance is a <emphasis>partial application</emphasis> of the new type, not the
2460 entire left hand side. We can imagine that the type declaration is
2461 "eta-converted" to generate the context of the instance
2466 We can even derive instances of multi-parameter classes, provided the
2467 newtype is the last class parameter. In this case, a ``partial
2468 application'' of the class appears in the <literal>deriving</literal>
2469 clause. For example, given the class
2472 class StateMonad s m | m -> s where ...
2473 instance Monad m => StateMonad s (State s m) where ...
2475 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2477 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2478 deriving (Monad, StateMonad [tok])
2481 The derived instance is obtained by completing the application of the
2482 class to the new type:
2485 instance StateMonad [tok] (State [tok] (Failure m)) =>
2486 StateMonad [tok] (Parser tok m)
2491 As a result of this extension, all derived instances in newtype
2492 declarations are treated uniformly (and implemented just by reusing
2493 the dictionary for the representation type), <emphasis>except</emphasis>
2494 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2495 the newtype and its representation.
2499 <sect3> <title> A more precise specification </title>
2501 Derived instance declarations are constructed as follows. Consider the
2502 declaration (after expansion of any type synonyms)
2505 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2511 The <literal>ci</literal> are partial applications of
2512 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2513 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2516 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2519 The type <literal>t</literal> is an arbitrary type.
2522 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2523 nor in the <literal>ci</literal>, and
2526 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2527 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2528 should not "look through" the type or its constructor. You can still
2529 derive these classes for a newtype, but it happens in the usual way, not
2530 via this new mechanism.
2533 Then, for each <literal>ci</literal>, the derived instance
2536 instance ci t => ci (T v1...vk)
2538 As an example which does <emphasis>not</emphasis> work, consider
2540 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2542 Here we cannot derive the instance
2544 instance Monad (State s m) => Monad (NonMonad m)
2547 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2548 and so cannot be "eta-converted" away. It is a good thing that this
2549 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2550 not, in fact, a monad --- for the same reason. Try defining
2551 <literal>>>=</literal> with the correct type: you won't be able to.
2555 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2556 important, since we can only derive instances for the last one. If the
2557 <literal>StateMonad</literal> class above were instead defined as
2560 class StateMonad m s | m -> s where ...
2563 then we would not have been able to derive an instance for the
2564 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2565 classes usually have one "main" parameter for which deriving new
2566 instances is most interesting.
2568 <para>Lastly, all of this applies only for classes other than
2569 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2570 and <literal>Data</literal>, for which the built-in derivation applies (section
2571 4.3.3. of the Haskell Report).
2572 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2573 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2574 the standard method is used or the one described here.)
2581 <!-- TYPE SYSTEM EXTENSIONS -->
2582 <sect1 id="type-class-extensions">
2583 <title>Class and instances declarations</title>
2585 <sect2 id="multi-param-type-classes">
2586 <title>Class declarations</title>
2589 This section, and the next one, documents GHC's type-class extensions.
2590 There's lots of background in the paper <ulink
2591 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2592 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2593 Jones, Erik Meijer).
2596 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2600 <title>Multi-parameter type classes</title>
2602 Multi-parameter type classes are permitted. For example:
2606 class Collection c a where
2607 union :: c a -> c a -> c a
2615 <title>The superclasses of a class declaration</title>
2618 There are no restrictions on the context in a class declaration
2619 (which introduces superclasses), except that the class hierarchy must
2620 be acyclic. So these class declarations are OK:
2624 class Functor (m k) => FiniteMap m k where
2627 class (Monad m, Monad (t m)) => Transform t m where
2628 lift :: m a -> (t m) a
2634 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2635 of "acyclic" involves only the superclass relationships. For example,
2641 op :: D b => a -> b -> b
2644 class C a => D a where { ... }
2648 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2649 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2650 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2657 <sect3 id="class-method-types">
2658 <title>Class method types</title>
2661 Haskell 98 prohibits class method types to mention constraints on the
2662 class type variable, thus:
2665 fromList :: [a] -> s a
2666 elem :: Eq a => a -> s a -> Bool
2668 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2669 contains the constraint <literal>Eq a</literal>, constrains only the
2670 class type variable (in this case <literal>a</literal>).
2671 GHC lifts this restriction.
2678 <sect2 id="functional-dependencies">
2679 <title>Functional dependencies
2682 <para> Functional dependencies are implemented as described by Mark Jones
2683 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2684 In Proceedings of the 9th European Symposium on Programming,
2685 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2689 Functional dependencies are introduced by a vertical bar in the syntax of a
2690 class declaration; e.g.
2692 class (Monad m) => MonadState s m | m -> s where ...
2694 class Foo a b c | a b -> c where ...
2696 There should be more documentation, but there isn't (yet). Yell if you need it.
2699 <sect3><title>Rules for functional dependencies </title>
2701 In a class declaration, all of the class type variables must be reachable (in the sense
2702 mentioned in <xref linkend="type-restrictions"/>)
2703 from the free variables of each method type.
2707 class Coll s a where
2709 insert :: s -> a -> s
2712 is not OK, because the type of <literal>empty</literal> doesn't mention
2713 <literal>a</literal>. Functional dependencies can make the type variable
2716 class Coll s a | s -> a where
2718 insert :: s -> a -> s
2721 Alternatively <literal>Coll</literal> might be rewritten
2724 class Coll s a where
2726 insert :: s a -> a -> s a
2730 which makes the connection between the type of a collection of
2731 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2732 Occasionally this really doesn't work, in which case you can split the
2740 class CollE s => Coll s a where
2741 insert :: s -> a -> s
2748 <title>Background on functional dependencies</title>
2750 <para>The following description of the motivation and use of functional dependencies is taken
2751 from the Hugs user manual, reproduced here (with minor changes) by kind
2752 permission of Mark Jones.
2755 Consider the following class, intended as part of a
2756 library for collection types:
2758 class Collects e ce where
2760 insert :: e -> ce -> ce
2761 member :: e -> ce -> Bool
2763 The type variable e used here represents the element type, while ce is the type
2764 of the container itself. Within this framework, we might want to define
2765 instances of this class for lists or characteristic functions (both of which
2766 can be used to represent collections of any equality type), bit sets (which can
2767 be used to represent collections of characters), or hash tables (which can be
2768 used to represent any collection whose elements have a hash function). Omitting
2769 standard implementation details, this would lead to the following declarations:
2771 instance Eq e => Collects e [e] where ...
2772 instance Eq e => Collects e (e -> Bool) where ...
2773 instance Collects Char BitSet where ...
2774 instance (Hashable e, Collects a ce)
2775 => Collects e (Array Int ce) where ...
2777 All this looks quite promising; we have a class and a range of interesting
2778 implementations. Unfortunately, there are some serious problems with the class
2779 declaration. First, the empty function has an ambiguous type:
2781 empty :: Collects e ce => ce
2783 By "ambiguous" we mean that there is a type variable e that appears on the left
2784 of the <literal>=></literal> symbol, but not on the right. The problem with
2785 this is that, according to the theoretical foundations of Haskell overloading,
2786 we cannot guarantee a well-defined semantics for any term with an ambiguous
2790 We can sidestep this specific problem by removing the empty member from the
2791 class declaration. However, although the remaining members, insert and member,
2792 do not have ambiguous types, we still run into problems when we try to use
2793 them. For example, consider the following two functions:
2795 f x y = insert x . insert y
2798 for which GHC infers the following types:
2800 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2801 g :: (Collects Bool c, Collects Char c) => c -> c
2803 Notice that the type for f allows the two parameters x and y to be assigned
2804 different types, even though it attempts to insert each of the two values, one
2805 after the other, into the same collection. If we're trying to model collections
2806 that contain only one type of value, then this is clearly an inaccurate
2807 type. Worse still, the definition for g is accepted, without causing a type
2808 error. As a result, the error in this code will not be flagged at the point
2809 where it appears. Instead, it will show up only when we try to use g, which
2810 might even be in a different module.
2813 <sect4><title>An attempt to use constructor classes</title>
2816 Faced with the problems described above, some Haskell programmers might be
2817 tempted to use something like the following version of the class declaration:
2819 class Collects e c where
2821 insert :: e -> c e -> c e
2822 member :: e -> c e -> Bool
2824 The key difference here is that we abstract over the type constructor c that is
2825 used to form the collection type c e, and not over that collection type itself,
2826 represented by ce in the original class declaration. This avoids the immediate
2827 problems that we mentioned above: empty has type <literal>Collects e c => c
2828 e</literal>, which is not ambiguous.
2831 The function f from the previous section has a more accurate type:
2833 f :: (Collects e c) => e -> e -> c e -> c e
2835 The function g from the previous section is now rejected with a type error as
2836 we would hope because the type of f does not allow the two arguments to have
2838 This, then, is an example of a multiple parameter class that does actually work
2839 quite well in practice, without ambiguity problems.
2840 There is, however, a catch. This version of the Collects class is nowhere near
2841 as general as the original class seemed to be: only one of the four instances
2842 for <literal>Collects</literal>
2843 given above can be used with this version of Collects because only one of
2844 them---the instance for lists---has a collection type that can be written in
2845 the form c e, for some type constructor c, and element type e.
2849 <sect4><title>Adding functional dependencies</title>
2852 To get a more useful version of the Collects class, Hugs provides a mechanism
2853 that allows programmers to specify dependencies between the parameters of a
2854 multiple parameter class (For readers with an interest in theoretical
2855 foundations and previous work: The use of dependency information can be seen
2856 both as a generalization of the proposal for `parametric type classes' that was
2857 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2858 later framework for "improvement" of qualified types. The
2859 underlying ideas are also discussed in a more theoretical and abstract setting
2860 in a manuscript [implparam], where they are identified as one point in a
2861 general design space for systems of implicit parameterization.).
2863 To start with an abstract example, consider a declaration such as:
2865 class C a b where ...
2867 which tells us simply that C can be thought of as a binary relation on types
2868 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2869 included in the definition of classes to add information about dependencies
2870 between parameters, as in the following examples:
2872 class D a b | a -> b where ...
2873 class E a b | a -> b, b -> a where ...
2875 The notation <literal>a -> b</literal> used here between the | and where
2876 symbols --- not to be
2877 confused with a function type --- indicates that the a parameter uniquely
2878 determines the b parameter, and might be read as "a determines b." Thus D is
2879 not just a relation, but actually a (partial) function. Similarly, from the two
2880 dependencies that are included in the definition of E, we can see that E
2881 represents a (partial) one-one mapping between types.
2884 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2885 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2886 m>=0, meaning that the y parameters are uniquely determined by the x
2887 parameters. Spaces can be used as separators if more than one variable appears
2888 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2889 annotated with multiple dependencies using commas as separators, as in the
2890 definition of E above. Some dependencies that we can write in this notation are
2891 redundant, and will be rejected because they don't serve any useful
2892 purpose, and may instead indicate an error in the program. Examples of
2893 dependencies like this include <literal>a -> a </literal>,
2894 <literal>a -> a a </literal>,
2895 <literal>a -> </literal>, etc. There can also be
2896 some redundancy if multiple dependencies are given, as in
2897 <literal>a->b</literal>,
2898 <literal>b->c </literal>, <literal>a->c </literal>, and
2899 in which some subset implies the remaining dependencies. Examples like this are
2900 not treated as errors. Note that dependencies appear only in class
2901 declarations, and not in any other part of the language. In particular, the
2902 syntax for instance declarations, class constraints, and types is completely
2906 By including dependencies in a class declaration, we provide a mechanism for
2907 the programmer to specify each multiple parameter class more precisely. The
2908 compiler, on the other hand, is responsible for ensuring that the set of
2909 instances that are in scope at any given point in the program is consistent
2910 with any declared dependencies. For example, the following pair of instance
2911 declarations cannot appear together in the same scope because they violate the
2912 dependency for D, even though either one on its own would be acceptable:
2914 instance D Bool Int where ...
2915 instance D Bool Char where ...
2917 Note also that the following declaration is not allowed, even by itself:
2919 instance D [a] b where ...
2921 The problem here is that this instance would allow one particular choice of [a]
2922 to be associated with more than one choice for b, which contradicts the
2923 dependency specified in the definition of D. More generally, this means that,
2924 in any instance of the form:
2926 instance D t s where ...
2928 for some particular types t and s, the only variables that can appear in s are
2929 the ones that appear in t, and hence, if the type t is known, then s will be
2930 uniquely determined.
2933 The benefit of including dependency information is that it allows us to define
2934 more general multiple parameter classes, without ambiguity problems, and with
2935 the benefit of more accurate types. To illustrate this, we return to the
2936 collection class example, and annotate the original definition of <literal>Collects</literal>
2937 with a simple dependency:
2939 class Collects e ce | ce -> e where
2941 insert :: e -> ce -> ce
2942 member :: e -> ce -> Bool
2944 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2945 determined by the type of the collection ce. Note that both parameters of
2946 Collects are of kind *; there are no constructor classes here. Note too that
2947 all of the instances of Collects that we gave earlier can be used
2948 together with this new definition.
2951 What about the ambiguity problems that we encountered with the original
2952 definition? The empty function still has type Collects e ce => ce, but it is no
2953 longer necessary to regard that as an ambiguous type: Although the variable e
2954 does not appear on the right of the => symbol, the dependency for class
2955 Collects tells us that it is uniquely determined by ce, which does appear on
2956 the right of the => symbol. Hence the context in which empty is used can still
2957 give enough information to determine types for both ce and e, without
2958 ambiguity. More generally, we need only regard a type as ambiguous if it
2959 contains a variable on the left of the => that is not uniquely determined
2960 (either directly or indirectly) by the variables on the right.
2963 Dependencies also help to produce more accurate types for user defined
2964 functions, and hence to provide earlier detection of errors, and less cluttered
2965 types for programmers to work with. Recall the previous definition for a
2968 f x y = insert x y = insert x . insert y
2970 for which we originally obtained a type:
2972 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2974 Given the dependency information that we have for Collects, however, we can
2975 deduce that a and b must be equal because they both appear as the second
2976 parameter in a Collects constraint with the same first parameter c. Hence we
2977 can infer a shorter and more accurate type for f:
2979 f :: (Collects a c) => a -> a -> c -> c
2981 In a similar way, the earlier definition of g will now be flagged as a type error.
2984 Although we have given only a few examples here, it should be clear that the
2985 addition of dependency information can help to make multiple parameter classes
2986 more useful in practice, avoiding ambiguity problems, and allowing more general
2987 sets of instance declarations.
2993 <sect2 id="instance-decls">
2994 <title>Instance declarations</title>
2996 <sect3 id="instance-rules">
2997 <title>Relaxed rules for instance declarations</title>
2999 <para>An instance declaration has the form
3001 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 ...
3003 The part before the "<literal>=></literal>" is the
3004 <emphasis>context</emphasis>, while the part after the
3005 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3009 In Haskell 98 the head of an instance declaration
3010 must be of the form <literal>C (T a1 ... an)</literal>, where
3011 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3012 and the <literal>a1 ... an</literal> are distinct type variables.
3013 Furthermore, the assertions in the context of the instance declaration
3014 must be of the form <literal>C a</literal> where <literal>a</literal>
3015 is a type variable that occurs in the head.
3018 The <option>-fglasgow-exts</option> flag loosens these restrictions
3019 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3020 the context and head of the instance declaration can each consist of arbitrary
3021 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3025 The Paterson Conditions: for each assertion in the context
3027 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3028 <listitem><para>The assertion has fewer constructors and variables (taken together
3029 and counting repetitions) than the head</para></listitem>
3033 <listitem><para>The Coverage Condition. For each functional dependency,
3034 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3035 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3036 every type variable in
3037 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3038 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3039 substitution mapping each type variable in the class declaration to the
3040 corresponding type in the instance declaration.
3043 These restrictions ensure that context reduction terminates: each reduction
3044 step makes the problem smaller by at least one
3045 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3046 if you give the <option>-fallow-undecidable-instances</option>
3047 flag (<xref linkend="undecidable-instances"/>).
3048 You can find lots of background material about the reason for these
3049 restrictions in the paper <ulink
3050 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3051 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3054 For example, these are OK:
3056 instance C Int [a] -- Multiple parameters
3057 instance Eq (S [a]) -- Structured type in head
3059 -- Repeated type variable in head
3060 instance C4 a a => C4 [a] [a]
3061 instance Stateful (ST s) (MutVar s)
3063 -- Head can consist of type variables only
3065 instance (Eq a, Show b) => C2 a b
3067 -- Non-type variables in context
3068 instance Show (s a) => Show (Sized s a)
3069 instance C2 Int a => C3 Bool [a]
3070 instance C2 Int a => C3 [a] b
3074 -- Context assertion no smaller than head
3075 instance C a => C a where ...
3076 -- (C b b) has more more occurrences of b than the head
3077 instance C b b => Foo [b] where ...
3082 The same restrictions apply to instances generated by
3083 <literal>deriving</literal> clauses. Thus the following is accepted:
3085 data MinHeap h a = H a (h a)
3088 because the derived instance
3090 instance (Show a, Show (h a)) => Show (MinHeap h a)
3092 conforms to the above rules.
3096 A useful idiom permitted by the above rules is as follows.
3097 If one allows overlapping instance declarations then it's quite
3098 convenient to have a "default instance" declaration that applies if
3099 something more specific does not:
3107 <sect3 id="undecidable-instances">
3108 <title>Undecidable instances</title>
3111 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3112 For example, sometimes you might want to use the following to get the
3113 effect of a "class synonym":
3115 class (C1 a, C2 a, C3 a) => C a where { }
3117 instance (C1 a, C2 a, C3 a) => C a where { }
3119 This allows you to write shorter signatures:
3125 f :: (C1 a, C2 a, C3 a) => ...
3127 The restrictions on functional dependencies (<xref
3128 linkend="functional-dependencies"/>) are particularly troublesome.
3129 It is tempting to introduce type variables in the context that do not appear in
3130 the head, something that is excluded by the normal rules. For example:
3132 class HasConverter a b | a -> b where
3135 data Foo a = MkFoo a
3137 instance (HasConverter a b,Show b) => Show (Foo a) where
3138 show (MkFoo value) = show (convert value)
3140 This is dangerous territory, however. Here, for example, is a program that would make the
3145 instance F [a] [[a]]
3146 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3148 Similarly, it can be tempting to lift the coverage condition:
3150 class Mul a b c | a b -> c where
3151 (.*.) :: a -> b -> c
3153 instance Mul Int Int Int where (.*.) = (*)
3154 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3155 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3157 The third instance declaration does not obey the coverage condition;
3158 and indeed the (somewhat strange) definition:
3160 f = \ b x y -> if b then x .*. [y] else y
3162 makes instance inference go into a loop, because it requires the constraint
3163 <literal>(Mul a [b] b)</literal>.
3166 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3167 the experimental flag <option>-XUndecidableInstances</option>
3168 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3169 both the Paterson Conditions and the Coverage Condition
3170 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3171 fixed-depth recursion stack. If you exceed the stack depth you get a
3172 sort of backtrace, and the opportunity to increase the stack depth
3173 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3179 <sect3 id="instance-overlap">
3180 <title>Overlapping instances</title>
3182 In general, <emphasis>GHC requires that that it be unambiguous which instance
3184 should be used to resolve a type-class constraint</emphasis>. This behaviour
3185 can be modified by two flags: <option>-XOverlappingInstances</option>
3186 <indexterm><primary>-XOverlappingInstances
3187 </primary></indexterm>
3188 and <option>-XIncoherentInstances</option>
3189 <indexterm><primary>-XIncoherentInstances
3190 </primary></indexterm>, as this section discusses. Both these
3191 flags are dynamic flags, and can be set on a per-module basis, using
3192 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3194 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3195 it tries to match every instance declaration against the
3197 by instantiating the head of the instance declaration. For example, consider
3200 instance context1 => C Int a where ... -- (A)
3201 instance context2 => C a Bool where ... -- (B)
3202 instance context3 => C Int [a] where ... -- (C)
3203 instance context4 => C Int [Int] where ... -- (D)
3205 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3206 but (C) and (D) do not. When matching, GHC takes
3207 no account of the context of the instance declaration
3208 (<literal>context1</literal> etc).
3209 GHC's default behaviour is that <emphasis>exactly one instance must match the
3210 constraint it is trying to resolve</emphasis>.
3211 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3212 including both declarations (A) and (B), say); an error is only reported if a
3213 particular constraint matches more than one.
3217 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3218 more than one instance to match, provided there is a most specific one. For
3219 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3220 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3221 most-specific match, the program is rejected.
3224 However, GHC is conservative about committing to an overlapping instance. For example:
3229 Suppose that from the RHS of <literal>f</literal> we get the constraint
3230 <literal>C Int [b]</literal>. But
3231 GHC does not commit to instance (C), because in a particular
3232 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3233 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3234 So GHC rejects the program.
3235 (If you add the flag <option>-XIncoherentInstances</option>,
3236 GHC will instead pick (C), without complaining about
3237 the problem of subsequent instantiations.)
3240 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3241 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3242 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3243 it instead. In this case, GHC will refrain from
3244 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3245 as before) but, rather than rejecting the program, it will infer the type
3247 f :: C Int b => [b] -> [b]
3249 That postpones the question of which instance to pick to the
3250 call site for <literal>f</literal>
3251 by which time more is known about the type <literal>b</literal>.
3254 The willingness to be overlapped or incoherent is a property of
3255 the <emphasis>instance declaration</emphasis> itself, controlled by the
3256 presence or otherwise of the <option>-XOverlappingInstances</option>
3257 and <option>-XIncoherentInstances</option> flags when that module is
3258 being defined. Neither flag is required in a module that imports and uses the
3259 instance declaration. Specifically, during the lookup process:
3262 An instance declaration is ignored during the lookup process if (a) a more specific
3263 match is found, and (b) the instance declaration was compiled with
3264 <option>-XOverlappingInstances</option>. The flag setting for the
3265 more-specific instance does not matter.
3268 Suppose an instance declaration does not match the constraint being looked up, but
3269 does unify with it, so that it might match when the constraint is further
3270 instantiated. Usually GHC will regard this as a reason for not committing to
3271 some other constraint. But if the instance declaration was compiled with
3272 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3273 check for that declaration.
3276 These rules make it possible for a library author to design a library that relies on
3277 overlapping instances without the library client having to know.
3280 If an instance declaration is compiled without
3281 <option>-XOverlappingInstances</option>,
3282 then that instance can never be overlapped. This could perhaps be
3283 inconvenient. Perhaps the rule should instead say that the
3284 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3285 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3286 at a usage site should be permitted regardless of how the instance declarations
3287 are compiled, if the <option>-XOverlappingInstances</option> flag is
3288 used at the usage site. (Mind you, the exact usage site can occasionally be
3289 hard to pin down.) We are interested to receive feedback on these points.
3291 <para>The <option>-XIncoherentInstances</option> flag implies the
3292 <option>-XOverlappingInstances</option> flag, but not vice versa.
3297 <title>Type synonyms in the instance head</title>
3300 <emphasis>Unlike Haskell 98, instance heads may use type
3301 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3302 As always, using a type synonym is just shorthand for
3303 writing the RHS of the type synonym definition. For example:
3307 type Point = (Int,Int)
3308 instance C Point where ...
3309 instance C [Point] where ...
3313 is legal. However, if you added
3317 instance C (Int,Int) where ...
3321 as well, then the compiler will complain about the overlapping
3322 (actually, identical) instance declarations. As always, type synonyms
3323 must be fully applied. You cannot, for example, write:
3328 instance Monad P where ...
3332 This design decision is independent of all the others, and easily
3333 reversed, but it makes sense to me.
3341 <sect2 id="overloaded-strings">
3342 <title>Overloaded string literals
3346 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3347 string literal has type <literal>String</literal>, but with overloaded string
3348 literals enabled (with <literal>-XOverloadedStrings</literal>)
3349 a string literal has type <literal>(IsString a) => a</literal>.
3352 This means that the usual string syntax can be used, e.g., for packed strings
3353 and other variations of string like types. String literals behave very much
3354 like integer literals, i.e., they can be used in both expressions and patterns.
3355 If used in a pattern the literal with be replaced by an equality test, in the same
3356 way as an integer literal is.
3359 The class <literal>IsString</literal> is defined as:
3361 class IsString a where
3362 fromString :: String -> a
3364 The only predefined instance is the obvious one to make strings work as usual:
3366 instance IsString [Char] where
3369 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3370 it explicitly (for example, to give an instance declaration for it), you can import it
3371 from module <literal>GHC.Exts</literal>.
3374 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3378 Each type in a default declaration must be an
3379 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3383 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3384 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3385 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3386 <emphasis>or</emphasis> <literal>IsString</literal>.
3395 import GHC.Exts( IsString(..) )
3397 newtype MyString = MyString String deriving (Eq, Show)
3398 instance IsString MyString where
3399 fromString = MyString
3401 greet :: MyString -> MyString
3402 greet "hello" = "world"
3406 print $ greet "hello"
3407 print $ greet "fool"
3411 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3412 to work since it gets translated into an equality comparison.
3418 <sect1 id="other-type-extensions">
3419 <title>Other type system extensions</title>
3421 <sect2 id="type-restrictions">
3422 <title>Type signatures</title>
3424 <sect3><title>The context of a type signature</title>
3426 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3427 the form <emphasis>(class type-variable)</emphasis> or
3428 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3429 these type signatures are perfectly OK
3432 g :: Ord (T a ()) => ...
3436 GHC imposes the following restrictions on the constraints in a type signature.
3440 forall tv1..tvn (c1, ...,cn) => type
3443 (Here, we write the "foralls" explicitly, although the Haskell source
3444 language omits them; in Haskell 98, all the free type variables of an
3445 explicit source-language type signature are universally quantified,
3446 except for the class type variables in a class declaration. However,
3447 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3456 <emphasis>Each universally quantified type variable
3457 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3459 A type variable <literal>a</literal> is "reachable" if it it appears
3460 in the same constraint as either a type variable free in in
3461 <literal>type</literal>, or another reachable type variable.
3462 A value with a type that does not obey
3463 this reachability restriction cannot be used without introducing
3464 ambiguity; that is why the type is rejected.
3465 Here, for example, is an illegal type:
3469 forall a. Eq a => Int
3473 When a value with this type was used, the constraint <literal>Eq tv</literal>
3474 would be introduced where <literal>tv</literal> is a fresh type variable, and
3475 (in the dictionary-translation implementation) the value would be
3476 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3477 can never know which instance of <literal>Eq</literal> to use because we never
3478 get any more information about <literal>tv</literal>.
3482 that the reachability condition is weaker than saying that <literal>a</literal> is
3483 functionally dependent on a type variable free in
3484 <literal>type</literal> (see <xref
3485 linkend="functional-dependencies"/>). The reason for this is there
3486 might be a "hidden" dependency, in a superclass perhaps. So
3487 "reachable" is a conservative approximation to "functionally dependent".
3488 For example, consider:
3490 class C a b | a -> b where ...
3491 class C a b => D a b where ...
3492 f :: forall a b. D a b => a -> a
3494 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3495 but that is not immediately apparent from <literal>f</literal>'s type.
3501 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3502 universally quantified type variables <literal>tvi</literal></emphasis>.
3504 For example, this type is OK because <literal>C a b</literal> mentions the
3505 universally quantified type variable <literal>b</literal>:
3509 forall a. C a b => burble
3513 The next type is illegal because the constraint <literal>Eq b</literal> does not
3514 mention <literal>a</literal>:
3518 forall a. Eq b => burble
3522 The reason for this restriction is milder than the other one. The
3523 excluded types are never useful or necessary (because the offending
3524 context doesn't need to be witnessed at this point; it can be floated
3525 out). Furthermore, floating them out increases sharing. Lastly,
3526 excluding them is a conservative choice; it leaves a patch of
3527 territory free in case we need it later.
3541 <sect2 id="implicit-parameters">
3542 <title>Implicit parameters</title>
3544 <para> Implicit parameters are implemented as described in
3545 "Implicit parameters: dynamic scoping with static types",
3546 J Lewis, MB Shields, E Meijer, J Launchbury,
3547 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3551 <para>(Most of the following, still rather incomplete, documentation is
3552 due to Jeff Lewis.)</para>
3554 <para>Implicit parameter support is enabled with the option
3555 <option>-XImplicitParams</option>.</para>
3558 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3559 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3560 context. In Haskell, all variables are statically bound. Dynamic
3561 binding of variables is a notion that goes back to Lisp, but was later
3562 discarded in more modern incarnations, such as Scheme. Dynamic binding
3563 can be very confusing in an untyped language, and unfortunately, typed
3564 languages, in particular Hindley-Milner typed languages like Haskell,
3565 only support static scoping of variables.
3568 However, by a simple extension to the type class system of Haskell, we
3569 can support dynamic binding. Basically, we express the use of a
3570 dynamically bound variable as a constraint on the type. These
3571 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3572 function uses a dynamically-bound variable <literal>?x</literal>
3573 of type <literal>t'</literal>". For
3574 example, the following expresses the type of a sort function,
3575 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3577 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3579 The dynamic binding constraints are just a new form of predicate in the type class system.
3582 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3583 where <literal>x</literal> is
3584 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3585 Use of this construct also introduces a new
3586 dynamic-binding constraint in the type of the expression.
3587 For example, the following definition
3588 shows how we can define an implicitly parameterized sort function in
3589 terms of an explicitly parameterized <literal>sortBy</literal> function:
3591 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3593 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3599 <title>Implicit-parameter type constraints</title>
3601 Dynamic binding constraints behave just like other type class
3602 constraints in that they are automatically propagated. Thus, when a
3603 function is used, its implicit parameters are inherited by the
3604 function that called it. For example, our <literal>sort</literal> function might be used
3605 to pick out the least value in a list:
3607 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3608 least xs = head (sort xs)
3610 Without lifting a finger, the <literal>?cmp</literal> parameter is
3611 propagated to become a parameter of <literal>least</literal> as well. With explicit
3612 parameters, the default is that parameters must always be explicit
3613 propagated. With implicit parameters, the default is to always
3617 An implicit-parameter type constraint differs from other type class constraints in the
3618 following way: All uses of a particular implicit parameter must have
3619 the same type. This means that the type of <literal>(?x, ?x)</literal>
3620 is <literal>(?x::a) => (a,a)</literal>, and not
3621 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3625 <para> You can't have an implicit parameter in the context of a class or instance
3626 declaration. For example, both these declarations are illegal:
3628 class (?x::Int) => C a where ...
3629 instance (?x::a) => Foo [a] where ...
3631 Reason: exactly which implicit parameter you pick up depends on exactly where
3632 you invoke a function. But the ``invocation'' of instance declarations is done
3633 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3634 Easiest thing is to outlaw the offending types.</para>
3636 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3638 f :: (?x :: [a]) => Int -> Int
3641 g :: (Read a, Show a) => String -> String
3644 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3645 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3646 quite unambiguous, and fixes the type <literal>a</literal>.
3651 <title>Implicit-parameter bindings</title>
3654 An implicit parameter is <emphasis>bound</emphasis> using the standard
3655 <literal>let</literal> or <literal>where</literal> binding forms.
3656 For example, we define the <literal>min</literal> function by binding
3657 <literal>cmp</literal>.
3660 min = let ?cmp = (<=) in least
3664 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3665 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3666 (including in a list comprehension, or do-notation, or pattern guards),
3667 or a <literal>where</literal> clause.
3668 Note the following points:
3671 An implicit-parameter binding group must be a
3672 collection of simple bindings to implicit-style variables (no
3673 function-style bindings, and no type signatures); these bindings are
3674 neither polymorphic or recursive.
3677 You may not mix implicit-parameter bindings with ordinary bindings in a
3678 single <literal>let</literal>
3679 expression; use two nested <literal>let</literal>s instead.
3680 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3684 You may put multiple implicit-parameter bindings in a
3685 single binding group; but they are <emphasis>not</emphasis> treated
3686 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3687 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3688 parameter. The bindings are not nested, and may be re-ordered without changing
3689 the meaning of the program.
3690 For example, consider:
3692 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3694 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3695 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3697 f :: (?x::Int) => Int -> Int
3705 <sect3><title>Implicit parameters and polymorphic recursion</title>
3708 Consider these two definitions:
3711 len1 xs = let ?acc = 0 in len_acc1 xs
3714 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3719 len2 xs = let ?acc = 0 in len_acc2 xs
3721 len_acc2 :: (?acc :: Int) => [a] -> Int
3723 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3725 The only difference between the two groups is that in the second group
3726 <literal>len_acc</literal> is given a type signature.
3727 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3728 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3729 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3730 has a type signature, the recursive call is made to the
3731 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3732 as an implicit parameter. So we get the following results in GHCi:
3739 Adding a type signature dramatically changes the result! This is a rather
3740 counter-intuitive phenomenon, worth watching out for.
3744 <sect3><title>Implicit parameters and monomorphism</title>
3746 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3747 Haskell Report) to implicit parameters. For example, consider:
3755 Since the binding for <literal>y</literal> falls under the Monomorphism
3756 Restriction it is not generalised, so the type of <literal>y</literal> is
3757 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3758 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3759 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3760 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3761 <literal>y</literal> in the body of the <literal>let</literal> will see the
3762 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3763 <literal>14</literal>.
3768 <!-- ======================= COMMENTED OUT ========================
3770 We intend to remove linear implicit parameters, so I'm at least removing
3771 them from the 6.6 user manual
3773 <sect2 id="linear-implicit-parameters">
3774 <title>Linear implicit parameters</title>
3776 Linear implicit parameters are an idea developed by Koen Claessen,
3777 Mark Shields, and Simon PJ. They address the long-standing
3778 problem that monads seem over-kill for certain sorts of problem, notably:
3781 <listitem> <para> distributing a supply of unique names </para> </listitem>
3782 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3783 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3787 Linear implicit parameters are just like ordinary implicit parameters,
3788 except that they are "linear"; that is, they cannot be copied, and
3789 must be explicitly "split" instead. Linear implicit parameters are
3790 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3791 (The '/' in the '%' suggests the split!)
3796 import GHC.Exts( Splittable )
3798 data NameSupply = ...
3800 splitNS :: NameSupply -> (NameSupply, NameSupply)
3801 newName :: NameSupply -> Name
3803 instance Splittable NameSupply where
3807 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3808 f env (Lam x e) = Lam x' (f env e)
3811 env' = extend env x x'
3812 ...more equations for f...
3814 Notice that the implicit parameter %ns is consumed
3816 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3817 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3821 So the translation done by the type checker makes
3822 the parameter explicit:
3824 f :: NameSupply -> Env -> Expr -> Expr
3825 f ns env (Lam x e) = Lam x' (f ns1 env e)
3827 (ns1,ns2) = splitNS ns
3829 env = extend env x x'
3831 Notice the call to 'split' introduced by the type checker.
3832 How did it know to use 'splitNS'? Because what it really did
3833 was to introduce a call to the overloaded function 'split',
3834 defined by the class <literal>Splittable</literal>:
3836 class Splittable a where
3839 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3840 split for name supplies. But we can simply write
3846 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3848 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3849 <literal>GHC.Exts</literal>.
3854 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3855 are entirely distinct implicit parameters: you
3856 can use them together and they won't interfere with each other. </para>
3859 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3861 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3862 in the context of a class or instance declaration. </para></listitem>
3866 <sect3><title>Warnings</title>
3869 The monomorphism restriction is even more important than usual.
3870 Consider the example above:
3872 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3873 f env (Lam x e) = Lam x' (f env e)
3876 env' = extend env x x'
3878 If we replaced the two occurrences of x' by (newName %ns), which is
3879 usually a harmless thing to do, we get:
3881 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3882 f env (Lam x e) = Lam (newName %ns) (f env e)
3884 env' = extend env x (newName %ns)
3886 But now the name supply is consumed in <emphasis>three</emphasis> places
3887 (the two calls to newName,and the recursive call to f), so
3888 the result is utterly different. Urk! We don't even have
3892 Well, this is an experimental change. With implicit
3893 parameters we have already lost beta reduction anyway, and
3894 (as John Launchbury puts it) we can't sensibly reason about
3895 Haskell programs without knowing their typing.
3900 <sect3><title>Recursive functions</title>
3901 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3904 foo :: %x::T => Int -> [Int]
3906 foo n = %x : foo (n-1)
3908 where T is some type in class Splittable.</para>
3910 Do you get a list of all the same T's or all different T's
3911 (assuming that split gives two distinct T's back)?
3913 If you supply the type signature, taking advantage of polymorphic
3914 recursion, you get what you'd probably expect. Here's the
3915 translated term, where the implicit param is made explicit:
3918 foo x n = let (x1,x2) = split x
3919 in x1 : foo x2 (n-1)
3921 But if you don't supply a type signature, GHC uses the Hindley
3922 Milner trick of using a single monomorphic instance of the function
3923 for the recursive calls. That is what makes Hindley Milner type inference
3924 work. So the translation becomes
3928 foom n = x : foom (n-1)
3932 Result: 'x' is not split, and you get a list of identical T's. So the
3933 semantics of the program depends on whether or not foo has a type signature.
3936 You may say that this is a good reason to dislike linear implicit parameters
3937 and you'd be right. That is why they are an experimental feature.
3943 ================ END OF Linear Implicit Parameters commented out -->
3945 <sect2 id="kinding">
3946 <title>Explicitly-kinded quantification</title>
3949 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3950 to give the kind explicitly as (machine-checked) documentation,
3951 just as it is nice to give a type signature for a function. On some occasions,
3952 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3953 John Hughes had to define the data type:
3955 data Set cxt a = Set [a]
3956 | Unused (cxt a -> ())
3958 The only use for the <literal>Unused</literal> constructor was to force the correct
3959 kind for the type variable <literal>cxt</literal>.
3962 GHC now instead allows you to specify the kind of a type variable directly, wherever
3963 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
3966 This flag enables kind signatures in the following places:
3968 <listitem><para><literal>data</literal> declarations:
3970 data Set (cxt :: * -> *) a = Set [a]
3971 </screen></para></listitem>
3972 <listitem><para><literal>type</literal> declarations:
3974 type T (f :: * -> *) = f Int
3975 </screen></para></listitem>
3976 <listitem><para><literal>class</literal> declarations:
3978 class (Eq a) => C (f :: * -> *) a where ...
3979 </screen></para></listitem>
3980 <listitem><para><literal>forall</literal>'s in type signatures:
3982 f :: forall (cxt :: * -> *). Set cxt Int
3983 </screen></para></listitem>
3988 The parentheses are required. Some of the spaces are required too, to
3989 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3990 will get a parse error, because "<literal>::*->*</literal>" is a
3991 single lexeme in Haskell.
3995 As part of the same extension, you can put kind annotations in types
3998 f :: (Int :: *) -> Int
3999 g :: forall a. a -> (a :: *)
4003 atype ::= '(' ctype '::' kind ')
4005 The parentheses are required.
4010 <sect2 id="universal-quantification">
4011 <title>Arbitrary-rank polymorphism
4015 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4016 allows us to say exactly what this means. For example:
4024 g :: forall b. (b -> b)
4026 The two are treated identically.
4030 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4031 explicit universal quantification in
4033 For example, all the following types are legal:
4035 f1 :: forall a b. a -> b -> a
4036 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4038 f2 :: (forall a. a->a) -> Int -> Int
4039 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4041 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4043 f4 :: Int -> (forall a. a -> a)
4045 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4046 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4047 The <literal>forall</literal> makes explicit the universal quantification that
4048 is implicitly added by Haskell.
4051 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4052 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4053 shows, the polymorphic type on the left of the function arrow can be overloaded.
4056 The function <literal>f3</literal> has a rank-3 type;
4057 it has rank-2 types on the left of a function arrow.
4060 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
4061 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
4062 that restriction has now been lifted.)
4063 In particular, a forall-type (also called a "type scheme"),
4064 including an operational type class context, is legal:
4066 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4067 of a function arrow </para> </listitem>
4068 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4069 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4070 field type signatures.</para> </listitem>
4071 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4072 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4074 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4075 a type variable any more!
4084 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4085 the types of the constructor arguments. Here are several examples:
4091 data T a = T1 (forall b. b -> b -> b) a
4093 data MonadT m = MkMonad { return :: forall a. a -> m a,
4094 bind :: forall a b. m a -> (a -> m b) -> m b
4097 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4103 The constructors have rank-2 types:
4109 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4110 MkMonad :: forall m. (forall a. a -> m a)
4111 -> (forall a b. m a -> (a -> m b) -> m b)
4113 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4119 Notice that you don't need to use a <literal>forall</literal> if there's an
4120 explicit context. For example in the first argument of the
4121 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4122 prefixed to the argument type. The implicit <literal>forall</literal>
4123 quantifies all type variables that are not already in scope, and are
4124 mentioned in the type quantified over.
4128 As for type signatures, implicit quantification happens for non-overloaded
4129 types too. So if you write this:
4132 data T a = MkT (Either a b) (b -> b)
4135 it's just as if you had written this:
4138 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4141 That is, since the type variable <literal>b</literal> isn't in scope, it's
4142 implicitly universally quantified. (Arguably, it would be better
4143 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4144 where that is what is wanted. Feedback welcomed.)
4148 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4149 the constructor to suitable values, just as usual. For example,
4160 a3 = MkSwizzle reverse
4163 a4 = let r x = Just x
4170 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4171 mkTs f x y = [T1 f x, T1 f y]
4177 The type of the argument can, as usual, be more general than the type
4178 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4179 does not need the <literal>Ord</literal> constraint.)
4183 When you use pattern matching, the bound variables may now have
4184 polymorphic types. For example:
4190 f :: T a -> a -> (a, Char)
4191 f (T1 w k) x = (w k x, w 'c' 'd')
4193 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4194 g (MkSwizzle s) xs f = s (map f (s xs))
4196 h :: MonadT m -> [m a] -> m [a]
4197 h m [] = return m []
4198 h m (x:xs) = bind m x $ \y ->
4199 bind m (h m xs) $ \ys ->
4206 In the function <function>h</function> we use the record selectors <literal>return</literal>
4207 and <literal>bind</literal> to extract the polymorphic bind and return functions
4208 from the <literal>MonadT</literal> data structure, rather than using pattern
4214 <title>Type inference</title>
4217 In general, type inference for arbitrary-rank types is undecidable.
4218 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4219 to get a decidable algorithm by requiring some help from the programmer.
4220 We do not yet have a formal specification of "some help" but the rule is this:
4223 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4224 provides an explicit polymorphic type for x, or GHC's type inference will assume
4225 that x's type has no foralls in it</emphasis>.
4228 What does it mean to "provide" an explicit type for x? You can do that by
4229 giving a type signature for x directly, using a pattern type signature
4230 (<xref linkend="scoped-type-variables"/>), thus:
4232 \ f :: (forall a. a->a) -> (f True, f 'c')
4234 Alternatively, you can give a type signature to the enclosing
4235 context, which GHC can "push down" to find the type for the variable:
4237 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4239 Here the type signature on the expression can be pushed inwards
4240 to give a type signature for f. Similarly, and more commonly,
4241 one can give a type signature for the function itself:
4243 h :: (forall a. a->a) -> (Bool,Char)
4244 h f = (f True, f 'c')
4246 You don't need to give a type signature if the lambda bound variable
4247 is a constructor argument. Here is an example we saw earlier:
4249 f :: T a -> a -> (a, Char)
4250 f (T1 w k) x = (w k x, w 'c' 'd')
4252 Here we do not need to give a type signature to <literal>w</literal>, because
4253 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4260 <sect3 id="implicit-quant">
4261 <title>Implicit quantification</title>
4264 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4265 user-written types, if and only if there is no explicit <literal>forall</literal>,
4266 GHC finds all the type variables mentioned in the type that are not already
4267 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4271 f :: forall a. a -> a
4278 h :: forall b. a -> b -> b
4284 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4287 f :: (a -> a) -> Int
4289 f :: forall a. (a -> a) -> Int
4291 f :: (forall a. a -> a) -> Int
4294 g :: (Ord a => a -> a) -> Int
4295 -- MEANS the illegal type
4296 g :: forall a. (Ord a => a -> a) -> Int
4298 g :: (forall a. Ord a => a -> a) -> Int
4300 The latter produces an illegal type, which you might think is silly,
4301 but at least the rule is simple. If you want the latter type, you
4302 can write your for-alls explicitly. Indeed, doing so is strongly advised
4309 <sect2 id="impredicative-polymorphism">
4310 <title>Impredicative polymorphism
4312 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
4313 that you can call a polymorphic function at a polymorphic type, and
4314 parameterise data structures over polymorphic types. For example:
4316 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4317 f (Just g) = Just (g [3], g "hello")
4320 Notice here that the <literal>Maybe</literal> type is parameterised by the
4321 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4324 <para>The technical details of this extension are described in the paper
4325 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
4326 type inference for higher-rank types and impredicativity</ulink>,
4327 which appeared at ICFP 2006.
4331 <sect2 id="scoped-type-variables">
4332 <title>Lexically scoped type variables
4336 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4337 which some type signatures are simply impossible to write. For example:
4339 f :: forall a. [a] -> [a]
4345 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4346 the entire definition of <literal>f</literal>.
4347 In particular, it is in scope at the type signature for <varname>ys</varname>.
4348 In Haskell 98 it is not possible to declare
4349 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4350 it becomes possible to do so.
4352 <para>Lexically-scoped type variables are enabled by
4353 <option>-fglasgow-exts</option>.
4355 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4356 variables work, compared to earlier releases. Read this section
4360 <title>Overview</title>
4362 <para>The design follows the following principles
4364 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4365 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4366 design.)</para></listitem>
4367 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4368 type variables. This means that every programmer-written type signature
4369 (including one that contains free scoped type variables) denotes a
4370 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4371 checker, and no inference is involved.</para></listitem>
4372 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4373 changing the program.</para></listitem>
4377 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4379 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4380 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4381 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4382 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4386 In Haskell, a programmer-written type signature is implicitly quantified over
4387 its free type variables (<ulink
4388 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
4390 of the Haskel Report).
4391 Lexically scoped type variables affect this implicit quantification rules
4392 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4393 quantified. For example, if type variable <literal>a</literal> is in scope,
4396 (e :: a -> a) means (e :: a -> a)
4397 (e :: b -> b) means (e :: forall b. b->b)
4398 (e :: a -> b) means (e :: forall b. a->b)
4406 <sect3 id="decl-type-sigs">
4407 <title>Declaration type signatures</title>
4408 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4409 quantification (using <literal>forall</literal>) brings into scope the
4410 explicitly-quantified
4411 type variables, in the definition of the named function(s). For example:
4413 f :: forall a. [a] -> [a]
4414 f (x:xs) = xs ++ [ x :: a ]
4416 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4417 the definition of "<literal>f</literal>".
4419 <para>This only happens if the quantification in <literal>f</literal>'s type
4420 signature is explicit. For example:
4423 g (x:xs) = xs ++ [ x :: a ]
4425 This program will be rejected, because "<literal>a</literal>" does not scope
4426 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4427 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4428 quantification rules.
4432 <sect3 id="exp-type-sigs">
4433 <title>Expression type signatures</title>
4435 <para>An expression type signature that has <emphasis>explicit</emphasis>
4436 quantification (using <literal>forall</literal>) brings into scope the
4437 explicitly-quantified
4438 type variables, in the annotated expression. For example:
4440 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4442 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4443 type variable <literal>s</literal> into scope, in the annotated expression
4444 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4449 <sect3 id="pattern-type-sigs">
4450 <title>Pattern type signatures</title>
4452 A type signature may occur in any pattern; this is a <emphasis>pattern type
4453 signature</emphasis>.
4456 -- f and g assume that 'a' is already in scope
4457 f = \(x::Int, y::a) -> x
4459 h ((x,y) :: (Int,Bool)) = (y,x)
4461 In the case where all the type variables in the pattern type signature are
4462 already in scope (i.e. bound by the enclosing context), matters are simple: the
4463 signature simply constrains the type of the pattern in the obvious way.
4466 Unlike expression and declaration type signatures, pattern type signatures are not implictly generalised.
4467 The pattern in a <emphasis>patterm binding</emphasis> may only mention type variables
4468 that are already in scope. For example:
4470 f :: forall a. [a] -> (Int, [a])
4473 (ys::[a], n) = (reverse xs, length xs) -- OK
4474 zs::[a] = xs ++ ys -- OK
4476 Just (v::b) = ... -- Not OK; b is not in scope
4478 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4479 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4483 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4484 type signature may mention a type variable that is not in scope; in this case,
4485 <emphasis>the signature brings that type variable into scope</emphasis>.
4486 This is particularly important for existential data constructors. For example:
4488 data T = forall a. MkT [a]
4491 k (MkT [t::a]) = MkT t3
4495 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4496 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4497 because it is bound by the pattern match. GHC's rule is that in this situation
4498 (and only then), a pattern type signature can mention a type variable that is
4499 not already in scope; the effect is to bring it into scope, standing for the
4500 existentially-bound type variable.
4503 When a pattern type signature binds a type variable in this way, GHC insists that the
4504 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4505 This means that any user-written type signature always stands for a completely known type.
4508 If all this seems a little odd, we think so too. But we must have
4509 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4510 could not name existentially-bound type variables in subsequent type signatures.
4513 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4514 signature is allowed to mention a lexical variable that is not already in
4516 For example, both <literal>f</literal> and <literal>g</literal> would be
4517 illegal if <literal>a</literal> was not already in scope.
4523 <!-- ==================== Commented out part about result type signatures
4525 <sect3 id="result-type-sigs">
4526 <title>Result type signatures</title>
4529 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4532 {- f assumes that 'a' is already in scope -}
4533 f x y :: [a] = [x,y,x]
4535 g = \ x :: [Int] -> [3,4]
4537 h :: forall a. [a] -> a
4541 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4542 the result of the function. Similarly, the body of the lambda in the RHS of
4543 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4544 alternative in <literal>h</literal> is <literal>a</literal>.
4546 <para> A result type signature never brings new type variables into scope.</para>
4548 There are a couple of syntactic wrinkles. First, notice that all three
4549 examples would parse quite differently with parentheses:
4551 {- f assumes that 'a' is already in scope -}
4552 f x (y :: [a]) = [x,y,x]
4554 g = \ (x :: [Int]) -> [3,4]
4556 h :: forall a. [a] -> a
4560 Now the signature is on the <emphasis>pattern</emphasis>; and
4561 <literal>h</literal> would certainly be ill-typed (since the pattern
4562 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4564 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4565 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4566 token or a parenthesised type of some sort). To see why,
4567 consider how one would parse this:
4576 <sect3 id="cls-inst-scoped-tyvars">
4577 <title>Class and instance declarations</title>
4580 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4581 scope over the methods defined in the <literal>where</literal> part. For example:
4599 <sect2 id="typing-binds">
4600 <title>Generalised typing of mutually recursive bindings</title>
4603 The Haskell Report specifies that a group of bindings (at top level, or in a
4604 <literal>let</literal> or <literal>where</literal>) should be sorted into
4605 strongly-connected components, and then type-checked in dependency order
4606 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4607 Report, Section 4.5.1</ulink>).
4608 As each group is type-checked, any binders of the group that
4610 an explicit type signature are put in the type environment with the specified
4612 and all others are monomorphic until the group is generalised
4613 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4616 <para>Following a suggestion of Mark Jones, in his paper
4617 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4619 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4621 <emphasis>the dependency analysis ignores references to variables that have an explicit
4622 type signature</emphasis>.
4623 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4624 typecheck. For example, consider:
4626 f :: Eq a => a -> Bool
4627 f x = (x == x) || g True || g "Yes"
4629 g y = (y <= y) || f True
4631 This is rejected by Haskell 98, but under Jones's scheme the definition for
4632 <literal>g</literal> is typechecked first, separately from that for
4633 <literal>f</literal>,
4634 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4635 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4636 type is generalised, to get
4638 g :: Ord a => a -> Bool
4640 Now, the definition for <literal>f</literal> is typechecked, with this type for
4641 <literal>g</literal> in the type environment.
4645 The same refined dependency analysis also allows the type signatures of
4646 mutually-recursive functions to have different contexts, something that is illegal in
4647 Haskell 98 (Section 4.5.2, last sentence). With
4648 <option>-XRelaxedPolyRec</option>
4649 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4650 type signatures; in practice this means that only variables bound by the same
4651 pattern binding must have the same context. For example, this is fine:
4653 f :: Eq a => a -> Bool
4654 f x = (x == x) || g True
4656 g :: Ord a => a -> Bool
4657 g y = (y <= y) || f True
4662 <sect2 id="type-families">
4663 <title>Type families
4667 GHC supports the definition of type families indexed by types. They may be
4668 seen as an extension of Haskell 98's class-based overloading of values to
4669 types. When type families are declared in classes, they are also known as
4673 There are two forms of type families: data families and type synonym families.
4674 Currently, only the former are fully implemented, while we are still working
4675 on the latter. As a result, the specification of the language extension is
4676 also still to some degree in flux. Hence, a more detailed description of
4677 the language extension and its use is currently available
4678 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4679 wiki page on type families</ulink>. The material will be moved to this user's
4680 guide when it has stabilised.
4683 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4690 <!-- ==================== End of type system extensions ================= -->
4692 <!-- ====================== TEMPLATE HASKELL ======================= -->
4694 <sect1 id="template-haskell">
4695 <title>Template Haskell</title>
4697 <para>Template Haskell allows you to do compile-time meta-programming in
4700 the main technical innovations is discussed in "<ulink
4701 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4702 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4705 There is a Wiki page about
4706 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4707 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4711 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4712 Haskell library reference material</ulink>
4713 (look for module <literal>Language.Haskell.TH</literal>).
4714 Many changes to the original design are described in
4715 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4716 Notes on Template Haskell version 2</ulink>.
4717 Not all of these changes are in GHC, however.
4720 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4721 as a worked example to help get you started.
4725 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4726 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4731 <title>Syntax</title>
4733 <para> Template Haskell has the following new syntactic
4734 constructions. You need to use the flag
4735 <option>-XTemplateHaskell</option>
4736 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4737 </indexterm>to switch these syntactic extensions on
4738 (<option>-XTemplateHaskell</option> is no longer implied by
4739 <option>-fglasgow-exts</option>).</para>
4743 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4744 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4745 There must be no space between the "$" and the identifier or parenthesis. This use
4746 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4747 of "." as an infix operator. If you want the infix operator, put spaces around it.
4749 <para> A splice can occur in place of
4751 <listitem><para> an expression; the spliced expression must
4752 have type <literal>Q Exp</literal></para></listitem>
4753 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4756 Inside a splice you can can only call functions defined in imported modules,
4757 not functions defined elsewhere in the same module.</listitem>
4761 A expression quotation is written in Oxford brackets, thus:
4763 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4764 the quotation has type <literal>Q Exp</literal>.</para></listitem>
4765 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4766 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4767 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4768 the quotation has type <literal>Q Typ</literal>.</para></listitem>
4769 </itemizedlist></para></listitem>
4772 A name can be quoted with either one or two prefix single quotes:
4774 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
4775 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
4776 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
4778 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
4779 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
4782 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, delarations etc. They
4783 may also be given as an argument to the <literal>reify</literal> function.
4789 (Compared to the original paper, there are many differnces of detail.
4790 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
4791 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
4792 Type splices are not implemented, and neither are pattern splices or quotations.
4796 <sect2> <title> Using Template Haskell </title>
4800 The data types and monadic constructor functions for Template Haskell are in the library
4801 <literal>Language.Haskell.THSyntax</literal>.
4805 You can only run a function at compile time if it is imported from another module. That is,
4806 you can't define a function in a module, and call it from within a splice in the same module.
4807 (It would make sense to do so, but it's hard to implement.)
4811 Furthermore, you can only run a function at compile time if it is imported
4812 from another module <emphasis>that is not part of a mutually-recursive group of modules
4813 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4814 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4815 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4819 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4822 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4823 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4824 compiles and runs a program, and then looks at the result. So it's important that
4825 the program it compiles produces results whose representations are identical to
4826 those of the compiler itself.
4830 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4831 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4836 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
4837 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4838 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4845 -- Import our template "pr"
4846 import Printf ( pr )
4848 -- The splice operator $ takes the Haskell source code
4849 -- generated at compile time by "pr" and splices it into
4850 -- the argument of "putStrLn".
4851 main = putStrLn ( $(pr "Hello") )
4857 -- Skeletal printf from the paper.
4858 -- It needs to be in a separate module to the one where
4859 -- you intend to use it.
4861 -- Import some Template Haskell syntax
4862 import Language.Haskell.TH
4864 -- Describe a format string
4865 data Format = D | S | L String
4867 -- Parse a format string. This is left largely to you
4868 -- as we are here interested in building our first ever
4869 -- Template Haskell program and not in building printf.
4870 parse :: String -> [Format]
4873 -- Generate Haskell source code from a parsed representation
4874 -- of the format string. This code will be spliced into
4875 -- the module which calls "pr", at compile time.
4876 gen :: [Format] -> Q Exp
4877 gen [D] = [| \n -> show n |]
4878 gen [S] = [| \s -> s |]
4879 gen [L s] = stringE s
4881 -- Here we generate the Haskell code for the splice
4882 -- from an input format string.
4883 pr :: String -> Q Exp
4884 pr s = gen (parse s)
4887 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4890 $ ghc --make -XTemplateHaskell main.hs -o main.exe
4893 <para>Run "main.exe" and here is your output:</para>
4903 <title>Using Template Haskell with Profiling</title>
4904 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4906 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4907 interpreter to run the splice expressions. The bytecode interpreter
4908 runs the compiled expression on top of the same runtime on which GHC
4909 itself is running; this means that the compiled code referred to by
4910 the interpreted expression must be compatible with this runtime, and
4911 in particular this means that object code that is compiled for
4912 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4913 expression, because profiled object code is only compatible with the
4914 profiling version of the runtime.</para>
4916 <para>This causes difficulties if you have a multi-module program
4917 containing Template Haskell code and you need to compile it for
4918 profiling, because GHC cannot load the profiled object code and use it
4919 when executing the splices. Fortunately GHC provides a workaround.
4920 The basic idea is to compile the program twice:</para>
4924 <para>Compile the program or library first the normal way, without
4925 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4928 <para>Then compile it again with <option>-prof</option>, and
4929 additionally use <option>-osuf
4930 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4931 to name the object files differently (you can choose any suffix
4932 that isn't the normal object suffix here). GHC will automatically
4933 load the object files built in the first step when executing splice
4934 expressions. If you omit the <option>-osuf</option> flag when
4935 building with <option>-prof</option> and Template Haskell is used,
4936 GHC will emit an error message. </para>
4943 <!-- ===================== Arrow notation =================== -->
4945 <sect1 id="arrow-notation">
4946 <title>Arrow notation
4949 <para>Arrows are a generalization of monads introduced by John Hughes.
4950 For more details, see
4955 “Generalising Monads to Arrows”,
4956 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4957 pp67–111, May 2000.
4963 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4964 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4970 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4971 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4977 and the arrows web page at
4978 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4979 With the <option>-XArrows</option> flag, GHC supports the arrow
4980 notation described in the second of these papers.
4981 What follows is a brief introduction to the notation;
4982 it won't make much sense unless you've read Hughes's paper.
4983 This notation is translated to ordinary Haskell,
4984 using combinators from the
4985 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4989 <para>The extension adds a new kind of expression for defining arrows:
4991 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4992 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4994 where <literal>proc</literal> is a new keyword.
4995 The variables of the pattern are bound in the body of the
4996 <literal>proc</literal>-expression,
4997 which is a new sort of thing called a <firstterm>command</firstterm>.
4998 The syntax of commands is as follows:
5000 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5001 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5002 | <replaceable>cmd</replaceable><superscript>0</superscript>
5004 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5005 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5006 infix operators as for expressions, and
5008 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5009 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5010 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5011 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5012 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5013 | <replaceable>fcmd</replaceable>
5015 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5016 | ( <replaceable>cmd</replaceable> )
5017 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5019 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5020 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5021 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5022 | <replaceable>cmd</replaceable>
5024 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5025 except that the bodies are commands instead of expressions.
5029 Commands produce values, but (like monadic computations)
5030 may yield more than one value,
5031 or none, and may do other things as well.
5032 For the most part, familiarity with monadic notation is a good guide to
5034 However the values of expressions, even monadic ones,
5035 are determined by the values of the variables they contain;
5036 this is not necessarily the case for commands.
5040 A simple example of the new notation is the expression
5042 proc x -> f -< x+1
5044 We call this a <firstterm>procedure</firstterm> or
5045 <firstterm>arrow abstraction</firstterm>.
5046 As with a lambda expression, the variable <literal>x</literal>
5047 is a new variable bound within the <literal>proc</literal>-expression.
5048 It refers to the input to the arrow.
5049 In the above example, <literal>-<</literal> is not an identifier but an
5050 new reserved symbol used for building commands from an expression of arrow
5051 type and an expression to be fed as input to that arrow.
5052 (The weird look will make more sense later.)
5053 It may be read as analogue of application for arrows.
5054 The above example is equivalent to the Haskell expression
5056 arr (\ x -> x+1) >>> f
5058 That would make no sense if the expression to the left of
5059 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5060 More generally, the expression to the left of <literal>-<</literal>
5061 may not involve any <firstterm>local variable</firstterm>,
5062 i.e. a variable bound in the current arrow abstraction.
5063 For such a situation there is a variant <literal>-<<</literal>, as in
5065 proc x -> f x -<< x+1
5067 which is equivalent to
5069 arr (\ x -> (f x, x+1)) >>> app
5071 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5073 Such an arrow is equivalent to a monad, so if you're using this form
5074 you may find a monadic formulation more convenient.
5078 <title>do-notation for commands</title>
5081 Another form of command is a form of <literal>do</literal>-notation.
5082 For example, you can write
5091 You can read this much like ordinary <literal>do</literal>-notation,
5092 but with commands in place of monadic expressions.
5093 The first line sends the value of <literal>x+1</literal> as an input to
5094 the arrow <literal>f</literal>, and matches its output against
5095 <literal>y</literal>.
5096 In the next line, the output is discarded.
5097 The arrow <function>returnA</function> is defined in the
5098 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5099 module as <literal>arr id</literal>.
5100 The above example is treated as an abbreviation for
5102 arr (\ x -> (x, x)) >>>
5103 first (arr (\ x -> x+1) >>> f) >>>
5104 arr (\ (y, x) -> (y, (x, y))) >>>
5105 first (arr (\ y -> 2*y) >>> g) >>>
5107 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5108 first (arr (\ (x, z) -> x*z) >>> h) >>>
5109 arr (\ (t, z) -> t+z) >>>
5112 Note that variables not used later in the composition are projected out.
5113 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5115 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5116 module, this reduces to
5118 arr (\ x -> (x+1, x)) >>>
5120 arr (\ (y, x) -> (2*y, (x, y))) >>>
5122 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5124 arr (\ (t, z) -> t+z)
5126 which is what you might have written by hand.
5127 With arrow notation, GHC keeps track of all those tuples of variables for you.
5131 Note that although the above translation suggests that
5132 <literal>let</literal>-bound variables like <literal>z</literal> must be
5133 monomorphic, the actual translation produces Core,
5134 so polymorphic variables are allowed.
5138 It's also possible to have mutually recursive bindings,
5139 using the new <literal>rec</literal> keyword, as in the following example:
5141 counter :: ArrowCircuit a => a Bool Int
5142 counter = proc reset -> do
5143 rec output <- returnA -< if reset then 0 else next
5144 next <- delay 0 -< output+1
5145 returnA -< output
5147 The translation of such forms uses the <function>loop</function> combinator,
5148 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5154 <title>Conditional commands</title>
5157 In the previous example, we used a conditional expression to construct the
5159 Sometimes we want to conditionally execute different commands, as in
5166 which is translated to
5168 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5169 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5171 Since the translation uses <function>|||</function>,
5172 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5176 There are also <literal>case</literal> commands, like
5182 y <- h -< (x1, x2)
5186 The syntax is the same as for <literal>case</literal> expressions,
5187 except that the bodies of the alternatives are commands rather than expressions.
5188 The translation is similar to that of <literal>if</literal> commands.
5194 <title>Defining your own control structures</title>
5197 As we're seen, arrow notation provides constructs,
5198 modelled on those for expressions,
5199 for sequencing, value recursion and conditionals.
5200 But suitable combinators,
5201 which you can define in ordinary Haskell,
5202 may also be used to build new commands out of existing ones.
5203 The basic idea is that a command defines an arrow from environments to values.
5204 These environments assign values to the free local variables of the command.
5205 Thus combinators that produce arrows from arrows
5206 may also be used to build commands from commands.
5207 For example, the <literal>ArrowChoice</literal> class includes a combinator
5209 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5211 so we can use it to build commands:
5213 expr' = proc x -> do
5216 symbol Plus -< ()
5217 y <- term -< ()
5220 symbol Minus -< ()
5221 y <- term -< ()
5224 (The <literal>do</literal> on the first line is needed to prevent the first
5225 <literal><+> ...</literal> from being interpreted as part of the
5226 expression on the previous line.)
5227 This is equivalent to
5229 expr' = (proc x -> returnA -< x)
5230 <+> (proc x -> do
5231 symbol Plus -< ()
5232 y <- term -< ()
5234 <+> (proc x -> do
5235 symbol Minus -< ()
5236 y <- term -< ()
5239 It is essential that this operator be polymorphic in <literal>e</literal>
5240 (representing the environment input to the command
5241 and thence to its subcommands)
5242 and satisfy the corresponding naturality property
5244 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5246 at least for strict <literal>k</literal>.
5247 (This should be automatic if you're not using <function>seq</function>.)
5248 This ensures that environments seen by the subcommands are environments
5249 of the whole command,
5250 and also allows the translation to safely trim these environments.
5251 The operator must also not use any variable defined within the current
5256 We could define our own operator
5258 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5259 untilA body cond = proc x ->
5260 if cond x then returnA -< ()
5263 untilA body cond -< x
5265 and use it in the same way.
5266 Of course this infix syntax only makes sense for binary operators;
5267 there is also a more general syntax involving special brackets:
5271 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5278 <title>Primitive constructs</title>
5281 Some operators will need to pass additional inputs to their subcommands.
5282 For example, in an arrow type supporting exceptions,
5283 the operator that attaches an exception handler will wish to pass the
5284 exception that occurred to the handler.
5285 Such an operator might have a type
5287 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5289 where <literal>Ex</literal> is the type of exceptions handled.
5290 You could then use this with arrow notation by writing a command
5292 body `handleA` \ ex -> handler
5294 so that if an exception is raised in the command <literal>body</literal>,
5295 the variable <literal>ex</literal> is bound to the value of the exception
5296 and the command <literal>handler</literal>,
5297 which typically refers to <literal>ex</literal>, is entered.
5298 Though the syntax here looks like a functional lambda,
5299 we are talking about commands, and something different is going on.
5300 The input to the arrow represented by a command consists of values for
5301 the free local variables in the command, plus a stack of anonymous values.
5302 In all the prior examples, this stack was empty.
5303 In the second argument to <function>handleA</function>,
5304 this stack consists of one value, the value of the exception.
5305 The command form of lambda merely gives this value a name.
5310 the values on the stack are paired to the right of the environment.
5311 So operators like <function>handleA</function> that pass
5312 extra inputs to their subcommands can be designed for use with the notation
5313 by pairing the values with the environment in this way.
5314 More precisely, the type of each argument of the operator (and its result)
5315 should have the form
5317 a (...(e,t1), ... tn) t
5319 where <replaceable>e</replaceable> is a polymorphic variable
5320 (representing the environment)
5321 and <replaceable>ti</replaceable> are the types of the values on the stack,
5322 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5323 The polymorphic variable <replaceable>e</replaceable> must not occur in
5324 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5325 <replaceable>t</replaceable>.
5326 However the arrows involved need not be the same.
5327 Here are some more examples of suitable operators:
5329 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5330 runReader :: ... => a e c -> a' (e,State) c
5331 runState :: ... => a e c -> a' (e,State) (c,State)
5333 We can supply the extra input required by commands built with the last two
5334 by applying them to ordinary expressions, as in
5338 (|runReader (do { ... })|) s
5340 which adds <literal>s</literal> to the stack of inputs to the command
5341 built using <function>runReader</function>.
5345 The command versions of lambda abstraction and application are analogous to
5346 the expression versions.
5347 In particular, the beta and eta rules describe equivalences of commands.
5348 These three features (operators, lambda abstraction and application)
5349 are the core of the notation; everything else can be built using them,
5350 though the results would be somewhat clumsy.
5351 For example, we could simulate <literal>do</literal>-notation by defining
5353 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5354 u `bind` f = returnA &&& u >>> f
5356 bind_ :: Arrow a => a e b -> a e c -> a e c
5357 u `bind_` f = u `bind` (arr fst >>> f)
5359 We could simulate <literal>if</literal> by defining
5361 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5362 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5369 <title>Differences with the paper</title>
5374 <para>Instead of a single form of arrow application (arrow tail) with two
5375 translations, the implementation provides two forms
5376 <quote><literal>-<</literal></quote> (first-order)
5377 and <quote><literal>-<<</literal></quote> (higher-order).
5382 <para>User-defined operators are flagged with banana brackets instead of
5383 a new <literal>form</literal> keyword.
5392 <title>Portability</title>
5395 Although only GHC implements arrow notation directly,
5396 there is also a preprocessor
5398 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5399 that translates arrow notation into Haskell 98
5400 for use with other Haskell systems.
5401 You would still want to check arrow programs with GHC;
5402 tracing type errors in the preprocessor output is not easy.
5403 Modules intended for both GHC and the preprocessor must observe some
5404 additional restrictions:
5409 The module must import
5410 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5416 The preprocessor cannot cope with other Haskell extensions.
5417 These would have to go in separate modules.
5423 Because the preprocessor targets Haskell (rather than Core),
5424 <literal>let</literal>-bound variables are monomorphic.
5435 <!-- ==================== BANG PATTERNS ================= -->
5437 <sect1 id="bang-patterns">
5438 <title>Bang patterns
5439 <indexterm><primary>Bang patterns</primary></indexterm>
5441 <para>GHC supports an extension of pattern matching called <emphasis>bang
5442 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5444 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5445 prime feature description</ulink> contains more discussion and examples
5446 than the material below.
5449 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5452 <sect2 id="bang-patterns-informal">
5453 <title>Informal description of bang patterns
5456 The main idea is to add a single new production to the syntax of patterns:
5460 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5461 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5466 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5467 whereas without the bang it would be lazy.
5468 Bang patterns can be nested of course:
5472 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5473 <literal>y</literal>.
5474 A bang only really has an effect if it precedes a variable or wild-card pattern:
5479 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5480 forces evaluation anyway does nothing.
5482 Bang patterns work in <literal>case</literal> expressions too, of course:
5484 g5 x = let y = f x in body
5485 g6 x = case f x of { y -> body }
5486 g7 x = case f x of { !y -> body }
5488 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5489 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5490 result, and then evaluates <literal>body</literal>.
5492 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5493 definitions too. For example:
5497 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5498 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5499 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5500 in a function argument <literal>![x,y]</literal> means the
5501 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5502 is part of the syntax of <literal>let</literal> bindings.
5507 <sect2 id="bang-patterns-sem">
5508 <title>Syntax and semantics
5512 We add a single new production to the syntax of patterns:
5516 There is one problem with syntactic ambiguity. Consider:
5520 Is this a definition of the infix function "<literal>(!)</literal>",
5521 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5522 ambiguity in favour of the latter. If you want to define
5523 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5528 The semantics of Haskell pattern matching is described in <ulink
5529 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5530 Section 3.17.2</ulink> of the Haskell Report. To this description add
5531 one extra item 10, saying:
5532 <itemizedlist><listitem><para>Matching
5533 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5534 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5535 <listitem><para>otherwise, <literal>pat</literal> is matched against
5536 <literal>v</literal></para></listitem>
5538 </para></listitem></itemizedlist>
5539 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5540 Section 3.17.3</ulink>, add a new case (t):
5542 case v of { !pat -> e; _ -> e' }
5543 = v `seq` case v of { pat -> e; _ -> e' }
5546 That leaves let expressions, whose translation is given in
5547 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5549 of the Haskell Report.
5550 In the translation box, first apply
5551 the following transformation: for each pattern <literal>pi</literal> that is of
5552 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5553 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5554 have a bang at the top, apply the rules in the existing box.
5556 <para>The effect of the let rule is to force complete matching of the pattern
5557 <literal>qi</literal> before evaluation of the body is begun. The bang is
5558 retained in the translated form in case <literal>qi</literal> is a variable,
5566 The let-binding can be recursive. However, it is much more common for
5567 the let-binding to be non-recursive, in which case the following law holds:
5568 <literal>(let !p = rhs in body)</literal>
5570 <literal>(case rhs of !p -> body)</literal>
5573 A pattern with a bang at the outermost level is not allowed at the top level of
5579 <!-- ==================== ASSERTIONS ================= -->
5581 <sect1 id="assertions">
5583 <indexterm><primary>Assertions</primary></indexterm>
5587 If you want to make use of assertions in your standard Haskell code, you
5588 could define a function like the following:
5594 assert :: Bool -> a -> a
5595 assert False x = error "assertion failed!"
5602 which works, but gives you back a less than useful error message --
5603 an assertion failed, but which and where?
5607 One way out is to define an extended <function>assert</function> function which also
5608 takes a descriptive string to include in the error message and
5609 perhaps combine this with the use of a pre-processor which inserts
5610 the source location where <function>assert</function> was used.
5614 Ghc offers a helping hand here, doing all of this for you. For every
5615 use of <function>assert</function> in the user's source:
5621 kelvinToC :: Double -> Double
5622 kelvinToC k = assert (k >= 0.0) (k+273.15)
5628 Ghc will rewrite this to also include the source location where the
5635 assert pred val ==> assertError "Main.hs|15" pred val
5641 The rewrite is only performed by the compiler when it spots
5642 applications of <function>Control.Exception.assert</function>, so you
5643 can still define and use your own versions of
5644 <function>assert</function>, should you so wish. If not, import
5645 <literal>Control.Exception</literal> to make use
5646 <function>assert</function> in your code.
5650 GHC ignores assertions when optimisation is turned on with the
5651 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5652 <literal>assert pred e</literal> will be rewritten to
5653 <literal>e</literal>. You can also disable assertions using the
5654 <option>-fignore-asserts</option>
5655 option<indexterm><primary><option>-fignore-asserts</option></primary>
5656 </indexterm>.</para>
5659 Assertion failures can be caught, see the documentation for the
5660 <literal>Control.Exception</literal> library for the details.
5666 <!-- =============================== PRAGMAS =========================== -->
5668 <sect1 id="pragmas">
5669 <title>Pragmas</title>
5671 <indexterm><primary>pragma</primary></indexterm>
5673 <para>GHC supports several pragmas, or instructions to the
5674 compiler placed in the source code. Pragmas don't normally affect
5675 the meaning of the program, but they might affect the efficiency
5676 of the generated code.</para>
5678 <para>Pragmas all take the form
5680 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5682 where <replaceable>word</replaceable> indicates the type of
5683 pragma, and is followed optionally by information specific to that
5684 type of pragma. Case is ignored in
5685 <replaceable>word</replaceable>. The various values for
5686 <replaceable>word</replaceable> that GHC understands are described
5687 in the following sections; any pragma encountered with an
5688 unrecognised <replaceable>word</replaceable> is (silently)
5691 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
5692 pragma must precede the <literal>module</literal> keyword in the file.
5693 There can be as many file-header pragmas as you please, and they can be
5694 preceded or followed by comments.</para>
5696 <sect2 id="language-pragma">
5697 <title>LANGUAGE pragma</title>
5699 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5700 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5702 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
5704 It is the intention that all Haskell compilers support the
5705 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5706 all extensions are supported by all compilers, of
5707 course. The <literal>LANGUAGE</literal> pragma should be used instead
5708 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5710 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5712 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5714 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5716 <para>Every language extension can also be turned into a command-line flag
5717 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
5718 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
5721 <para>A list of all supported language extensions can be obtained by invoking
5722 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
5724 <para>Any extension from the <literal>Extension</literal> type defined in
5726 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
5727 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
5731 <sect2 id="options-pragma">
5732 <title>OPTIONS_GHC pragma</title>
5733 <indexterm><primary>OPTIONS_GHC</primary>
5735 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5738 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5739 additional options that are given to the compiler when compiling
5740 this source file. See <xref linkend="source-file-options"/> for
5743 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5744 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5747 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5749 <sect2 id="include-pragma">
5750 <title>INCLUDE pragma</title>
5752 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5753 of C header files that should be <literal>#include</literal>'d into
5754 the C source code generated by the compiler for the current module (if
5755 compiling via C). For example:</para>
5758 {-# INCLUDE "foo.h" #-}
5759 {-# INCLUDE <stdio.h> #-}</programlisting>
5761 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
5763 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5764 to the <option>-#include</option> option (<xref
5765 linkend="options-C-compiler" />), because the
5766 <literal>INCLUDE</literal> pragma is understood by other
5767 compilers. Yet another alternative is to add the include file to each
5768 <literal>foreign import</literal> declaration in your code, but we
5769 don't recommend using this approach with GHC.</para>
5772 <sect2 id="deprecated-pragma">
5773 <title>DEPRECATED pragma</title>
5774 <indexterm><primary>DEPRECATED</primary>
5777 <para>The DEPRECATED pragma lets you specify that a particular
5778 function, class, or type, is deprecated. There are two
5783 <para>You can deprecate an entire module thus:</para>
5785 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5788 <para>When you compile any module that import
5789 <literal>Wibble</literal>, GHC will print the specified
5794 <para>You can deprecate a function, class, type, or data constructor, with the
5795 following top-level declaration:</para>
5797 {-# DEPRECATED f, C, T "Don't use these" #-}
5799 <para>When you compile any module that imports and uses any
5800 of the specified entities, GHC will print the specified
5802 <para> You can only deprecate entities declared at top level in the module
5803 being compiled, and you can only use unqualified names in the list of
5804 entities being deprecated. A capitalised name, such as <literal>T</literal>
5805 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5806 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5807 both are in scope. If both are in scope, there is currently no way to deprecate
5808 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5811 Any use of the deprecated item, or of anything from a deprecated
5812 module, will be flagged with an appropriate message. However,
5813 deprecations are not reported for
5814 (a) uses of a deprecated function within its defining module, and
5815 (b) uses of a deprecated function in an export list.
5816 The latter reduces spurious complaints within a library
5817 in which one module gathers together and re-exports
5818 the exports of several others.
5820 <para>You can suppress the warnings with the flag
5821 <option>-fno-warn-deprecations</option>.</para>
5824 <sect2 id="inline-noinline-pragma">
5825 <title>INLINE and NOINLINE pragmas</title>
5827 <para>These pragmas control the inlining of function
5830 <sect3 id="inline-pragma">
5831 <title>INLINE pragma</title>
5832 <indexterm><primary>INLINE</primary></indexterm>
5834 <para>GHC (with <option>-O</option>, as always) tries to
5835 inline (or “unfold”) functions/values that are
5836 “small enough,” thus avoiding the call overhead
5837 and possibly exposing other more-wonderful optimisations.
5838 Normally, if GHC decides a function is “too
5839 expensive” to inline, it will not do so, nor will it
5840 export that unfolding for other modules to use.</para>
5842 <para>The sledgehammer you can bring to bear is the
5843 <literal>INLINE</literal><indexterm><primary>INLINE
5844 pragma</primary></indexterm> pragma, used thusly:</para>
5847 key_function :: Int -> String -> (Bool, Double)
5849 #ifdef __GLASGOW_HASKELL__
5850 {-# INLINE key_function #-}
5854 <para>(You don't need to do the C pre-processor carry-on
5855 unless you're going to stick the code through HBC—it
5856 doesn't like <literal>INLINE</literal> pragmas.)</para>
5858 <para>The major effect of an <literal>INLINE</literal> pragma
5859 is to declare a function's “cost” to be very low.
5860 The normal unfolding machinery will then be very keen to
5861 inline it. However, an <literal>INLINE</literal> pragma for a
5862 function "<literal>f</literal>" has a number of other effects:
5865 No funtions are inlined into <literal>f</literal>. Otherwise
5866 GHC might inline a big function into <literal>f</literal>'s right hand side,
5867 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
5870 The float-in, float-out, and common-sub-expression transformations are not
5871 applied to the body of <literal>f</literal>.
5874 An INLINE function is not worker/wrappered by strictness analysis.
5875 It's going to be inlined wholesale instead.
5878 All of these effects are aimed at ensuring that what gets inlined is
5879 exactly what you asked for, no more and no less.
5881 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5882 function can be put anywhere its type signature could be
5885 <para><literal>INLINE</literal> pragmas are a particularly
5887 <literal>then</literal>/<literal>return</literal> (or
5888 <literal>bind</literal>/<literal>unit</literal>) functions in
5889 a monad. For example, in GHC's own
5890 <literal>UniqueSupply</literal> monad code, we have:</para>
5893 #ifdef __GLASGOW_HASKELL__
5894 {-# INLINE thenUs #-}
5895 {-# INLINE returnUs #-}
5899 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5900 linkend="noinline-pragma"/>).</para>
5903 <sect3 id="noinline-pragma">
5904 <title>NOINLINE pragma</title>
5906 <indexterm><primary>NOINLINE</primary></indexterm>
5907 <indexterm><primary>NOTINLINE</primary></indexterm>
5909 <para>The <literal>NOINLINE</literal> pragma does exactly what
5910 you'd expect: it stops the named function from being inlined
5911 by the compiler. You shouldn't ever need to do this, unless
5912 you're very cautious about code size.</para>
5914 <para><literal>NOTINLINE</literal> is a synonym for
5915 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5916 specified by Haskell 98 as the standard way to disable
5917 inlining, so it should be used if you want your code to be
5921 <sect3 id="phase-control">
5922 <title>Phase control</title>
5924 <para> Sometimes you want to control exactly when in GHC's
5925 pipeline the INLINE pragma is switched on. Inlining happens
5926 only during runs of the <emphasis>simplifier</emphasis>. Each
5927 run of the simplifier has a different <emphasis>phase
5928 number</emphasis>; the phase number decreases towards zero.
5929 If you use <option>-dverbose-core2core</option> you'll see the
5930 sequence of phase numbers for successive runs of the
5931 simplifier. In an INLINE pragma you can optionally specify a
5935 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5936 <literal>f</literal>
5937 until phase <literal>k</literal>, but from phase
5938 <literal>k</literal> onwards be very keen to inline it.
5941 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5942 <literal>f</literal>
5943 until phase <literal>k</literal>, but from phase
5944 <literal>k</literal> onwards do not inline it.
5947 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5948 <literal>f</literal>
5949 until phase <literal>k</literal>, but from phase
5950 <literal>k</literal> onwards be willing to inline it (as if
5951 there was no pragma).
5954 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5955 <literal>f</literal>
5956 until phase <literal>k</literal>, but from phase
5957 <literal>k</literal> onwards do not inline it.
5960 The same information is summarised here:
5962 -- Before phase 2 Phase 2 and later
5963 {-# INLINE [2] f #-} -- No Yes
5964 {-# INLINE [~2] f #-} -- Yes No
5965 {-# NOINLINE [2] f #-} -- No Maybe
5966 {-# NOINLINE [~2] f #-} -- Maybe No
5968 {-# INLINE f #-} -- Yes Yes
5969 {-# NOINLINE f #-} -- No No
5971 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5972 function body is small, or it is applied to interesting-looking arguments etc).
5973 Another way to understand the semantics is this:
5975 <listitem><para>For both INLINE and NOINLINE, the phase number says
5976 when inlining is allowed at all.</para></listitem>
5977 <listitem><para>The INLINE pragma has the additional effect of making the
5978 function body look small, so that when inlining is allowed it is very likely to
5983 <para>The same phase-numbering control is available for RULES
5984 (<xref linkend="rewrite-rules"/>).</para>
5988 <sect2 id="line-pragma">
5989 <title>LINE pragma</title>
5991 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5992 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5993 <para>This pragma is similar to C's <literal>#line</literal>
5994 pragma, and is mainly for use in automatically generated Haskell
5995 code. It lets you specify the line number and filename of the
5996 original code; for example</para>
5998 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6000 <para>if you'd generated the current file from something called
6001 <filename>Foo.vhs</filename> and this line corresponds to line
6002 42 in the original. GHC will adjust its error messages to refer
6003 to the line/file named in the <literal>LINE</literal>
6008 <title>RULES pragma</title>
6010 <para>The RULES pragma lets you specify rewrite rules. It is
6011 described in <xref linkend="rewrite-rules"/>.</para>
6014 <sect2 id="specialize-pragma">
6015 <title>SPECIALIZE pragma</title>
6017 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6018 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6019 <indexterm><primary>overloading, death to</primary></indexterm>
6021 <para>(UK spelling also accepted.) For key overloaded
6022 functions, you can create extra versions (NB: more code space)
6023 specialised to particular types. Thus, if you have an
6024 overloaded function:</para>
6027 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6030 <para>If it is heavily used on lists with
6031 <literal>Widget</literal> keys, you could specialise it as
6035 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6038 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6039 be put anywhere its type signature could be put.</para>
6041 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6042 (a) a specialised version of the function and (b) a rewrite rule
6043 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6044 un-specialised function into a call to the specialised one.</para>
6046 <para>The type in a SPECIALIZE pragma can be any type that is less
6047 polymorphic than the type of the original function. In concrete terms,
6048 if the original function is <literal>f</literal> then the pragma
6050 {-# SPECIALIZE f :: <type> #-}
6052 is valid if and only if the definition
6054 f_spec :: <type>
6057 is valid. Here are some examples (where we only give the type signature
6058 for the original function, not its code):
6060 f :: Eq a => a -> b -> b
6061 {-# SPECIALISE f :: Int -> b -> b #-}
6063 g :: (Eq a, Ix b) => a -> b -> b
6064 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6066 h :: Eq a => a -> a -> a
6067 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6069 The last of these examples will generate a
6070 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6071 well. If you use this kind of specialisation, let us know how well it works.
6074 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6075 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6076 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6077 The <literal>INLINE</literal> pragma affects the specialised version of the
6078 function (only), and applies even if the function is recursive. The motivating
6081 -- A GADT for arrays with type-indexed representation
6083 ArrInt :: !Int -> ByteArray# -> Arr Int
6084 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6086 (!:) :: Arr e -> Int -> e
6087 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6088 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6089 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6090 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6092 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6093 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6094 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6095 the specialised function will be inlined. It has two calls to
6096 <literal>(!:)</literal>,
6097 both at type <literal>Int</literal>. Both these calls fire the first
6098 specialisation, whose body is also inlined. The result is a type-based
6099 unrolling of the indexing function.</para>
6100 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6101 on an ordinarily-recursive function.</para>
6103 <para>Note: In earlier versions of GHC, it was possible to provide your own
6104 specialised function for a given type:
6107 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6110 This feature has been removed, as it is now subsumed by the
6111 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6115 <sect2 id="specialize-instance-pragma">
6116 <title>SPECIALIZE instance pragma
6120 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6121 <indexterm><primary>overloading, death to</primary></indexterm>
6122 Same idea, except for instance declarations. For example:
6125 instance (Eq a) => Eq (Foo a) where {
6126 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6130 The pragma must occur inside the <literal>where</literal> part
6131 of the instance declaration.
6134 Compatible with HBC, by the way, except perhaps in the placement
6140 <sect2 id="unpack-pragma">
6141 <title>UNPACK pragma</title>
6143 <indexterm><primary>UNPACK</primary></indexterm>
6145 <para>The <literal>UNPACK</literal> indicates to the compiler
6146 that it should unpack the contents of a constructor field into
6147 the constructor itself, removing a level of indirection. For
6151 data T = T {-# UNPACK #-} !Float
6152 {-# UNPACK #-} !Float
6155 <para>will create a constructor <literal>T</literal> containing
6156 two unboxed floats. This may not always be an optimisation: if
6157 the <function>T</function> constructor is scrutinised and the
6158 floats passed to a non-strict function for example, they will
6159 have to be reboxed (this is done automatically by the
6162 <para>Unpacking constructor fields should only be used in
6163 conjunction with <option>-O</option>, in order to expose
6164 unfoldings to the compiler so the reboxing can be removed as
6165 often as possible. For example:</para>
6169 f (T f1 f2) = f1 + f2
6172 <para>The compiler will avoid reboxing <function>f1</function>
6173 and <function>f2</function> by inlining <function>+</function>
6174 on floats, but only when <option>-O</option> is on.</para>
6176 <para>Any single-constructor data is eligible for unpacking; for
6180 data T = T {-# UNPACK #-} !(Int,Int)
6183 <para>will store the two <literal>Int</literal>s directly in the
6184 <function>T</function> constructor, by flattening the pair.
6185 Multi-level unpacking is also supported:</para>
6188 data T = T {-# UNPACK #-} !S
6189 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6192 <para>will store two unboxed <literal>Int#</literal>s
6193 directly in the <function>T</function> constructor. The
6194 unpacker can see through newtypes, too.</para>
6196 <para>If a field cannot be unpacked, you will not get a warning,
6197 so it might be an idea to check the generated code with
6198 <option>-ddump-simpl</option>.</para>
6200 <para>See also the <option>-funbox-strict-fields</option> flag,
6201 which essentially has the effect of adding
6202 <literal>{-# UNPACK #-}</literal> to every strict
6203 constructor field.</para>
6208 <!-- ======================= REWRITE RULES ======================== -->
6210 <sect1 id="rewrite-rules">
6211 <title>Rewrite rules
6213 <indexterm><primary>RULES pragma</primary></indexterm>
6214 <indexterm><primary>pragma, RULES</primary></indexterm>
6215 <indexterm><primary>rewrite rules</primary></indexterm></title>
6218 The programmer can specify rewrite rules as part of the source program
6219 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
6220 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
6221 and (b) the <option>-frules-off</option> flag
6222 (<xref linkend="options-f"/>) is not specified, and (c) the
6223 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
6232 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6239 <title>Syntax</title>
6242 From a syntactic point of view:
6248 There may be zero or more rules in a <literal>RULES</literal> pragma.
6255 Each rule has a name, enclosed in double quotes. The name itself has
6256 no significance at all. It is only used when reporting how many times the rule fired.
6262 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6263 immediately after the name of the rule. Thus:
6266 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6269 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6270 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6279 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
6280 is set, so you must lay out your rules starting in the same column as the
6281 enclosing definitions.
6288 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6289 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6290 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6291 by spaces, just like in a type <literal>forall</literal>.
6297 A pattern variable may optionally have a type signature.
6298 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6299 For example, here is the <literal>foldr/build</literal> rule:
6302 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6303 foldr k z (build g) = g k z
6306 Since <function>g</function> has a polymorphic type, it must have a type signature.
6313 The left hand side of a rule must consist of a top-level variable applied
6314 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6317 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6318 "wrong2" forall f. f True = True
6321 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6328 A rule does not need to be in the same module as (any of) the
6329 variables it mentions, though of course they need to be in scope.
6335 Rules are automatically exported from a module, just as instance declarations are.
6346 <title>Semantics</title>
6349 From a semantic point of view:
6355 Rules are only applied if you use the <option>-O</option> flag.
6361 Rules are regarded as left-to-right rewrite rules.
6362 When GHC finds an expression that is a substitution instance of the LHS
6363 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6364 By "a substitution instance" we mean that the LHS can be made equal to the
6365 expression by substituting for the pattern variables.
6372 The LHS and RHS of a rule are typechecked, and must have the
6380 GHC makes absolutely no attempt to verify that the LHS and RHS
6381 of a rule have the same meaning. That is undecidable in general, and
6382 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6389 GHC makes no attempt to make sure that the rules are confluent or
6390 terminating. For example:
6393 "loop" forall x,y. f x y = f y x
6396 This rule will cause the compiler to go into an infinite loop.
6403 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6409 GHC currently uses a very simple, syntactic, matching algorithm
6410 for matching a rule LHS with an expression. It seeks a substitution
6411 which makes the LHS and expression syntactically equal modulo alpha
6412 conversion. The pattern (rule), but not the expression, is eta-expanded if
6413 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6414 But not beta conversion (that's called higher-order matching).
6418 Matching is carried out on GHC's intermediate language, which includes
6419 type abstractions and applications. So a rule only matches if the
6420 types match too. See <xref linkend="rule-spec"/> below.
6426 GHC keeps trying to apply the rules as it optimises the program.
6427 For example, consider:
6436 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6437 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6438 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6439 not be substituted, and the rule would not fire.
6446 In the earlier phases of compilation, GHC inlines <emphasis>nothing
6447 that appears on the LHS of a rule</emphasis>, because once you have substituted
6448 for something you can't match against it (given the simple minded
6449 matching). So if you write the rule
6452 "map/map" forall f,g. map f . map g = map (f.g)
6455 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
6456 It will only match something written with explicit use of ".".
6457 Well, not quite. It <emphasis>will</emphasis> match the expression
6463 where <function>wibble</function> is defined:
6466 wibble f g = map f . map g
6469 because <function>wibble</function> will be inlined (it's small).
6471 Later on in compilation, GHC starts inlining even things on the
6472 LHS of rules, but still leaves the rules enabled. This inlining
6473 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
6480 All rules are implicitly exported from the module, and are therefore
6481 in force in any module that imports the module that defined the rule, directly
6482 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6483 in force when compiling A.) The situation is very similar to that for instance
6495 <title>List fusion</title>
6498 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6499 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6500 intermediate list should be eliminated entirely.
6504 The following are good producers:
6516 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6522 Explicit lists (e.g. <literal>[True, False]</literal>)
6528 The cons constructor (e.g <literal>3:4:[]</literal>)
6534 <function>++</function>
6540 <function>map</function>
6546 <function>take</function>, <function>filter</function>
6552 <function>iterate</function>, <function>repeat</function>
6558 <function>zip</function>, <function>zipWith</function>
6567 The following are good consumers:
6579 <function>array</function> (on its second argument)
6585 <function>++</function> (on its first argument)
6591 <function>foldr</function>
6597 <function>map</function>
6603 <function>take</function>, <function>filter</function>
6609 <function>concat</function>
6615 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6621 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6622 will fuse with one but not the other)
6628 <function>partition</function>
6634 <function>head</function>
6640 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6646 <function>sequence_</function>
6652 <function>msum</function>
6658 <function>sortBy</function>
6667 So, for example, the following should generate no intermediate lists:
6670 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6676 This list could readily be extended; if there are Prelude functions that you use
6677 a lot which are not included, please tell us.
6681 If you want to write your own good consumers or producers, look at the
6682 Prelude definitions of the above functions to see how to do so.
6687 <sect2 id="rule-spec">
6688 <title>Specialisation
6692 Rewrite rules can be used to get the same effect as a feature
6693 present in earlier versions of GHC.
6694 For example, suppose that:
6697 genericLookup :: Ord a => Table a b -> a -> b
6698 intLookup :: Table Int b -> Int -> b
6701 where <function>intLookup</function> is an implementation of
6702 <function>genericLookup</function> that works very fast for
6703 keys of type <literal>Int</literal>. You might wish
6704 to tell GHC to use <function>intLookup</function> instead of
6705 <function>genericLookup</function> whenever the latter was called with
6706 type <literal>Table Int b -> Int -> b</literal>.
6707 It used to be possible to write
6710 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6713 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6716 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6719 This slightly odd-looking rule instructs GHC to replace
6720 <function>genericLookup</function> by <function>intLookup</function>
6721 <emphasis>whenever the types match</emphasis>.
6722 What is more, this rule does not need to be in the same
6723 file as <function>genericLookup</function>, unlike the
6724 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6725 have an original definition available to specialise).
6728 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6729 <function>intLookup</function> really behaves as a specialised version
6730 of <function>genericLookup</function>!!!</para>
6732 <para>An example in which using <literal>RULES</literal> for
6733 specialisation will Win Big:
6736 toDouble :: Real a => a -> Double
6737 toDouble = fromRational . toRational
6739 {-# RULES "toDouble/Int" toDouble = i2d #-}
6740 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6743 The <function>i2d</function> function is virtually one machine
6744 instruction; the default conversion—via an intermediate
6745 <literal>Rational</literal>—is obscenely expensive by
6752 <title>Controlling what's going on</title>
6760 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6766 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6767 If you add <option>-dppr-debug</option> you get a more detailed listing.
6773 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
6776 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6777 {-# INLINE build #-}
6781 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6782 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6783 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6784 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6791 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6792 see how to write rules that will do fusion and yet give an efficient
6793 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6803 <sect2 id="core-pragma">
6804 <title>CORE pragma</title>
6806 <indexterm><primary>CORE pragma</primary></indexterm>
6807 <indexterm><primary>pragma, CORE</primary></indexterm>
6808 <indexterm><primary>core, annotation</primary></indexterm>
6811 The external core format supports <quote>Note</quote> annotations;
6812 the <literal>CORE</literal> pragma gives a way to specify what these
6813 should be in your Haskell source code. Syntactically, core
6814 annotations are attached to expressions and take a Haskell string
6815 literal as an argument. The following function definition shows an
6819 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6822 Semantically, this is equivalent to:
6830 However, when external for is generated (via
6831 <option>-fext-core</option>), there will be Notes attached to the
6832 expressions <function>show</function> and <varname>x</varname>.
6833 The core function declaration for <function>f</function> is:
6837 f :: %forall a . GHCziShow.ZCTShow a ->
6838 a -> GHCziBase.ZMZN GHCziBase.Char =
6839 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6841 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6843 (tpl1::GHCziBase.Int ->
6845 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6847 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6848 (tpl3::GHCziBase.ZMZN a ->
6849 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6857 Here, we can see that the function <function>show</function> (which
6858 has been expanded out to a case expression over the Show dictionary)
6859 has a <literal>%note</literal> attached to it, as does the
6860 expression <varname>eta</varname> (which used to be called
6861 <varname>x</varname>).
6868 <sect1 id="special-ids">
6869 <title>Special built-in functions</title>
6870 <para>GHC has a few built-in functions with special behaviour. These
6871 are now described in the module <ulink
6872 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
6873 in the library documentation.</para>
6877 <sect1 id="generic-classes">
6878 <title>Generic classes</title>
6881 The ideas behind this extension are described in detail in "Derivable type classes",
6882 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6883 An example will give the idea:
6891 fromBin :: [Int] -> (a, [Int])
6893 toBin {| Unit |} Unit = []
6894 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6895 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6896 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6898 fromBin {| Unit |} bs = (Unit, bs)
6899 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6900 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6901 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6902 (y,bs'') = fromBin bs'
6905 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6906 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6907 which are defined thus in the library module <literal>Generics</literal>:
6911 data a :+: b = Inl a | Inr b
6912 data a :*: b = a :*: b
6915 Now you can make a data type into an instance of Bin like this:
6917 instance (Bin a, Bin b) => Bin (a,b)
6918 instance Bin a => Bin [a]
6920 That is, just leave off the "where" clause. Of course, you can put in the
6921 where clause and over-ride whichever methods you please.
6925 <title> Using generics </title>
6926 <para>To use generics you need to</para>
6929 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6930 <option>-XGenerics</option> (to generate extra per-data-type code),
6931 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6935 <para>Import the module <literal>Generics</literal> from the
6936 <literal>lang</literal> package. This import brings into
6937 scope the data types <literal>Unit</literal>,
6938 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6939 don't need this import if you don't mention these types
6940 explicitly; for example, if you are simply giving instance
6941 declarations.)</para>
6946 <sect2> <title> Changes wrt the paper </title>
6948 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6949 can be written infix (indeed, you can now use
6950 any operator starting in a colon as an infix type constructor). Also note that
6951 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6952 Finally, note that the syntax of the type patterns in the class declaration
6953 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6954 alone would ambiguous when they appear on right hand sides (an extension we
6955 anticipate wanting).
6959 <sect2> <title>Terminology and restrictions</title>
6961 Terminology. A "generic default method" in a class declaration
6962 is one that is defined using type patterns as above.
6963 A "polymorphic default method" is a default method defined as in Haskell 98.
6964 A "generic class declaration" is a class declaration with at least one
6965 generic default method.
6973 Alas, we do not yet implement the stuff about constructor names and
6980 A generic class can have only one parameter; you can't have a generic
6981 multi-parameter class.
6987 A default method must be defined entirely using type patterns, or entirely
6988 without. So this is illegal:
6991 op :: a -> (a, Bool)
6992 op {| Unit |} Unit = (Unit, True)
6995 However it is perfectly OK for some methods of a generic class to have
6996 generic default methods and others to have polymorphic default methods.
7002 The type variable(s) in the type pattern for a generic method declaration
7003 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:
7007 op {| p :*: q |} (x :*: y) = op (x :: p)
7015 The type patterns in a generic default method must take one of the forms:
7021 where "a" and "b" are type variables. Furthermore, all the type patterns for
7022 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7023 must use the same type variables. So this is illegal:
7027 op {| a :+: b |} (Inl x) = True
7028 op {| p :+: q |} (Inr y) = False
7030 The type patterns must be identical, even in equations for different methods of the class.
7031 So this too is illegal:
7035 op1 {| a :*: b |} (x :*: y) = True
7038 op2 {| p :*: q |} (x :*: y) = False
7040 (The reason for this restriction is that we gather all the equations for a particular type constructor
7041 into a single generic instance declaration.)
7047 A generic method declaration must give a case for each of the three type constructors.
7053 The type for a generic method can be built only from:
7055 <listitem> <para> Function arrows </para> </listitem>
7056 <listitem> <para> Type variables </para> </listitem>
7057 <listitem> <para> Tuples </para> </listitem>
7058 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7060 Here are some example type signatures for generic methods:
7063 op2 :: Bool -> (a,Bool)
7064 op3 :: [Int] -> a -> a
7067 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7071 This restriction is an implementation restriction: we just haven't got around to
7072 implementing the necessary bidirectional maps over arbitrary type constructors.
7073 It would be relatively easy to add specific type constructors, such as Maybe and list,
7074 to the ones that are allowed.</para>
7079 In an instance declaration for a generic class, the idea is that the compiler
7080 will fill in the methods for you, based on the generic templates. However it can only
7085 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7090 No constructor of the instance type has unboxed fields.
7094 (Of course, these things can only arise if you are already using GHC extensions.)
7095 However, you can still give an instance declarations for types which break these rules,
7096 provided you give explicit code to override any generic default methods.
7104 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7105 what the compiler does with generic declarations.
7110 <sect2> <title> Another example </title>
7112 Just to finish with, here's another example I rather like:
7116 nCons {| Unit |} _ = 1
7117 nCons {| a :*: b |} _ = 1
7118 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7121 tag {| Unit |} _ = 1
7122 tag {| a :*: b |} _ = 1
7123 tag {| a :+: b |} (Inl x) = tag x
7124 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7130 <sect1 id="monomorphism">
7131 <title>Control over monomorphism</title>
7133 <para>GHC supports two flags that control the way in which generalisation is
7134 carried out at let and where bindings.
7138 <title>Switching off the dreaded Monomorphism Restriction</title>
7139 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7141 <para>Haskell's monomorphism restriction (see
7142 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
7144 of the Haskell Report)
7145 can be completely switched off by
7146 <option>-XNoMonomorphismRestriction</option>.
7151 <title>Monomorphic pattern bindings</title>
7152 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7153 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7155 <para> As an experimental change, we are exploring the possibility of
7156 making pattern bindings monomorphic; that is, not generalised at all.
7157 A pattern binding is a binding whose LHS has no function arguments,
7158 and is not a simple variable. For example:
7160 f x = x -- Not a pattern binding
7161 f = \x -> x -- Not a pattern binding
7162 f :: Int -> Int = \x -> x -- Not a pattern binding
7164 (g,h) = e -- A pattern binding
7165 (f) = e -- A pattern binding
7166 [x] = e -- A pattern binding
7168 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7169 default</emphasis>. Use <option>-XMonoPatBinds</option> to recover the
7178 ;;; Local Variables: ***
7180 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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