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>The flag <option>-fglasgow-exts</option>
56 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
57 is equivalent to enabling the following extensions:
58 <option>-XPrintExplicitForalls</option>,
59 <option>-XForeignFunctionInterface</option>,
60 <option>-XUnliftedFFITypes</option>,
61 <option>-XGADTs</option>,
62 <option>-XImplicitParams</option>,
63 <option>-XScopedTypeVariables</option>,
64 <option>-XUnboxedTuples</option>,
65 <option>-XTypeSynonymInstances</option>,
66 <option>-XStandaloneDeriving</option>,
67 <option>-XDeriveDataTypeable</option>,
68 <option>-XFlexibleContexts</option>,
69 <option>-XFlexibleInstances</option>,
70 <option>-XConstrainedClassMethods</option>,
71 <option>-XMultiParamTypeClasses</option>,
72 <option>-XFunctionalDependencies</option>,
73 <option>-XMagicHash</option>,
74 <option>-XPolymorphicComponents</option>,
75 <option>-XExistentialQuantification</option>,
76 <option>-XUnicodeSyntax</option>,
77 <option>-XPostfixOperators</option>,
78 <option>-XPatternGuards</option>,
79 <option>-XLiberalTypeSynonyms</option>,
80 <option>-XRankNTypes</option>,
81 <option>-XImpredicativeTypes</option>,
82 <option>-XTypeOperators</option>,
83 <option>-XRecursiveDo</option>,
84 <option>-XParallelListComp</option>,
85 <option>-XEmptyDataDecls</option>,
86 <option>-XKindSignatures</option>,
87 <option>-XGeneralizedNewtypeDeriving</option>,
88 <option>-XTypeFamilies</option>.
89 Enabling these options is the <emphasis>only</emphasis>
90 effect of <option>-fglasgow-exts</option>.
91 We are trying to move away from this portmanteau flag,
92 and towards enabling features individually.</para>
96 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
97 <sect1 id="primitives">
98 <title>Unboxed types and primitive operations</title>
100 <para>GHC is built on a raft of primitive data types and operations;
101 "primitive" in the sense that they cannot be defined in Haskell itself.
102 While you really can use this stuff to write fast code,
103 we generally find it a lot less painful, and more satisfying in the
104 long run, to use higher-level language features and libraries. With
105 any luck, the code you write will be optimised to the efficient
106 unboxed version in any case. And if it isn't, we'd like to know
109 <para>All these primitive data types and operations are exported by the
110 library <literal>GHC.Prim</literal>, for which there is
111 <ulink url="../libraries/base/GHC.Prim.html">detailed online documentation</ulink>.
112 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
115 If you want to mention any of the primitive data types or operations in your
116 program, you must first import <literal>GHC.Prim</literal> to bring them
117 into scope. Many of them have names ending in "#", and to mention such
118 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
121 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
122 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
123 we briefly summarise here. </para>
125 <sect2 id="glasgow-unboxed">
130 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
133 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
134 that values of that type are represented by a pointer to a heap
135 object. The representation of a Haskell <literal>Int</literal>, for
136 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
137 type, however, is represented by the value itself, no pointers or heap
138 allocation are involved.
142 Unboxed types correspond to the “raw machine” types you
143 would use in C: <literal>Int#</literal> (long int),
144 <literal>Double#</literal> (double), <literal>Addr#</literal>
145 (void *), etc. The <emphasis>primitive operations</emphasis>
146 (PrimOps) on these types are what you might expect; e.g.,
147 <literal>(+#)</literal> is addition on
148 <literal>Int#</literal>s, and is the machine-addition that we all
149 know and love—usually one instruction.
153 Primitive (unboxed) types cannot be defined in Haskell, and are
154 therefore built into the language and compiler. Primitive types are
155 always unlifted; that is, a value of a primitive type cannot be
156 bottom. We use the convention (but it is only a convention)
157 that primitive types, values, and
158 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
159 For some primitive types we have special syntax for literals, also
160 described in the <link linkend="magic-hash">same section</link>.
164 Primitive values are often represented by a simple bit-pattern, such
165 as <literal>Int#</literal>, <literal>Float#</literal>,
166 <literal>Double#</literal>. But this is not necessarily the case:
167 a primitive value might be represented by a pointer to a
168 heap-allocated object. Examples include
169 <literal>Array#</literal>, the type of primitive arrays. A
170 primitive array is heap-allocated because it is too big a value to fit
171 in a register, and would be too expensive to copy around; in a sense,
172 it is accidental that it is represented by a pointer. If a pointer
173 represents a primitive value, then it really does point to that value:
174 no unevaluated thunks, no indirections…nothing can be at the
175 other end of the pointer than the primitive value.
176 A numerically-intensive program using unboxed types can
177 go a <emphasis>lot</emphasis> faster than its “standard”
178 counterpart—we saw a threefold speedup on one example.
182 There are some restrictions on the use of primitive types:
184 <listitem><para>The main restriction
185 is that you can't pass a primitive value to a polymorphic
186 function or store one in a polymorphic data type. This rules out
187 things like <literal>[Int#]</literal> (i.e. lists of primitive
188 integers). The reason for this restriction is that polymorphic
189 arguments and constructor fields are assumed to be pointers: if an
190 unboxed integer is stored in one of these, the garbage collector would
191 attempt to follow it, leading to unpredictable space leaks. Or a
192 <function>seq</function> operation on the polymorphic component may
193 attempt to dereference the pointer, with disastrous results. Even
194 worse, the unboxed value might be larger than a pointer
195 (<literal>Double#</literal> for instance).
198 <listitem><para> You cannot define a newtype whose representation type
199 (the argument type of the data constructor) is an unboxed type. Thus,
205 <listitem><para> You cannot bind a variable with an unboxed type
206 in a <emphasis>top-level</emphasis> binding.
208 <listitem><para> You cannot bind a variable with an unboxed type
209 in a <emphasis>recursive</emphasis> binding.
211 <listitem><para> You may bind unboxed variables in a (non-recursive,
212 non-top-level) pattern binding, but any such variable causes the entire
214 to become strict. For example:
216 data Foo = Foo Int Int#
218 f x = let (Foo a b, w) = ..rhs.. in ..body..
220 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
222 is strict, and the program behaves as if you had written
224 data Foo = Foo Int Int#
226 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
235 <sect2 id="unboxed-tuples">
236 <title>Unboxed Tuples
240 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
241 they're available by default with <option>-fglasgow-exts</option>. An
242 unboxed tuple looks like this:
254 where <literal>e_1..e_n</literal> are expressions of any
255 type (primitive or non-primitive). The type of an unboxed tuple looks
260 Unboxed tuples are used for functions that need to return multiple
261 values, but they avoid the heap allocation normally associated with
262 using fully-fledged tuples. When an unboxed tuple is returned, the
263 components are put directly into registers or on the stack; the
264 unboxed tuple itself does not have a composite representation. Many
265 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
267 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
268 tuples to avoid unnecessary allocation during sequences of operations.
272 There are some pretty stringent restrictions on the use of unboxed tuples:
277 Values of unboxed tuple types are subject to the same restrictions as
278 other unboxed types; i.e. they may not be stored in polymorphic data
279 structures or passed to polymorphic functions.
286 No variable can have an unboxed tuple type, nor may a constructor or function
287 argument have an unboxed tuple type. The following are all illegal:
291 data Foo = Foo (# Int, Int #)
293 f :: (# Int, Int #) -> (# Int, Int #)
296 g :: (# Int, Int #) -> Int
299 h x = let y = (# x,x #) in ...
306 The typical use of unboxed tuples is simply to return multiple values,
307 binding those multiple results with a <literal>case</literal> expression, thus:
309 f x y = (# x+1, y-1 #)
310 g x = case f x x of { (# a, b #) -> a + b }
312 You can have an unboxed tuple in a pattern binding, thus
314 f x = let (# p,q #) = h x in ..body..
316 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
317 the resulting binding is lazy like any other Haskell pattern binding. The
318 above example desugars like this:
320 f x = let t = case h x o f{ (# p,q #) -> (p,q)
325 Indeed, the bindings can even be recursive.
332 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
334 <sect1 id="syntax-extns">
335 <title>Syntactic extensions</title>
337 <sect2 id="magic-hash">
338 <title>The magic hash</title>
339 <para>The language extension <option>-XMagicHash</option> allows "#" as a
340 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
341 a valid type constructor or data constructor.</para>
343 <para>The hash sign does not change sematics at all. We tend to use variable
344 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
345 but there is no requirement to do so; they are just plain ordinary variables.
346 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
347 For example, to bring <literal>Int#</literal> into scope you must
348 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
349 the <option>-XMagicHash</option> extension
350 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
351 that is now in scope.</para>
352 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
354 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
355 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
356 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
357 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
358 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
359 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
360 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
361 is a <literal>Word#</literal>. </para> </listitem>
362 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
363 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
368 <sect2 id="new-qualified-operators">
369 <title>New qualified operator syntax</title>
371 <para>A new syntax for referencing qualified operators is
372 planned to be introduced by Haskell', and is enabled in GHC
374 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
375 option. In the new syntax, the prefix form of a qualified
377 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
378 (in Haskell 98 this would
379 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
380 and the infix form is
381 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
382 (in Haskell 98 this would
383 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
386 add x y = Prelude.(+) x y
387 subtract y = (`Prelude.(-)` y)
389 The new form of qualified operators is intended to regularise
390 the syntax by eliminating odd cases
391 like <literal>Prelude..</literal>. For example,
392 when <literal>NewQualifiedOperators</literal> is on, it is possible to
393 write the enerated sequence <literal>[Monday..]</literal>
394 without spaces, whereas in Haskell 98 this would be a
395 reference to the operator ‘<literal>.</literal>‘
396 from module <literal>Monday</literal>.</para>
398 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
399 98 syntax for qualified operators is not accepted, so this
400 option may cause existing Haskell 98 code to break.</para>
405 <!-- ====================== HIERARCHICAL MODULES ======================= -->
408 <sect2 id="hierarchical-modules">
409 <title>Hierarchical Modules</title>
411 <para>GHC supports a small extension to the syntax of module
412 names: a module name is allowed to contain a dot
413 <literal>‘.’</literal>. This is also known as the
414 “hierarchical module namespace” extension, because
415 it extends the normally flat Haskell module namespace into a
416 more flexible hierarchy of modules.</para>
418 <para>This extension has very little impact on the language
419 itself; modules names are <emphasis>always</emphasis> fully
420 qualified, so you can just think of the fully qualified module
421 name as <quote>the module name</quote>. In particular, this
422 means that the full module name must be given after the
423 <literal>module</literal> keyword at the beginning of the
424 module; for example, the module <literal>A.B.C</literal> must
427 <programlisting>module A.B.C</programlisting>
430 <para>It is a common strategy to use the <literal>as</literal>
431 keyword to save some typing when using qualified names with
432 hierarchical modules. For example:</para>
435 import qualified Control.Monad.ST.Strict as ST
438 <para>For details on how GHC searches for source and interface
439 files in the presence of hierarchical modules, see <xref
440 linkend="search-path"/>.</para>
442 <para>GHC comes with a large collection of libraries arranged
443 hierarchically; see the accompanying <ulink
444 url="../libraries/index.html">library
445 documentation</ulink>. More libraries to install are available
447 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
450 <!-- ====================== PATTERN GUARDS ======================= -->
452 <sect2 id="pattern-guards">
453 <title>Pattern guards</title>
456 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
457 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.)
461 Suppose we have an abstract data type of finite maps, with a
465 lookup :: FiniteMap -> Int -> Maybe Int
468 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
469 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
473 clunky env var1 var2 | ok1 && ok2 = val1 + val2
474 | otherwise = var1 + var2
485 The auxiliary functions are
489 maybeToBool :: Maybe a -> Bool
490 maybeToBool (Just x) = True
491 maybeToBool Nothing = False
493 expectJust :: Maybe a -> a
494 expectJust (Just x) = x
495 expectJust Nothing = error "Unexpected Nothing"
499 What is <function>clunky</function> doing? The guard <literal>ok1 &&
500 ok2</literal> checks that both lookups succeed, using
501 <function>maybeToBool</function> to convert the <function>Maybe</function>
502 types to booleans. The (lazily evaluated) <function>expectJust</function>
503 calls extract the values from the results of the lookups, and binds the
504 returned values to <varname>val1</varname> and <varname>val2</varname>
505 respectively. If either lookup fails, then clunky takes the
506 <literal>otherwise</literal> case and returns the sum of its arguments.
510 This is certainly legal Haskell, but it is a tremendously verbose and
511 un-obvious way to achieve the desired effect. Arguably, a more direct way
512 to write clunky would be to use case expressions:
516 clunky env var1 var2 = case lookup env var1 of
518 Just val1 -> case lookup env var2 of
520 Just val2 -> val1 + val2
526 This is a bit shorter, but hardly better. Of course, we can rewrite any set
527 of pattern-matching, guarded equations as case expressions; that is
528 precisely what the compiler does when compiling equations! The reason that
529 Haskell provides guarded equations is because they allow us to write down
530 the cases we want to consider, one at a time, independently of each other.
531 This structure is hidden in the case version. Two of the right-hand sides
532 are really the same (<function>fail</function>), and the whole expression
533 tends to become more and more indented.
537 Here is how I would write clunky:
542 | Just val1 <- lookup env var1
543 , Just val2 <- lookup env var2
545 ...other equations for clunky...
549 The semantics should be clear enough. The qualifiers are matched in order.
550 For a <literal><-</literal> qualifier, which I call a pattern guard, the
551 right hand side is evaluated and matched against the pattern on the left.
552 If the match fails then the whole guard fails and the next equation is
553 tried. If it succeeds, then the appropriate binding takes place, and the
554 next qualifier is matched, in the augmented environment. Unlike list
555 comprehensions, however, the type of the expression to the right of the
556 <literal><-</literal> is the same as the type of the pattern to its
557 left. The bindings introduced by pattern guards scope over all the
558 remaining guard qualifiers, and over the right hand side of the equation.
562 Just as with list comprehensions, boolean expressions can be freely mixed
563 with among the pattern guards. For example:
574 Haskell's current guards therefore emerge as a special case, in which the
575 qualifier list has just one element, a boolean expression.
579 <!-- ===================== View patterns =================== -->
581 <sect2 id="view-patterns">
586 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
587 More information and examples of view patterns can be found on the
588 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
593 View patterns are somewhat like pattern guards that can be nested inside
594 of other patterns. They are a convenient way of pattern-matching
595 against values of abstract types. For example, in a programming language
596 implementation, we might represent the syntax of the types of the
605 view :: Type -> TypeView
607 -- additional operations for constructing Typ's ...
610 The representation of Typ is held abstract, permitting implementations
611 to use a fancy representation (e.g., hash-consing to manage sharing).
613 Without view patterns, using this signature a little inconvenient:
615 size :: Typ -> Integer
616 size t = case view t of
618 Arrow t1 t2 -> size t1 + size t2
621 It is necessary to iterate the case, rather than using an equational
622 function definition. And the situation is even worse when the matching
623 against <literal>t</literal> is buried deep inside another pattern.
627 View patterns permit calling the view function inside the pattern and
628 matching against the result:
630 size (view -> Unit) = 1
631 size (view -> Arrow t1 t2) = size t1 + size t2
634 That is, we add a new form of pattern, written
635 <replaceable>expression</replaceable> <literal>-></literal>
636 <replaceable>pattern</replaceable> that means "apply the expression to
637 whatever we're trying to match against, and then match the result of
638 that application against the pattern". The expression can be any Haskell
639 expression of function type, and view patterns can be used wherever
644 The semantics of a pattern <literal>(</literal>
645 <replaceable>exp</replaceable> <literal>-></literal>
646 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
652 <para>The variables bound by the view pattern are the variables bound by
653 <replaceable>pat</replaceable>.
657 Any variables in <replaceable>exp</replaceable> are bound occurrences,
658 but variables bound "to the left" in a pattern are in scope. This
659 feature permits, for example, one argument to a function to be used in
660 the view of another argument. For example, the function
661 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
662 written using view patterns as follows:
665 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
666 ...other equations for clunky...
671 More precisely, the scoping rules are:
675 In a single pattern, variables bound by patterns to the left of a view
676 pattern expression are in scope. For example:
678 example :: Maybe ((String -> Integer,Integer), String) -> Bool
679 example Just ((f,_), f -> 4) = True
682 Additionally, in function definitions, variables bound by matching earlier curried
683 arguments may be used in view pattern expressions in later arguments:
685 example :: (String -> Integer) -> String -> Bool
686 example f (f -> 4) = True
688 That is, the scoping is the same as it would be if the curried arguments
689 were collected into a tuple.
695 In mutually recursive bindings, such as <literal>let</literal>,
696 <literal>where</literal>, or the top level, view patterns in one
697 declaration may not mention variables bound by other declarations. That
698 is, each declaration must be self-contained. For example, the following
699 program is not allowed:
706 restriction in the future; the only cost is that type checking patterns
707 would get a little more complicated.)
717 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
718 <replaceable>T1</replaceable> <literal>-></literal>
719 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
720 a <replaceable>T2</replaceable>, then the whole view pattern matches a
721 <replaceable>T1</replaceable>.
724 <listitem><para> Matching: To the equations in Section 3.17.3 of the
725 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
726 Report</ulink>, add the following:
728 case v of { (e -> p) -> e1 ; _ -> e2 }
730 case (e v) of { p -> e1 ; _ -> e2 }
732 That is, to match a variable <replaceable>v</replaceable> against a pattern
733 <literal>(</literal> <replaceable>exp</replaceable>
734 <literal>-></literal> <replaceable>pat</replaceable>
735 <literal>)</literal>, evaluate <literal>(</literal>
736 <replaceable>exp</replaceable> <replaceable> v</replaceable>
737 <literal>)</literal> and match the result against
738 <replaceable>pat</replaceable>.
741 <listitem><para> Efficiency: When the same view function is applied in
742 multiple branches of a function definition or a case expression (e.g.,
743 in <literal>size</literal> above), GHC makes an attempt to collect these
744 applications into a single nested case expression, so that the view
745 function is only applied once. Pattern compilation in GHC follows the
746 matrix algorithm described in Chapter 4 of <ulink
747 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
748 Implementation of Functional Programming Languages</ulink>. When the
749 top rows of the first column of a matrix are all view patterns with the
750 "same" expression, these patterns are transformed into a single nested
751 case. This includes, for example, adjacent view patterns that line up
754 f ((view -> A, p1), p2) = e1
755 f ((view -> B, p3), p4) = e2
759 <para> The current notion of when two view pattern expressions are "the
760 same" is very restricted: it is not even full syntactic equality.
761 However, it does include variables, literals, applications, and tuples;
762 e.g., two instances of <literal>view ("hi", "there")</literal> will be
763 collected. However, the current implementation does not compare up to
764 alpha-equivalence, so two instances of <literal>(x, view x ->
765 y)</literal> will not be coalesced.
775 <!-- ===================== Recursive do-notation =================== -->
777 <sect2 id="mdo-notation">
778 <title>The recursive do-notation
781 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
782 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
783 by Levent Erkok, John Launchbury,
784 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
785 This paper is essential reading for anyone making non-trivial use of mdo-notation,
786 and we do not repeat it here.
789 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
790 that is, the variables bound in a do-expression are visible only in the textually following
791 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
792 group. It turns out that several applications can benefit from recursive bindings in
793 the do-notation, and this extension provides the necessary syntactic support.
796 Here is a simple (yet contrived) example:
799 import Control.Monad.Fix
801 justOnes = mdo xs <- Just (1:xs)
805 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
809 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
812 class Monad m => MonadFix m where
813 mfix :: (a -> m a) -> m a
816 The function <literal>mfix</literal>
817 dictates how the required recursion operation should be performed. For example,
818 <literal>justOnes</literal> desugars as follows:
820 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
822 For full details of the way in which mdo is typechecked and desugared, see
823 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
824 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
827 If recursive bindings are required for a monad,
828 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
829 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
830 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
831 for Haskell's internal state monad (strict and lazy, respectively).
834 Here are some important points in using the recursive-do notation:
837 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
838 than <literal>do</literal>).
842 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
843 <literal>-fglasgow-exts</literal>.
847 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
848 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
849 be distinct (Section 3.3 of the paper).
853 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
854 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
855 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
856 and improve termination (Section 3.2 of the paper).
862 Historical note: The old implementation of the mdo-notation (and most
863 of the existing documents) used the name
864 <literal>MonadRec</literal> for the class and the corresponding library.
865 This name is not supported by GHC.
871 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
873 <sect2 id="parallel-list-comprehensions">
874 <title>Parallel List Comprehensions</title>
875 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
877 <indexterm><primary>parallel list comprehensions</primary>
880 <para>Parallel list comprehensions are a natural extension to list
881 comprehensions. List comprehensions can be thought of as a nice
882 syntax for writing maps and filters. Parallel comprehensions
883 extend this to include the zipWith family.</para>
885 <para>A parallel list comprehension has multiple independent
886 branches of qualifier lists, each separated by a `|' symbol. For
887 example, the following zips together two lists:</para>
890 [ (x, y) | x <- xs | y <- ys ]
893 <para>The behavior of parallel list comprehensions follows that of
894 zip, in that the resulting list will have the same length as the
895 shortest branch.</para>
897 <para>We can define parallel list comprehensions by translation to
898 regular comprehensions. Here's the basic idea:</para>
900 <para>Given a parallel comprehension of the form: </para>
903 [ e | p1 <- e11, p2 <- e12, ...
904 | q1 <- e21, q2 <- e22, ...
909 <para>This will be translated to: </para>
912 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
913 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
918 <para>where `zipN' is the appropriate zip for the given number of
923 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
925 <sect2 id="generalised-list-comprehensions">
926 <title>Generalised (SQL-Like) List Comprehensions</title>
927 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
929 <indexterm><primary>extended list comprehensions</primary>
931 <indexterm><primary>group</primary></indexterm>
932 <indexterm><primary>sql</primary></indexterm>
935 <para>Generalised list comprehensions are a further enhancement to the
936 list comprehension syntatic sugar to allow operations such as sorting
937 and grouping which are familiar from SQL. They are fully described in the
938 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
939 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
940 except that the syntax we use differs slightly from the paper.</para>
941 <para>Here is an example:
943 employees = [ ("Simon", "MS", 80)
944 , ("Erik", "MS", 100)
946 , ("Gordon", "Ed", 45)
947 , ("Paul", "Yale", 60)]
949 output = [ (the dept, sum salary)
950 | (name, dept, salary) <- employees
952 , then sortWith by (sum salary)
955 In this example, the list <literal>output</literal> would take on
959 [("Yale", 60), ("Ed", 85), ("MS", 180)]
962 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
963 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
964 function that is exported by <literal>GHC.Exts</literal>.)</para>
966 <para>There are five new forms of comprehension qualifier,
967 all introduced by the (existing) keyword <literal>then</literal>:
975 This statement requires that <literal>f</literal> have the type <literal>
976 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
977 motivating example, as this form is used to apply <literal>take 5</literal>.
988 This form is similar to the previous one, but allows you to create a function
989 which will be passed as the first argument to f. As a consequence f must have
990 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
991 from the type, this function lets f "project out" some information
992 from the elements of the list it is transforming.</para>
994 <para>An example is shown in the opening example, where <literal>sortWith</literal>
995 is supplied with a function that lets it find out the <literal>sum salary</literal>
996 for any item in the list comprehension it transforms.</para>
1004 then group by e using f
1007 <para>This is the most general of the grouping-type statements. In this form,
1008 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1009 As with the <literal>then f by e</literal> case above, the first argument
1010 is a function supplied to f by the compiler which lets it compute e on every
1011 element of the list being transformed. However, unlike the non-grouping case,
1012 f additionally partitions the list into a number of sublists: this means that
1013 at every point after this statement, binders occurring before it in the comprehension
1014 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1015 this, let's look at an example:</para>
1018 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1019 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1020 groupRuns f = groupBy (\x y -> f x == f y)
1022 output = [ (the x, y)
1023 | x <- ([1..3] ++ [1..2])
1025 , then group by x using groupRuns ]
1028 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1031 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1034 <para>Note that we have used the <literal>the</literal> function to change the type
1035 of x from a list to its original numeric type. The variable y, in contrast, is left
1036 unchanged from the list form introduced by the grouping.</para>
1046 <para>This form of grouping is essentially the same as the one described above. However,
1047 since no function to use for the grouping has been supplied it will fall back on the
1048 <literal>groupWith</literal> function defined in
1049 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1050 is the form of the group statement that we made use of in the opening example.</para>
1061 <para>With this form of the group statement, f is required to simply have the type
1062 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1063 comprehension so far directly. An example of this form is as follows:</para>
1069 , then group using inits]
1072 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1075 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1083 <!-- ===================== REBINDABLE SYNTAX =================== -->
1085 <sect2 id="rebindable-syntax">
1086 <title>Rebindable syntax and the implicit Prelude import</title>
1088 <para><indexterm><primary>-XNoImplicitPrelude
1089 option</primary></indexterm> GHC normally imports
1090 <filename>Prelude.hi</filename> files for you. If you'd
1091 rather it didn't, then give it a
1092 <option>-XNoImplicitPrelude</option> option. The idea is
1093 that you can then import a Prelude of your own. (But don't
1094 call it <literal>Prelude</literal>; the Haskell module
1095 namespace is flat, and you must not conflict with any
1096 Prelude module.)</para>
1098 <para>Suppose you are importing a Prelude of your own
1099 in order to define your own numeric class
1100 hierarchy. It completely defeats that purpose if the
1101 literal "1" means "<literal>Prelude.fromInteger
1102 1</literal>", which is what the Haskell Report specifies.
1103 So the <option>-XNoImplicitPrelude</option>
1104 flag <emphasis>also</emphasis> causes
1105 the following pieces of built-in syntax to refer to
1106 <emphasis>whatever is in scope</emphasis>, not the Prelude
1110 <para>An integer literal <literal>368</literal> means
1111 "<literal>fromInteger (368::Integer)</literal>", rather than
1112 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1115 <listitem><para>Fractional literals are handed in just the same way,
1116 except that the translation is
1117 <literal>fromRational (3.68::Rational)</literal>.
1120 <listitem><para>The equality test in an overloaded numeric pattern
1121 uses whatever <literal>(==)</literal> is in scope.
1124 <listitem><para>The subtraction operation, and the
1125 greater-than-or-equal test, in <literal>n+k</literal> patterns
1126 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1130 <para>Negation (e.g. "<literal>- (f x)</literal>")
1131 means "<literal>negate (f x)</literal>", both in numeric
1132 patterns, and expressions.
1136 <para>"Do" notation is translated using whatever
1137 functions <literal>(>>=)</literal>,
1138 <literal>(>>)</literal>, and <literal>fail</literal>,
1139 are in scope (not the Prelude
1140 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1141 comprehensions, are unaffected. </para></listitem>
1145 notation (see <xref linkend="arrow-notation"/>)
1146 uses whatever <literal>arr</literal>,
1147 <literal>(>>>)</literal>, <literal>first</literal>,
1148 <literal>app</literal>, <literal>(|||)</literal> and
1149 <literal>loop</literal> functions are in scope. But unlike the
1150 other constructs, the types of these functions must match the
1151 Prelude types very closely. Details are in flux; if you want
1155 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1156 even if that is a little unexpected. For example, the
1157 static semantics of the literal <literal>368</literal>
1158 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1159 <literal>fromInteger</literal> to have any of the types:
1161 fromInteger :: Integer -> Integer
1162 fromInteger :: forall a. Foo a => Integer -> a
1163 fromInteger :: Num a => a -> Integer
1164 fromInteger :: Integer -> Bool -> Bool
1168 <para>Be warned: this is an experimental facility, with
1169 fewer checks than usual. Use <literal>-dcore-lint</literal>
1170 to typecheck the desugared program. If Core Lint is happy
1171 you should be all right.</para>
1175 <sect2 id="postfix-operators">
1176 <title>Postfix operators</title>
1179 The <option>-XPostfixOperators</option> flag enables a small
1180 extension to the syntax of left operator sections, which allows you to
1181 define postfix operators. The extension is this: the left section
1185 is equivalent (from the point of view of both type checking and execution) to the expression
1189 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1190 The strict Haskell 98 interpretation is that the section is equivalent to
1194 That is, the operator must be a function of two arguments. GHC allows it to
1195 take only one argument, and that in turn allows you to write the function
1198 <para>The extension does not extend to the left-hand side of function
1199 definitions; you must define such a function in prefix form.</para>
1203 <sect2 id="disambiguate-fields">
1204 <title>Record field disambiguation</title>
1206 In record construction and record pattern matching
1207 it is entirely unambiguous which field is referred to, even if there are two different
1208 data types in scope with a common field name. For example:
1211 data S = MkS { x :: Int, y :: Bool }
1216 data T = MkT { x :: Int }
1218 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1220 ok2 n = MkT { x = n+1 } -- Unambiguous
1222 bad1 k = k { x = 3 } -- Ambiguous
1223 bad2 k = x k -- Ambiguous
1225 Even though there are two <literal>x</literal>'s in scope,
1226 it is clear that the <literal>x</literal> in the pattern in the
1227 definition of <literal>ok1</literal> can only mean the field
1228 <literal>x</literal> from type <literal>S</literal>. Similarly for
1229 the function <literal>ok2</literal>. However, in the record update
1230 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1231 it is not clear which of the two types is intended.
1234 Haskell 98 regards all four as ambiguous, but with the
1235 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1236 the former two. The rules are precisely the same as those for instance
1237 declarations in Haskell 98, where the method names on the left-hand side
1238 of the method bindings in an instance declaration refer unambiguously
1239 to the method of that class (provided they are in scope at all), even
1240 if there are other variables in scope with the same name.
1241 This reduces the clutter of qualified names when you import two
1242 records from different modules that use the same field name.
1246 <!-- ===================== Record puns =================== -->
1248 <sect2 id="record-puns">
1253 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1257 When using records, it is common to write a pattern that binds a
1258 variable with the same name as a record field, such as:
1261 data C = C {a :: Int}
1267 Record punning permits the variable name to be elided, so one can simply
1274 to mean the same pattern as above. That is, in a record pattern, the
1275 pattern <literal>a</literal> expands into the pattern <literal>a =
1276 a</literal> for the same name <literal>a</literal>.
1280 Note that puns and other patterns can be mixed in the same record:
1282 data C = C {a :: Int, b :: Int}
1283 f (C {a, b = 4}) = a
1285 and that puns can be used wherever record patterns occur (e.g. in
1286 <literal>let</literal> bindings or at the top-level).
1290 Record punning can also be used in an expression, writing, for example,
1296 let a = 1 in C {a = a}
1299 Note that this expansion is purely syntactic, so the record pun
1300 expression refers to the nearest enclosing variable that is spelled the
1301 same as the field name.
1306 <!-- ===================== Record wildcards =================== -->
1308 <sect2 id="record-wildcards">
1309 <title>Record wildcards
1313 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1317 For records with many fields, it can be tiresome to write out each field
1318 individually in a record pattern, as in
1320 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1321 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1326 Record wildcard syntax permits a (<literal>..</literal>) in a record
1327 pattern, where each elided field <literal>f</literal> is replaced by the
1328 pattern <literal>f = f</literal>. For example, the above pattern can be
1331 f (C {a = 1, ..}) = b + c + d
1336 Note that wildcards can be mixed with other patterns, including puns
1337 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1338 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1339 wherever record patterns occur, including in <literal>let</literal>
1340 bindings and at the top-level. For example, the top-level binding
1344 defines <literal>b</literal>, <literal>c</literal>, and
1345 <literal>d</literal>.
1349 Record wildcards can also be used in expressions, writing, for example,
1352 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1358 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1361 Note that this expansion is purely syntactic, so the record wildcard
1362 expression refers to the nearest enclosing variables that are spelled
1363 the same as the omitted field names.
1368 <!-- ===================== Local fixity declarations =================== -->
1370 <sect2 id="local-fixity-declarations">
1371 <title>Local Fixity Declarations
1374 <para>A careful reading of the Haskell 98 Report reveals that fixity
1375 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1376 <literal>infixr</literal>) are permitted to appear inside local bindings
1377 such those introduced by <literal>let</literal> and
1378 <literal>where</literal>. However, the Haskell Report does not specify
1379 the semantics of such bindings very precisely.
1382 <para>In GHC, a fixity declaration may accompany a local binding:
1389 and the fixity declaration applies wherever the binding is in scope.
1390 For example, in a <literal>let</literal>, it applies in the right-hand
1391 sides of other <literal>let</literal>-bindings and the body of the
1392 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1393 expressions (<xref linkend="mdo-notation"/>), the local fixity
1394 declarations of a <literal>let</literal> statement scope over other
1395 statements in the group, just as the bound name does.
1399 Moreover, a local fixity declaration *must* accompany a local binding of
1400 that name: it is not possible to revise the fixity of name bound
1403 let infixr 9 $ in ...
1406 Because local fixity declarations are technically Haskell 98, no flag is
1407 necessary to enable them.
1411 <sect2 id="package-imports">
1412 <title>Package-qualified imports</title>
1414 <para>With the <option>-XPackageImports</option> flag, GHC allows
1415 import declarations to be qualified by the package name that the
1416 module is intended to be imported from. For example:</para>
1419 import "network" Network.Socket
1422 <para>would import the module <literal>Network.Socket</literal> from
1423 the package <literal>network</literal> (any version). This may
1424 be used to disambiguate an import when the same module is
1425 available from multiple packages, or is present in both the
1426 current package being built and an external package.</para>
1428 <para>Note: you probably don't need to use this feature, it was
1429 added mainly so that we can build backwards-compatible versions of
1430 packages when APIs change. It can lead to fragile dependencies in
1431 the common case: modules occasionally move from one package to
1432 another, rendering any package-qualified imports broken.</para>
1435 <sect2 id="syntax-stolen">
1436 <title>Summary of stolen syntax</title>
1438 <para>Turning on an option that enables special syntax
1439 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1440 to compile, perhaps because it uses a variable name which has
1441 become a reserved word. This section lists the syntax that is
1442 "stolen" by language extensions.
1444 notation and nonterminal names from the Haskell 98 lexical syntax
1445 (see the Haskell 98 Report).
1446 We only list syntax changes here that might affect
1447 existing working programs (i.e. "stolen" syntax). Many of these
1448 extensions will also enable new context-free syntax, but in all
1449 cases programs written to use the new syntax would not be
1450 compilable without the option enabled.</para>
1452 <para>There are two classes of special
1457 <para>New reserved words and symbols: character sequences
1458 which are no longer available for use as identifiers in the
1462 <para>Other special syntax: sequences of characters that have
1463 a different meaning when this particular option is turned
1468 The following syntax is stolen:
1473 <literal>forall</literal>
1474 <indexterm><primary><literal>forall</literal></primary></indexterm>
1477 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1478 <option>-XLiberalTypeSynonyms</option>,
1479 <option>-XRank2Types</option>,
1480 <option>-XRankNTypes</option>,
1481 <option>-XPolymorphicComponents</option>,
1482 <option>-XExistentialQuantification</option>
1488 <literal>mdo</literal>
1489 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1492 Stolen by: <option>-XRecursiveDo</option>,
1498 <literal>foreign</literal>
1499 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1502 Stolen by: <option>-XForeignFunctionInterface</option>,
1508 <literal>rec</literal>,
1509 <literal>proc</literal>, <literal>-<</literal>,
1510 <literal>>-</literal>, <literal>-<<</literal>,
1511 <literal>>>-</literal>, and <literal>(|</literal>,
1512 <literal>|)</literal> brackets
1513 <indexterm><primary><literal>proc</literal></primary></indexterm>
1516 Stolen by: <option>-XArrows</option>,
1522 <literal>?<replaceable>varid</replaceable></literal>,
1523 <literal>%<replaceable>varid</replaceable></literal>
1524 <indexterm><primary>implicit parameters</primary></indexterm>
1527 Stolen by: <option>-XImplicitParams</option>,
1533 <literal>[|</literal>,
1534 <literal>[e|</literal>, <literal>[p|</literal>,
1535 <literal>[d|</literal>, <literal>[t|</literal>,
1536 <literal>$(</literal>,
1537 <literal>$<replaceable>varid</replaceable></literal>
1538 <indexterm><primary>Template Haskell</primary></indexterm>
1541 Stolen by: <option>-XTemplateHaskell</option>,
1547 <literal>[:<replaceable>varid</replaceable>|</literal>
1548 <indexterm><primary>quasi-quotation</primary></indexterm>
1551 Stolen by: <option>-XQuasiQuotes</option>,
1557 <replaceable>varid</replaceable>{<literal>#</literal>},
1558 <replaceable>char</replaceable><literal>#</literal>,
1559 <replaceable>string</replaceable><literal>#</literal>,
1560 <replaceable>integer</replaceable><literal>#</literal>,
1561 <replaceable>float</replaceable><literal>#</literal>,
1562 <replaceable>float</replaceable><literal>##</literal>,
1563 <literal>(#</literal>, <literal>#)</literal>,
1566 Stolen by: <option>-XMagicHash</option>,
1575 <!-- TYPE SYSTEM EXTENSIONS -->
1576 <sect1 id="data-type-extensions">
1577 <title>Extensions to data types and type synonyms</title>
1579 <sect2 id="nullary-types">
1580 <title>Data types with no constructors</title>
1582 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1583 a data type with no constructors. For example:</para>
1587 data T a -- T :: * -> *
1590 <para>Syntactically, the declaration lacks the "= constrs" part. The
1591 type can be parameterised over types of any kind, but if the kind is
1592 not <literal>*</literal> then an explicit kind annotation must be used
1593 (see <xref linkend="kinding"/>).</para>
1595 <para>Such data types have only one value, namely bottom.
1596 Nevertheless, they can be useful when defining "phantom types".</para>
1599 <sect2 id="infix-tycons">
1600 <title>Infix type constructors, classes, and type variables</title>
1603 GHC allows type constructors, classes, and type variables to be operators, and
1604 to be written infix, very much like expressions. More specifically:
1607 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1608 The lexical syntax is the same as that for data constructors.
1611 Data type and type-synonym declarations can be written infix, parenthesised
1612 if you want further arguments. E.g.
1614 data a :*: b = Foo a b
1615 type a :+: b = Either a b
1616 class a :=: b where ...
1618 data (a :**: b) x = Baz a b x
1619 type (a :++: b) y = Either (a,b) y
1623 Types, and class constraints, can be written infix. For example
1626 f :: (a :=: b) => a -> b
1630 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1631 The lexical syntax is the same as that for variable operators, excluding "(.)",
1632 "(!)", and "(*)". In a binding position, the operator must be
1633 parenthesised. For example:
1635 type T (+) = Int + Int
1639 liftA2 :: Arrow (~>)
1640 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1646 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1647 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1650 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1651 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1652 sets the fixity for a data constructor and the corresponding type constructor. For example:
1656 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1657 and similarly for <literal>:*:</literal>.
1658 <literal>Int `a` Bool</literal>.
1661 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1668 <sect2 id="type-synonyms">
1669 <title>Liberalised type synonyms</title>
1672 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1673 on individual synonym declarations.
1674 With the <option>-XLiberalTypeSynonyms</option> extension,
1675 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1676 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1679 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1680 in a type synonym, thus:
1682 type Discard a = forall b. Show b => a -> b -> (a, String)
1687 g :: Discard Int -> (Int,String) -- A rank-2 type
1694 If you also use <option>-XUnboxedTuples</option>,
1695 you can write an unboxed tuple in a type synonym:
1697 type Pr = (# Int, Int #)
1705 You can apply a type synonym to a forall type:
1707 type Foo a = a -> a -> Bool
1709 f :: Foo (forall b. b->b)
1711 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1713 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1718 You can apply a type synonym to a partially applied type synonym:
1720 type Generic i o = forall x. i x -> o x
1723 foo :: Generic Id []
1725 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1727 foo :: forall x. x -> [x]
1735 GHC currently does kind checking before expanding synonyms (though even that
1739 After expanding type synonyms, GHC does validity checking on types, looking for
1740 the following mal-formedness which isn't detected simply by kind checking:
1743 Type constructor applied to a type involving for-alls.
1746 Unboxed tuple on left of an arrow.
1749 Partially-applied type synonym.
1753 this will be rejected:
1755 type Pr = (# Int, Int #)
1760 because GHC does not allow unboxed tuples on the left of a function arrow.
1765 <sect2 id="existential-quantification">
1766 <title>Existentially quantified data constructors
1770 The idea of using existential quantification in data type declarations
1771 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1772 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1773 London, 1991). It was later formalised by Laufer and Odersky
1774 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1775 TOPLAS, 16(5), pp1411-1430, 1994).
1776 It's been in Lennart
1777 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1778 proved very useful. Here's the idea. Consider the declaration:
1784 data Foo = forall a. MkFoo a (a -> Bool)
1791 The data type <literal>Foo</literal> has two constructors with types:
1797 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1804 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1805 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1806 For example, the following expression is fine:
1812 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1818 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1819 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1820 isUpper</function> packages a character with a compatible function. These
1821 two things are each of type <literal>Foo</literal> and can be put in a list.
1825 What can we do with a value of type <literal>Foo</literal>?. In particular,
1826 what happens when we pattern-match on <function>MkFoo</function>?
1832 f (MkFoo val fn) = ???
1838 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1839 are compatible, the only (useful) thing we can do with them is to
1840 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1847 f (MkFoo val fn) = fn val
1853 What this allows us to do is to package heterogeneous values
1854 together with a bunch of functions that manipulate them, and then treat
1855 that collection of packages in a uniform manner. You can express
1856 quite a bit of object-oriented-like programming this way.
1859 <sect3 id="existential">
1860 <title>Why existential?
1864 What has this to do with <emphasis>existential</emphasis> quantification?
1865 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1871 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1877 But Haskell programmers can safely think of the ordinary
1878 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1879 adding a new existential quantification construct.
1884 <sect3 id="existential-with-context">
1885 <title>Existentials and type classes</title>
1888 An easy extension is to allow
1889 arbitrary contexts before the constructor. For example:
1895 data Baz = forall a. Eq a => Baz1 a a
1896 | forall b. Show b => Baz2 b (b -> b)
1902 The two constructors have the types you'd expect:
1908 Baz1 :: forall a. Eq a => a -> a -> Baz
1909 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1915 But when pattern matching on <function>Baz1</function> the matched values can be compared
1916 for equality, and when pattern matching on <function>Baz2</function> the first matched
1917 value can be converted to a string (as well as applying the function to it).
1918 So this program is legal:
1925 f (Baz1 p q) | p == q = "Yes"
1927 f (Baz2 v fn) = show (fn v)
1933 Operationally, in a dictionary-passing implementation, the
1934 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1935 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1936 extract it on pattern matching.
1941 <sect3 id="existential-records">
1942 <title>Record Constructors</title>
1945 GHC allows existentials to be used with records syntax as well. For example:
1948 data Counter a = forall self. NewCounter
1950 , _inc :: self -> self
1951 , _display :: self -> IO ()
1955 Here <literal>tag</literal> is a public field, with a well-typed selector
1956 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1957 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1958 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1959 compile-time error. In other words, <emphasis>GHC defines a record selector function
1960 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1961 (This example used an underscore in the fields for which record selectors
1962 will not be defined, but that is only programming style; GHC ignores them.)
1966 To make use of these hidden fields, we need to create some helper functions:
1969 inc :: Counter a -> Counter a
1970 inc (NewCounter x i d t) = NewCounter
1971 { _this = i x, _inc = i, _display = d, tag = t }
1973 display :: Counter a -> IO ()
1974 display NewCounter{ _this = x, _display = d } = d x
1977 Now we can define counters with different underlying implementations:
1980 counterA :: Counter String
1981 counterA = NewCounter
1982 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1984 counterB :: Counter String
1985 counterB = NewCounter
1986 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1989 display (inc counterA) -- prints "1"
1990 display (inc (inc counterB)) -- prints "##"
1993 Record update syntax is supported for existentials (and GADTs):
1995 setTag :: Counter a -> a -> Counter a
1996 setTag obj t = obj{ tag = t }
1998 The rule for record update is this: <emphasis>
1999 the types of the updated fields may
2000 mention only the universally-quantified type variables
2001 of the data constructor. For GADTs, the field may mention only types
2002 that appear as a simple type-variable argument in the constructor's result
2003 type</emphasis>. For example:
2005 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2006 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2007 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2008 -- existentially quantified)
2010 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2011 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2012 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2013 -- type-variable argument in G1's result type)
2021 <title>Restrictions</title>
2024 There are several restrictions on the ways in which existentially-quantified
2025 constructors can be use.
2034 When pattern matching, each pattern match introduces a new,
2035 distinct, type for each existential type variable. These types cannot
2036 be unified with any other type, nor can they escape from the scope of
2037 the pattern match. For example, these fragments are incorrect:
2045 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2046 is the result of <function>f1</function>. One way to see why this is wrong is to
2047 ask what type <function>f1</function> has:
2051 f1 :: Foo -> a -- Weird!
2055 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2060 f1 :: forall a. Foo -> a -- Wrong!
2064 The original program is just plain wrong. Here's another sort of error
2068 f2 (Baz1 a b) (Baz1 p q) = a==q
2072 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2073 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2074 from the two <function>Baz1</function> constructors.
2082 You can't pattern-match on an existentially quantified
2083 constructor in a <literal>let</literal> or <literal>where</literal> group of
2084 bindings. So this is illegal:
2088 f3 x = a==b where { Baz1 a b = x }
2091 Instead, use a <literal>case</literal> expression:
2094 f3 x = case x of Baz1 a b -> a==b
2097 In general, you can only pattern-match
2098 on an existentially-quantified constructor in a <literal>case</literal> expression or
2099 in the patterns of a function definition.
2101 The reason for this restriction is really an implementation one.
2102 Type-checking binding groups is already a nightmare without
2103 existentials complicating the picture. Also an existential pattern
2104 binding at the top level of a module doesn't make sense, because it's
2105 not clear how to prevent the existentially-quantified type "escaping".
2106 So for now, there's a simple-to-state restriction. We'll see how
2114 You can't use existential quantification for <literal>newtype</literal>
2115 declarations. So this is illegal:
2119 newtype T = forall a. Ord a => MkT a
2123 Reason: a value of type <literal>T</literal> must be represented as a
2124 pair of a dictionary for <literal>Ord t</literal> and a value of type
2125 <literal>t</literal>. That contradicts the idea that
2126 <literal>newtype</literal> should have no concrete representation.
2127 You can get just the same efficiency and effect by using
2128 <literal>data</literal> instead of <literal>newtype</literal>. If
2129 there is no overloading involved, then there is more of a case for
2130 allowing an existentially-quantified <literal>newtype</literal>,
2131 because the <literal>data</literal> version does carry an
2132 implementation cost, but single-field existentially quantified
2133 constructors aren't much use. So the simple restriction (no
2134 existential stuff on <literal>newtype</literal>) stands, unless there
2135 are convincing reasons to change it.
2143 You can't use <literal>deriving</literal> to define instances of a
2144 data type with existentially quantified data constructors.
2146 Reason: in most cases it would not make sense. For example:;
2149 data T = forall a. MkT [a] deriving( Eq )
2152 To derive <literal>Eq</literal> in the standard way we would need to have equality
2153 between the single component of two <function>MkT</function> constructors:
2157 (MkT a) == (MkT b) = ???
2160 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2161 It's just about possible to imagine examples in which the derived instance
2162 would make sense, but it seems altogether simpler simply to prohibit such
2163 declarations. Define your own instances!
2174 <!-- ====================== Generalised algebraic data types ======================= -->
2176 <sect2 id="gadt-style">
2177 <title>Declaring data types with explicit constructor signatures</title>
2179 <para>GHC allows you to declare an algebraic data type by
2180 giving the type signatures of constructors explicitly. For example:
2184 Just :: a -> Maybe a
2186 The form is called a "GADT-style declaration"
2187 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2188 can only be declared using this form.</para>
2189 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2190 For example, these two declarations are equivalent:
2192 data Foo = forall a. MkFoo a (a -> Bool)
2193 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2196 <para>Any data type that can be declared in standard Haskell-98 syntax
2197 can also be declared using GADT-style syntax.
2198 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2199 they treat class constraints on the data constructors differently.
2200 Specifically, if the constructor is given a type-class context, that
2201 context is made available by pattern matching. For example:
2204 MkSet :: Eq a => [a] -> Set a
2206 makeSet :: Eq a => [a] -> Set a
2207 makeSet xs = MkSet (nub xs)
2209 insert :: a -> Set a -> Set a
2210 insert a (MkSet as) | a `elem` as = MkSet as
2211 | otherwise = MkSet (a:as)
2213 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2214 gives rise to a <literal>(Eq a)</literal>
2215 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2216 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2217 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2218 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2219 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2220 In the example, the equality dictionary is used to satisfy the equality constraint
2221 generated by the call to <literal>elem</literal>, so that the type of
2222 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2225 For example, one possible application is to reify dictionaries:
2227 data NumInst a where
2228 MkNumInst :: Num a => NumInst a
2230 intInst :: NumInst Int
2233 plus :: NumInst a -> a -> a -> a
2234 plus MkNumInst p q = p + q
2236 Here, a value of type <literal>NumInst a</literal> is equivalent
2237 to an explicit <literal>(Num a)</literal> dictionary.
2240 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2241 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2245 = Num a => MkNumInst (NumInst a)
2247 Notice that, unlike the situation when declaring an existential, there is
2248 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2249 data type's universally quantified type variable <literal>a</literal>.
2250 A constructor may have both universal and existential type variables: for example,
2251 the following two declarations are equivalent:
2254 = forall b. (Num a, Eq b) => MkT1 a b
2256 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2259 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2260 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2261 In Haskell 98 the definition
2263 data Eq a => Set' a = MkSet' [a]
2265 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2266 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2267 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2268 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2269 GHC's behaviour is much more useful, as well as much more intuitive.
2273 The rest of this section gives further details about GADT-style data
2278 The result type of each data constructor must begin with the type constructor being defined.
2279 If the result type of all constructors
2280 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2281 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2282 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2286 The type signature of
2287 each constructor is independent, and is implicitly universally quantified as usual.
2288 Different constructors may have different universally-quantified type variables
2289 and different type-class constraints.
2290 For example, this is fine:
2293 T1 :: Eq b => b -> T b
2294 T2 :: (Show c, Ix c) => c -> [c] -> T c
2299 Unlike a Haskell-98-style
2300 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2301 have no scope. Indeed, one can write a kind signature instead:
2303 data Set :: * -> * where ...
2305 or even a mixture of the two:
2307 data Foo a :: (* -> *) -> * where ...
2309 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2312 data Foo a (b :: * -> *) where ...
2318 You can use strictness annotations, in the obvious places
2319 in the constructor type:
2322 Lit :: !Int -> Term Int
2323 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2324 Pair :: Term a -> Term b -> Term (a,b)
2329 You can use a <literal>deriving</literal> clause on a GADT-style data type
2330 declaration. For example, these two declarations are equivalent
2332 data Maybe1 a where {
2333 Nothing1 :: Maybe1 a ;
2334 Just1 :: a -> Maybe1 a
2335 } deriving( Eq, Ord )
2337 data Maybe2 a = Nothing2 | Just2 a
2343 You can use record syntax on a GADT-style data type declaration:
2347 Adult { name :: String, children :: [Person] } :: Person
2348 Child { name :: String } :: Person
2350 As usual, for every constructor that has a field <literal>f</literal>, the type of
2351 field <literal>f</literal> must be the same (modulo alpha conversion).
2354 At the moment, record updates are not yet possible with GADT-style declarations,
2355 so support is limited to record construction, selection and pattern matching.
2358 aPerson = Adult { name = "Fred", children = [] }
2360 shortName :: Person -> Bool
2361 hasChildren (Adult { children = kids }) = not (null kids)
2362 hasChildren (Child {}) = False
2367 As in the case of existentials declared using the Haskell-98-like record syntax
2368 (<xref linkend="existential-records"/>),
2369 record-selector functions are generated only for those fields that have well-typed
2371 Here is the example of that section, in GADT-style syntax:
2373 data Counter a where
2374 NewCounter { _this :: self
2375 , _inc :: self -> self
2376 , _display :: self -> IO ()
2381 As before, only one selector function is generated here, that for <literal>tag</literal>.
2382 Nevertheless, you can still use all the field names in pattern matching and record construction.
2384 </itemizedlist></para>
2388 <title>Generalised Algebraic Data Types (GADTs)</title>
2390 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2391 by allowing constructors to have richer return types. Here is an example:
2394 Lit :: Int -> Term Int
2395 Succ :: Term Int -> Term Int
2396 IsZero :: Term Int -> Term Bool
2397 If :: Term Bool -> Term a -> Term a -> Term a
2398 Pair :: Term a -> Term b -> Term (a,b)
2400 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2401 case with ordinary data types. This generality allows us to
2402 write a well-typed <literal>eval</literal> function
2403 for these <literal>Terms</literal>:
2407 eval (Succ t) = 1 + eval t
2408 eval (IsZero t) = eval t == 0
2409 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2410 eval (Pair e1 e2) = (eval e1, eval e2)
2412 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2413 For example, in the right hand side of the equation
2418 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2419 A precise specification of the type rules is beyond what this user manual aspires to,
2420 but the design closely follows that described in
2422 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2423 unification-based type inference for GADTs</ulink>,
2425 The general principle is this: <emphasis>type refinement is only carried out
2426 based on user-supplied type annotations</emphasis>.
2427 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2428 and lots of obscure error messages will
2429 occur. However, the refinement is quite general. For example, if we had:
2431 eval :: Term a -> a -> a
2432 eval (Lit i) j = i+j
2434 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2435 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2436 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2439 These and many other examples are given in papers by Hongwei Xi, and
2440 Tim Sheard. There is a longer introduction
2441 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2443 <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
2444 may use different notation to that implemented in GHC.
2447 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2448 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2451 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2452 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2453 The result type of each constructor must begin with the type constructor being defined,
2454 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2455 For example, in the <literal>Term</literal> data
2456 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2457 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2462 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2463 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2464 whose result type is not just <literal>T a b</literal>.
2468 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2469 an ordinary data type.
2473 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2477 Lit { val :: Int } :: Term Int
2478 Succ { num :: Term Int } :: Term Int
2479 Pred { num :: Term Int } :: Term Int
2480 IsZero { arg :: Term Int } :: Term Bool
2481 Pair { arg1 :: Term a
2484 If { cnd :: Term Bool
2489 However, for GADTs there is the following additional constraint:
2490 every constructor that has a field <literal>f</literal> must have
2491 the same result type (modulo alpha conversion)
2492 Hence, in the above example, we cannot merge the <literal>num</literal>
2493 and <literal>arg</literal> fields above into a
2494 single name. Although their field types are both <literal>Term Int</literal>,
2495 their selector functions actually have different types:
2498 num :: Term Int -> Term Int
2499 arg :: Term Bool -> Term Int
2504 When pattern-matching against data constructors drawn from a GADT,
2505 for example in a <literal>case</literal> expression, the following rules apply:
2507 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2508 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2509 <listitem><para>The type of any free variable mentioned in any of
2510 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2512 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2513 way to ensure that a variable a rigid type is to give it a type signature.
2514 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2515 Simple unification-based type inference for GADTs
2516 </ulink>. The criteria implemented by GHC are given in the Appendix.
2526 <!-- ====================== End of Generalised algebraic data types ======================= -->
2528 <sect1 id="deriving">
2529 <title>Extensions to the "deriving" mechanism</title>
2531 <sect2 id="deriving-inferred">
2532 <title>Inferred context for deriving clauses</title>
2535 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2538 data T0 f a = MkT0 a deriving( Eq )
2539 data T1 f a = MkT1 (f a) deriving( Eq )
2540 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2542 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2544 instance Eq a => Eq (T0 f a) where ...
2545 instance Eq (f a) => Eq (T1 f a) where ...
2546 instance Eq (f (f a)) => Eq (T2 f a) where ...
2548 The first of these is obviously fine. The second is still fine, although less obviously.
2549 The third is not Haskell 98, and risks losing termination of instances.
2552 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2553 each constraint in the inferred instance context must consist only of type variables,
2554 with no repetitions.
2557 This rule is applied regardless of flags. If you want a more exotic context, you can write
2558 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2562 <sect2 id="stand-alone-deriving">
2563 <title>Stand-alone deriving declarations</title>
2566 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2568 data Foo a = Bar a | Baz String
2570 deriving instance Eq a => Eq (Foo a)
2572 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2573 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2574 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2575 exactly as you would in an ordinary instance declaration.
2576 (In contrast the context is inferred in a <literal>deriving</literal> clause
2577 attached to a data type declaration.)
2579 A <literal>deriving instance</literal> declaration
2580 must obey the same rules concerning form and termination as ordinary instance declarations,
2581 controlled by the same flags; see <xref linkend="instance-decls"/>.
2584 Unlike a <literal>deriving</literal>
2585 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2586 than the data type (assuming you also use
2587 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2590 data Foo a = Bar a | Baz String
2592 deriving instance Eq a => Eq (Foo [a])
2593 deriving instance Eq a => Eq (Foo (Maybe a))
2595 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2596 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2599 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2600 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2603 newtype Foo a = MkFoo (State Int a)
2605 deriving instance MonadState Int Foo
2607 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2608 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2614 <sect2 id="deriving-typeable">
2615 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2618 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2619 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2620 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2621 classes <literal>Eq</literal>, <literal>Ord</literal>,
2622 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2625 GHC extends this list with two more classes that may be automatically derived
2626 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2627 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2628 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2629 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2631 <para>An instance of <literal>Typeable</literal> can only be derived if the
2632 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2633 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2635 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2636 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2638 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2639 are used, and only <literal>Typeable1</literal> up to
2640 <literal>Typeable7</literal> are provided in the library.)
2641 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2642 class, whose kind suits that of the data type constructor, and
2643 then writing the data type instance by hand.
2647 <sect2 id="newtype-deriving">
2648 <title>Generalised derived instances for newtypes</title>
2651 When you define an abstract type using <literal>newtype</literal>, you may want
2652 the new type to inherit some instances from its representation. In
2653 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2654 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2655 other classes you have to write an explicit instance declaration. For
2656 example, if you define
2659 newtype Dollars = Dollars Int
2662 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2663 explicitly define an instance of <literal>Num</literal>:
2666 instance Num Dollars where
2667 Dollars a + Dollars b = Dollars (a+b)
2670 All the instance does is apply and remove the <literal>newtype</literal>
2671 constructor. It is particularly galling that, since the constructor
2672 doesn't appear at run-time, this instance declaration defines a
2673 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2674 dictionary, only slower!
2678 <sect3> <title> Generalising the deriving clause </title>
2680 GHC now permits such instances to be derived instead,
2681 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2684 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2687 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2688 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2689 derives an instance declaration of the form
2692 instance Num Int => Num Dollars
2695 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2699 We can also derive instances of constructor classes in a similar
2700 way. For example, suppose we have implemented state and failure monad
2701 transformers, such that
2704 instance Monad m => Monad (State s m)
2705 instance Monad m => Monad (Failure m)
2707 In Haskell 98, we can define a parsing monad by
2709 type Parser tok m a = State [tok] (Failure m) a
2712 which is automatically a monad thanks to the instance declarations
2713 above. With the extension, we can make the parser type abstract,
2714 without needing to write an instance of class <literal>Monad</literal>, via
2717 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2720 In this case the derived instance declaration is of the form
2722 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2725 Notice that, since <literal>Monad</literal> is a constructor class, the
2726 instance is a <emphasis>partial application</emphasis> of the new type, not the
2727 entire left hand side. We can imagine that the type declaration is
2728 "eta-converted" to generate the context of the instance
2733 We can even derive instances of multi-parameter classes, provided the
2734 newtype is the last class parameter. In this case, a ``partial
2735 application'' of the class appears in the <literal>deriving</literal>
2736 clause. For example, given the class
2739 class StateMonad s m | m -> s where ...
2740 instance Monad m => StateMonad s (State s m) where ...
2742 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2744 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2745 deriving (Monad, StateMonad [tok])
2748 The derived instance is obtained by completing the application of the
2749 class to the new type:
2752 instance StateMonad [tok] (State [tok] (Failure m)) =>
2753 StateMonad [tok] (Parser tok m)
2758 As a result of this extension, all derived instances in newtype
2759 declarations are treated uniformly (and implemented just by reusing
2760 the dictionary for the representation type), <emphasis>except</emphasis>
2761 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2762 the newtype and its representation.
2766 <sect3> <title> A more precise specification </title>
2768 Derived instance declarations are constructed as follows. Consider the
2769 declaration (after expansion of any type synonyms)
2772 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2778 The <literal>ci</literal> are partial applications of
2779 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2780 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2783 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2786 The type <literal>t</literal> is an arbitrary type.
2789 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2790 nor in the <literal>ci</literal>, and
2793 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2794 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2795 should not "look through" the type or its constructor. You can still
2796 derive these classes for a newtype, but it happens in the usual way, not
2797 via this new mechanism.
2800 Then, for each <literal>ci</literal>, the derived instance
2803 instance ci t => ci (T v1...vk)
2805 As an example which does <emphasis>not</emphasis> work, consider
2807 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2809 Here we cannot derive the instance
2811 instance Monad (State s m) => Monad (NonMonad m)
2814 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2815 and so cannot be "eta-converted" away. It is a good thing that this
2816 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2817 not, in fact, a monad --- for the same reason. Try defining
2818 <literal>>>=</literal> with the correct type: you won't be able to.
2822 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2823 important, since we can only derive instances for the last one. If the
2824 <literal>StateMonad</literal> class above were instead defined as
2827 class StateMonad m s | m -> s where ...
2830 then we would not have been able to derive an instance for the
2831 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2832 classes usually have one "main" parameter for which deriving new
2833 instances is most interesting.
2835 <para>Lastly, all of this applies only for classes other than
2836 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2837 and <literal>Data</literal>, for which the built-in derivation applies (section
2838 4.3.3. of the Haskell Report).
2839 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2840 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2841 the standard method is used or the one described here.)
2848 <!-- TYPE SYSTEM EXTENSIONS -->
2849 <sect1 id="type-class-extensions">
2850 <title>Class and instances declarations</title>
2852 <sect2 id="multi-param-type-classes">
2853 <title>Class declarations</title>
2856 This section, and the next one, documents GHC's type-class extensions.
2857 There's lots of background in the paper <ulink
2858 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2859 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2860 Jones, Erik Meijer).
2863 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2867 <title>Multi-parameter type classes</title>
2869 Multi-parameter type classes are permitted. For example:
2873 class Collection c a where
2874 union :: c a -> c a -> c a
2882 <title>The superclasses of a class declaration</title>
2885 There are no restrictions on the context in a class declaration
2886 (which introduces superclasses), except that the class hierarchy must
2887 be acyclic. So these class declarations are OK:
2891 class Functor (m k) => FiniteMap m k where
2894 class (Monad m, Monad (t m)) => Transform t m where
2895 lift :: m a -> (t m) a
2901 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2902 of "acyclic" involves only the superclass relationships. For example,
2908 op :: D b => a -> b -> b
2911 class C a => D a where { ... }
2915 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2916 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2917 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2924 <sect3 id="class-method-types">
2925 <title>Class method types</title>
2928 Haskell 98 prohibits class method types to mention constraints on the
2929 class type variable, thus:
2932 fromList :: [a] -> s a
2933 elem :: Eq a => a -> s a -> Bool
2935 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2936 contains the constraint <literal>Eq a</literal>, constrains only the
2937 class type variable (in this case <literal>a</literal>).
2938 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2945 <sect2 id="functional-dependencies">
2946 <title>Functional dependencies
2949 <para> Functional dependencies are implemented as described by Mark Jones
2950 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2951 In Proceedings of the 9th European Symposium on Programming,
2952 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2956 Functional dependencies are introduced by a vertical bar in the syntax of a
2957 class declaration; e.g.
2959 class (Monad m) => MonadState s m | m -> s where ...
2961 class Foo a b c | a b -> c where ...
2963 There should be more documentation, but there isn't (yet). Yell if you need it.
2966 <sect3><title>Rules for functional dependencies </title>
2968 In a class declaration, all of the class type variables must be reachable (in the sense
2969 mentioned in <xref linkend="type-restrictions"/>)
2970 from the free variables of each method type.
2974 class Coll s a where
2976 insert :: s -> a -> s
2979 is not OK, because the type of <literal>empty</literal> doesn't mention
2980 <literal>a</literal>. Functional dependencies can make the type variable
2983 class Coll s a | s -> a where
2985 insert :: s -> a -> s
2988 Alternatively <literal>Coll</literal> might be rewritten
2991 class Coll s a where
2993 insert :: s a -> a -> s a
2997 which makes the connection between the type of a collection of
2998 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2999 Occasionally this really doesn't work, in which case you can split the
3007 class CollE s => Coll s a where
3008 insert :: s -> a -> s
3015 <title>Background on functional dependencies</title>
3017 <para>The following description of the motivation and use of functional dependencies is taken
3018 from the Hugs user manual, reproduced here (with minor changes) by kind
3019 permission of Mark Jones.
3022 Consider the following class, intended as part of a
3023 library for collection types:
3025 class Collects e ce where
3027 insert :: e -> ce -> ce
3028 member :: e -> ce -> Bool
3030 The type variable e used here represents the element type, while ce is the type
3031 of the container itself. Within this framework, we might want to define
3032 instances of this class for lists or characteristic functions (both of which
3033 can be used to represent collections of any equality type), bit sets (which can
3034 be used to represent collections of characters), or hash tables (which can be
3035 used to represent any collection whose elements have a hash function). Omitting
3036 standard implementation details, this would lead to the following declarations:
3038 instance Eq e => Collects e [e] where ...
3039 instance Eq e => Collects e (e -> Bool) where ...
3040 instance Collects Char BitSet where ...
3041 instance (Hashable e, Collects a ce)
3042 => Collects e (Array Int ce) where ...
3044 All this looks quite promising; we have a class and a range of interesting
3045 implementations. Unfortunately, there are some serious problems with the class
3046 declaration. First, the empty function has an ambiguous type:
3048 empty :: Collects e ce => ce
3050 By "ambiguous" we mean that there is a type variable e that appears on the left
3051 of the <literal>=></literal> symbol, but not on the right. The problem with
3052 this is that, according to the theoretical foundations of Haskell overloading,
3053 we cannot guarantee a well-defined semantics for any term with an ambiguous
3057 We can sidestep this specific problem by removing the empty member from the
3058 class declaration. However, although the remaining members, insert and member,
3059 do not have ambiguous types, we still run into problems when we try to use
3060 them. For example, consider the following two functions:
3062 f x y = insert x . insert y
3065 for which GHC infers the following types:
3067 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3068 g :: (Collects Bool c, Collects Char c) => c -> c
3070 Notice that the type for f allows the two parameters x and y to be assigned
3071 different types, even though it attempts to insert each of the two values, one
3072 after the other, into the same collection. If we're trying to model collections
3073 that contain only one type of value, then this is clearly an inaccurate
3074 type. Worse still, the definition for g is accepted, without causing a type
3075 error. As a result, the error in this code will not be flagged at the point
3076 where it appears. Instead, it will show up only when we try to use g, which
3077 might even be in a different module.
3080 <sect4><title>An attempt to use constructor classes</title>
3083 Faced with the problems described above, some Haskell programmers might be
3084 tempted to use something like the following version of the class declaration:
3086 class Collects e c where
3088 insert :: e -> c e -> c e
3089 member :: e -> c e -> Bool
3091 The key difference here is that we abstract over the type constructor c that is
3092 used to form the collection type c e, and not over that collection type itself,
3093 represented by ce in the original class declaration. This avoids the immediate
3094 problems that we mentioned above: empty has type <literal>Collects e c => c
3095 e</literal>, which is not ambiguous.
3098 The function f from the previous section has a more accurate type:
3100 f :: (Collects e c) => e -> e -> c e -> c e
3102 The function g from the previous section is now rejected with a type error as
3103 we would hope because the type of f does not allow the two arguments to have
3105 This, then, is an example of a multiple parameter class that does actually work
3106 quite well in practice, without ambiguity problems.
3107 There is, however, a catch. This version of the Collects class is nowhere near
3108 as general as the original class seemed to be: only one of the four instances
3109 for <literal>Collects</literal>
3110 given above can be used with this version of Collects because only one of
3111 them---the instance for lists---has a collection type that can be written in
3112 the form c e, for some type constructor c, and element type e.
3116 <sect4><title>Adding functional dependencies</title>
3119 To get a more useful version of the Collects class, Hugs provides a mechanism
3120 that allows programmers to specify dependencies between the parameters of a
3121 multiple parameter class (For readers with an interest in theoretical
3122 foundations and previous work: The use of dependency information can be seen
3123 both as a generalization of the proposal for `parametric type classes' that was
3124 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3125 later framework for "improvement" of qualified types. The
3126 underlying ideas are also discussed in a more theoretical and abstract setting
3127 in a manuscript [implparam], where they are identified as one point in a
3128 general design space for systems of implicit parameterization.).
3130 To start with an abstract example, consider a declaration such as:
3132 class C a b where ...
3134 which tells us simply that C can be thought of as a binary relation on types
3135 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3136 included in the definition of classes to add information about dependencies
3137 between parameters, as in the following examples:
3139 class D a b | a -> b where ...
3140 class E a b | a -> b, b -> a where ...
3142 The notation <literal>a -> b</literal> used here between the | and where
3143 symbols --- not to be
3144 confused with a function type --- indicates that the a parameter uniquely
3145 determines the b parameter, and might be read as "a determines b." Thus D is
3146 not just a relation, but actually a (partial) function. Similarly, from the two
3147 dependencies that are included in the definition of E, we can see that E
3148 represents a (partial) one-one mapping between types.
3151 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3152 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3153 m>=0, meaning that the y parameters are uniquely determined by the x
3154 parameters. Spaces can be used as separators if more than one variable appears
3155 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3156 annotated with multiple dependencies using commas as separators, as in the
3157 definition of E above. Some dependencies that we can write in this notation are
3158 redundant, and will be rejected because they don't serve any useful
3159 purpose, and may instead indicate an error in the program. Examples of
3160 dependencies like this include <literal>a -> a </literal>,
3161 <literal>a -> a a </literal>,
3162 <literal>a -> </literal>, etc. There can also be
3163 some redundancy if multiple dependencies are given, as in
3164 <literal>a->b</literal>,
3165 <literal>b->c </literal>, <literal>a->c </literal>, and
3166 in which some subset implies the remaining dependencies. Examples like this are
3167 not treated as errors. Note that dependencies appear only in class
3168 declarations, and not in any other part of the language. In particular, the
3169 syntax for instance declarations, class constraints, and types is completely
3173 By including dependencies in a class declaration, we provide a mechanism for
3174 the programmer to specify each multiple parameter class more precisely. The
3175 compiler, on the other hand, is responsible for ensuring that the set of
3176 instances that are in scope at any given point in the program is consistent
3177 with any declared dependencies. For example, the following pair of instance
3178 declarations cannot appear together in the same scope because they violate the
3179 dependency for D, even though either one on its own would be acceptable:
3181 instance D Bool Int where ...
3182 instance D Bool Char where ...
3184 Note also that the following declaration is not allowed, even by itself:
3186 instance D [a] b where ...
3188 The problem here is that this instance would allow one particular choice of [a]
3189 to be associated with more than one choice for b, which contradicts the
3190 dependency specified in the definition of D. More generally, this means that,
3191 in any instance of the form:
3193 instance D t s where ...
3195 for some particular types t and s, the only variables that can appear in s are
3196 the ones that appear in t, and hence, if the type t is known, then s will be
3197 uniquely determined.
3200 The benefit of including dependency information is that it allows us to define
3201 more general multiple parameter classes, without ambiguity problems, and with
3202 the benefit of more accurate types. To illustrate this, we return to the
3203 collection class example, and annotate the original definition of <literal>Collects</literal>
3204 with a simple dependency:
3206 class Collects e ce | ce -> e where
3208 insert :: e -> ce -> ce
3209 member :: e -> ce -> Bool
3211 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3212 determined by the type of the collection ce. Note that both parameters of
3213 Collects are of kind *; there are no constructor classes here. Note too that
3214 all of the instances of Collects that we gave earlier can be used
3215 together with this new definition.
3218 What about the ambiguity problems that we encountered with the original
3219 definition? The empty function still has type Collects e ce => ce, but it is no
3220 longer necessary to regard that as an ambiguous type: Although the variable e
3221 does not appear on the right of the => symbol, the dependency for class
3222 Collects tells us that it is uniquely determined by ce, which does appear on
3223 the right of the => symbol. Hence the context in which empty is used can still
3224 give enough information to determine types for both ce and e, without
3225 ambiguity. More generally, we need only regard a type as ambiguous if it
3226 contains a variable on the left of the => that is not uniquely determined
3227 (either directly or indirectly) by the variables on the right.
3230 Dependencies also help to produce more accurate types for user defined
3231 functions, and hence to provide earlier detection of errors, and less cluttered
3232 types for programmers to work with. Recall the previous definition for a
3235 f x y = insert x y = insert x . insert y
3237 for which we originally obtained a type:
3239 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3241 Given the dependency information that we have for Collects, however, we can
3242 deduce that a and b must be equal because they both appear as the second
3243 parameter in a Collects constraint with the same first parameter c. Hence we
3244 can infer a shorter and more accurate type for f:
3246 f :: (Collects a c) => a -> a -> c -> c
3248 In a similar way, the earlier definition of g will now be flagged as a type error.
3251 Although we have given only a few examples here, it should be clear that the
3252 addition of dependency information can help to make multiple parameter classes
3253 more useful in practice, avoiding ambiguity problems, and allowing more general
3254 sets of instance declarations.
3260 <sect2 id="instance-decls">
3261 <title>Instance declarations</title>
3263 <para>An instance declaration has the form
3265 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 ...
3267 The part before the "<literal>=></literal>" is the
3268 <emphasis>context</emphasis>, while the part after the
3269 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3272 <sect3 id="flexible-instance-head">
3273 <title>Relaxed rules for the instance head</title>
3276 In Haskell 98 the head of an instance declaration
3277 must be of the form <literal>C (T a1 ... an)</literal>, where
3278 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3279 and the <literal>a1 ... an</literal> are distinct type variables.
3280 GHC relaxes these rules in two ways.
3284 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3285 declaration to mention arbitrary nested types.
3286 For example, this becomes a legal instance declaration
3288 instance C (Maybe Int) where ...
3290 See also the <link linkend="instance-overlap">rules on overlap</link>.
3293 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3294 synonyms. As always, using a type synonym is just shorthand for
3295 writing the RHS of the type synonym definition. For example:
3299 type Point = (Int,Int)
3300 instance C Point where ...
3301 instance C [Point] where ...
3305 is legal. However, if you added
3309 instance C (Int,Int) where ...
3313 as well, then the compiler will complain about the overlapping
3314 (actually, identical) instance declarations. As always, type synonyms
3315 must be fully applied. You cannot, for example, write:
3319 instance Monad P where ...
3327 <sect3 id="instance-rules">
3328 <title>Relaxed rules for instance contexts</title>
3330 <para>In Haskell 98, the assertions in the context of the instance declaration
3331 must be of the form <literal>C a</literal> where <literal>a</literal>
3332 is a type variable that occurs in the head.
3336 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3337 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3338 With this flag the context of the instance declaration can each consist of arbitrary
3339 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3343 The Paterson Conditions: for each assertion in the context
3345 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3346 <listitem><para>The assertion has fewer constructors and variables (taken together
3347 and counting repetitions) than the head</para></listitem>
3351 <listitem><para>The Coverage Condition. For each functional dependency,
3352 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3353 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3354 every type variable in
3355 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3356 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3357 substitution mapping each type variable in the class declaration to the
3358 corresponding type in the instance declaration.
3361 These restrictions ensure that context reduction terminates: each reduction
3362 step makes the problem smaller by at least one
3363 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3364 if you give the <option>-XUndecidableInstances</option>
3365 flag (<xref linkend="undecidable-instances"/>).
3366 You can find lots of background material about the reason for these
3367 restrictions in the paper <ulink
3368 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3369 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3372 For example, these are OK:
3374 instance C Int [a] -- Multiple parameters
3375 instance Eq (S [a]) -- Structured type in head
3377 -- Repeated type variable in head
3378 instance C4 a a => C4 [a] [a]
3379 instance Stateful (ST s) (MutVar s)
3381 -- Head can consist of type variables only
3383 instance (Eq a, Show b) => C2 a b
3385 -- Non-type variables in context
3386 instance Show (s a) => Show (Sized s a)
3387 instance C2 Int a => C3 Bool [a]
3388 instance C2 Int a => C3 [a] b
3392 -- Context assertion no smaller than head
3393 instance C a => C a where ...
3394 -- (C b b) has more more occurrences of b than the head
3395 instance C b b => Foo [b] where ...
3400 The same restrictions apply to instances generated by
3401 <literal>deriving</literal> clauses. Thus the following is accepted:
3403 data MinHeap h a = H a (h a)
3406 because the derived instance
3408 instance (Show a, Show (h a)) => Show (MinHeap h a)
3410 conforms to the above rules.
3414 A useful idiom permitted by the above rules is as follows.
3415 If one allows overlapping instance declarations then it's quite
3416 convenient to have a "default instance" declaration that applies if
3417 something more specific does not:
3425 <sect3 id="undecidable-instances">
3426 <title>Undecidable instances</title>
3429 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3430 For example, sometimes you might want to use the following to get the
3431 effect of a "class synonym":
3433 class (C1 a, C2 a, C3 a) => C a where { }
3435 instance (C1 a, C2 a, C3 a) => C a where { }
3437 This allows you to write shorter signatures:
3443 f :: (C1 a, C2 a, C3 a) => ...
3445 The restrictions on functional dependencies (<xref
3446 linkend="functional-dependencies"/>) are particularly troublesome.
3447 It is tempting to introduce type variables in the context that do not appear in
3448 the head, something that is excluded by the normal rules. For example:
3450 class HasConverter a b | a -> b where
3453 data Foo a = MkFoo a
3455 instance (HasConverter a b,Show b) => Show (Foo a) where
3456 show (MkFoo value) = show (convert value)
3458 This is dangerous territory, however. Here, for example, is a program that would make the
3463 instance F [a] [[a]]
3464 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3466 Similarly, it can be tempting to lift the coverage condition:
3468 class Mul a b c | a b -> c where
3469 (.*.) :: a -> b -> c
3471 instance Mul Int Int Int where (.*.) = (*)
3472 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3473 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3475 The third instance declaration does not obey the coverage condition;
3476 and indeed the (somewhat strange) definition:
3478 f = \ b x y -> if b then x .*. [y] else y
3480 makes instance inference go into a loop, because it requires the constraint
3481 <literal>(Mul a [b] b)</literal>.
3484 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3485 the experimental flag <option>-XUndecidableInstances</option>
3486 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3487 both the Paterson Conditions and the Coverage Condition
3488 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3489 fixed-depth recursion stack. If you exceed the stack depth you get a
3490 sort of backtrace, and the opportunity to increase the stack depth
3491 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3497 <sect3 id="instance-overlap">
3498 <title>Overlapping instances</title>
3500 In general, <emphasis>GHC requires that that it be unambiguous which instance
3502 should be used to resolve a type-class constraint</emphasis>. This behaviour
3503 can be modified by two flags: <option>-XOverlappingInstances</option>
3504 <indexterm><primary>-XOverlappingInstances
3505 </primary></indexterm>
3506 and <option>-XIncoherentInstances</option>
3507 <indexterm><primary>-XIncoherentInstances
3508 </primary></indexterm>, as this section discusses. Both these
3509 flags are dynamic flags, and can be set on a per-module basis, using
3510 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3512 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3513 it tries to match every instance declaration against the
3515 by instantiating the head of the instance declaration. For example, consider
3518 instance context1 => C Int a where ... -- (A)
3519 instance context2 => C a Bool where ... -- (B)
3520 instance context3 => C Int [a] where ... -- (C)
3521 instance context4 => C Int [Int] where ... -- (D)
3523 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3524 but (C) and (D) do not. When matching, GHC takes
3525 no account of the context of the instance declaration
3526 (<literal>context1</literal> etc).
3527 GHC's default behaviour is that <emphasis>exactly one instance must match the
3528 constraint it is trying to resolve</emphasis>.
3529 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3530 including both declarations (A) and (B), say); an error is only reported if a
3531 particular constraint matches more than one.
3535 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3536 more than one instance to match, provided there is a most specific one. For
3537 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3538 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3539 most-specific match, the program is rejected.
3542 However, GHC is conservative about committing to an overlapping instance. For example:
3547 Suppose that from the RHS of <literal>f</literal> we get the constraint
3548 <literal>C Int [b]</literal>. But
3549 GHC does not commit to instance (C), because in a particular
3550 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3551 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3552 So GHC rejects the program.
3553 (If you add the flag <option>-XIncoherentInstances</option>,
3554 GHC will instead pick (C), without complaining about
3555 the problem of subsequent instantiations.)
3558 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3559 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3560 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3561 it instead. In this case, GHC will refrain from
3562 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3563 as before) but, rather than rejecting the program, it will infer the type
3565 f :: C Int [b] => [b] -> [b]
3567 That postpones the question of which instance to pick to the
3568 call site for <literal>f</literal>
3569 by which time more is known about the type <literal>b</literal>.
3570 You can write this type signature yourself if you use the
3571 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3575 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3579 instance Foo [b] where
3582 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3583 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3584 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3585 declaration. The solution is to postpone the choice by adding the constraint to the context
3586 of the instance declaration, thus:
3588 instance C Int [b] => Foo [b] where
3591 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3594 The willingness to be overlapped or incoherent is a property of
3595 the <emphasis>instance declaration</emphasis> itself, controlled by the
3596 presence or otherwise of the <option>-XOverlappingInstances</option>
3597 and <option>-XIncoherentInstances</option> flags when that module is
3598 being defined. Neither flag is required in a module that imports and uses the
3599 instance declaration. Specifically, during the lookup process:
3602 An instance declaration is ignored during the lookup process if (a) a more specific
3603 match is found, and (b) the instance declaration was compiled with
3604 <option>-XOverlappingInstances</option>. The flag setting for the
3605 more-specific instance does not matter.
3608 Suppose an instance declaration does not match the constraint being looked up, but
3609 does unify with it, so that it might match when the constraint is further
3610 instantiated. Usually GHC will regard this as a reason for not committing to
3611 some other constraint. But if the instance declaration was compiled with
3612 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3613 check for that declaration.
3616 These rules make it possible for a library author to design a library that relies on
3617 overlapping instances without the library client having to know.
3620 If an instance declaration is compiled without
3621 <option>-XOverlappingInstances</option>,
3622 then that instance can never be overlapped. This could perhaps be
3623 inconvenient. Perhaps the rule should instead say that the
3624 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3625 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3626 at a usage site should be permitted regardless of how the instance declarations
3627 are compiled, if the <option>-XOverlappingInstances</option> flag is
3628 used at the usage site. (Mind you, the exact usage site can occasionally be
3629 hard to pin down.) We are interested to receive feedback on these points.
3631 <para>The <option>-XIncoherentInstances</option> flag implies the
3632 <option>-XOverlappingInstances</option> flag, but not vice versa.
3640 <sect2 id="overloaded-strings">
3641 <title>Overloaded string literals
3645 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3646 string literal has type <literal>String</literal>, but with overloaded string
3647 literals enabled (with <literal>-XOverloadedStrings</literal>)
3648 a string literal has type <literal>(IsString a) => a</literal>.
3651 This means that the usual string syntax can be used, e.g., for packed strings
3652 and other variations of string like types. String literals behave very much
3653 like integer literals, i.e., they can be used in both expressions and patterns.
3654 If used in a pattern the literal with be replaced by an equality test, in the same
3655 way as an integer literal is.
3658 The class <literal>IsString</literal> is defined as:
3660 class IsString a where
3661 fromString :: String -> a
3663 The only predefined instance is the obvious one to make strings work as usual:
3665 instance IsString [Char] where
3668 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3669 it explicitly (for example, to give an instance declaration for it), you can import it
3670 from module <literal>GHC.Exts</literal>.
3673 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3677 Each type in a default declaration must be an
3678 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3682 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3683 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3684 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3685 <emphasis>or</emphasis> <literal>IsString</literal>.
3694 import GHC.Exts( IsString(..) )
3696 newtype MyString = MyString String deriving (Eq, Show)
3697 instance IsString MyString where
3698 fromString = MyString
3700 greet :: MyString -> MyString
3701 greet "hello" = "world"
3705 print $ greet "hello"
3706 print $ greet "fool"
3710 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3711 to work since it gets translated into an equality comparison.
3717 <sect1 id="type-families">
3718 <title>Type families</title>
3721 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3722 facilitate type-level
3723 programming. Type families are a generalisation of <firstterm>associated
3724 data types</firstterm>
3725 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3726 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3727 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3728 Symposium on Principles of Programming Languages (POPL'05)”, pages
3729 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3730 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3731 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3733 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3734 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3735 themselves are described in the paper “<ulink
3736 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3737 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3739 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3740 13th ACM SIGPLAN International Conference on Functional
3741 Programming”, ACM Press, pages 51-62, 2008. Type families
3742 essentially provide type-indexed data types and named functions on types,
3743 which are useful for generic programming and highly parameterised library
3744 interfaces as well as interfaces with enhanced static information, much like
3745 dependent types. They might also be regarded as an alternative to functional
3746 dependencies, but provide a more functional style of type-level programming
3747 than the relational style of functional dependencies.
3750 Indexed type families, or type families for short, are type constructors that
3751 represent sets of types. Set members are denoted by supplying the type family
3752 constructor with type parameters, which are called <firstterm>type
3753 indices</firstterm>. The
3754 difference between vanilla parametrised type constructors and family
3755 constructors is much like between parametrically polymorphic functions and
3756 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3757 behave the same at all type instances, whereas class methods can change their
3758 behaviour in dependence on the class type parameters. Similarly, vanilla type
3759 constructors imply the same data representation for all type instances, but
3760 family constructors can have varying representation types for varying type
3764 Indexed type families come in two flavours: <firstterm>data
3765 families</firstterm> and <firstterm>type synonym
3766 families</firstterm>. They are the indexed family variants of algebraic
3767 data types and type synonyms, respectively. The instances of data families
3768 can be data types and newtypes.
3771 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3772 Additional information on the use of type families in GHC is available on
3773 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3774 Haskell wiki page on type families</ulink>.
3777 <sect2 id="data-families">
3778 <title>Data families</title>
3781 Data families appear in two flavours: (1) they can be defined on the
3783 or (2) they can appear inside type classes (in which case they are known as
3784 associated types). The former is the more general variant, as it lacks the
3785 requirement for the type-indexes to coincide with the class
3786 parameters. However, the latter can lead to more clearly structured code and
3787 compiler warnings if some type instances were - possibly accidentally -
3788 omitted. In the following, we always discuss the general toplevel form first
3789 and then cover the additional constraints placed on associated types.
3792 <sect3 id="data-family-declarations">
3793 <title>Data family declarations</title>
3796 Indexed data families are introduced by a signature, such as
3798 data family GMap k :: * -> *
3800 The special <literal>family</literal> distinguishes family from standard
3801 data declarations. The result kind annotation is optional and, as
3802 usual, defaults to <literal>*</literal> if omitted. An example is
3806 Named arguments can also be given explicit kind signatures if needed.
3808 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3809 declarations] named arguments are entirely optional, so that we can
3810 declare <literal>Array</literal> alternatively with
3812 data family Array :: * -> *
3816 <sect4 id="assoc-data-family-decl">
3817 <title>Associated data family declarations</title>
3819 When a data family is declared as part of a type class, we drop
3820 the <literal>family</literal> special. The <literal>GMap</literal>
3821 declaration takes the following form
3823 class GMapKey k where
3824 data GMap k :: * -> *
3827 In contrast to toplevel declarations, named arguments must be used for
3828 all type parameters that are to be used as type-indexes. Moreover,
3829 the argument names must be class parameters. Each class parameter may
3830 only be used at most once per associated type, but some may be omitted
3831 and they may be in an order other than in the class head. Hence, the
3832 following contrived example is admissible:
3841 <sect3 id="data-instance-declarations">
3842 <title>Data instance declarations</title>
3845 Instance declarations of data and newtype families are very similar to
3846 standard data and newtype declarations. The only two differences are
3847 that the keyword <literal>data</literal> or <literal>newtype</literal>
3848 is followed by <literal>instance</literal> and that some or all of the
3849 type arguments can be non-variable types, but may not contain forall
3850 types or type synonym families. However, data families are generally
3851 allowed in type parameters, and type synonyms are allowed as long as
3852 they are fully applied and expand to a type that is itself admissible -
3853 exactly as this is required for occurrences of type synonyms in class
3854 instance parameters. For example, the <literal>Either</literal>
3855 instance for <literal>GMap</literal> is
3857 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3859 In this example, the declaration has only one variant. In general, it
3863 Data and newtype instance declarations are only legit when an
3864 appropriate family declaration is in scope - just like class instances
3865 require the class declaration to be visible. Moreover, each instance
3866 declaration has to conform to the kind determined by its family
3867 declaration. This implies that the number of parameters of an instance
3868 declaration matches the arity determined by the kind of the family.
3869 Although, all data families are declared with
3870 the <literal>data</literal> keyword, instances can be
3871 either <literal>data</literal> or <literal>newtype</literal>s, or a mix
3875 Even if type families are defined as toplevel declarations, functions
3876 that perform different computations for different family instances still
3877 need to be defined as methods of type classes. In particular, the
3878 following is not possible:
3881 data instance T Int = A
3882 data instance T Char = B
3883 nonsence :: T a -> Int
3884 nonsence A = 1 -- WRONG: These two equations together...
3885 nonsence B = 2 -- ...will produce a type error.
3887 Given the functionality provided by GADTs (Generalised Algebraic Data
3888 Types), it might seem as if a definition, such as the above, should be
3889 feasible. However, type families are - in contrast to GADTs - are
3890 <emphasis>open;</emphasis> i.e., new instances can always be added,
3892 modules. Supporting pattern matching across different data instances
3893 would require a form of extensible case construct.
3896 <sect4 id="assoc-data-inst">
3897 <title>Associated data instances</title>
3899 When an associated data family instance is declared within a type
3900 class instance, we drop the <literal>instance</literal> keyword in the
3901 family instance. So, the <literal>Either</literal> instance
3902 for <literal>GMap</literal> becomes:
3904 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
3905 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3908 The most important point about associated family instances is that the
3909 type indexes corresponding to class parameters must be identical to
3910 the type given in the instance head; here this is the first argument
3911 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
3912 which coincides with the only class parameter. Any parameters to the
3913 family constructor that do not correspond to class parameters, need to
3914 be variables in every instance; here this is the
3915 variable <literal>v</literal>.
3918 Instances for an associated family can only appear as part of
3919 instances declarations of the class in which the family was declared -
3920 just as with the equations of the methods of a class. Also in
3921 correspondence to how methods are handled, declarations of associated
3922 types can be omitted in class instances. If an associated family
3923 instance is omitted, the corresponding instance type is not inhabited;
3924 i.e., only diverging expressions, such
3925 as <literal>undefined</literal>, can assume the type.
3929 <sect4 id="scoping-class-params">
3930 <title>Scoping of class parameters</title>
3932 In the case of multi-parameter type classes, the visibility of class
3933 parameters in the right-hand side of associated family instances
3934 depends <emphasis>solely</emphasis> on the parameters of the data
3935 family. As an example, consider the simple class declaration
3940 Only one of the two class parameters is a parameter to the data
3941 family. Hence, the following instance declaration is invalid:
3943 instance C [c] d where
3944 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
3946 Here, the right-hand side of the data instance mentions the type
3947 variable <literal>d</literal> that does not occur in its left-hand
3948 side. We cannot admit such data instances as they would compromise
3953 <sect4 id="family-class-inst">
3954 <title>Type class instances of family instances</title>
3956 Type class instances of instances of data families can be defined as
3957 usual, and in particular data instance declarations can
3958 have <literal>deriving</literal> clauses. For example, we can write
3960 data GMap () v = GMapUnit (Maybe v)
3963 which implicitly defines an instance of the form
3965 instance Show v => Show (GMap () v) where ...
3969 Note that class instances are always for
3970 particular <emphasis>instances</emphasis> of a data family and never
3971 for an entire family as a whole. This is for essentially the same
3972 reasons that we cannot define a toplevel function that performs
3973 pattern matching on the data constructors
3974 of <emphasis>different</emphasis> instances of a single type family.
3975 It would require a form of extensible case construct.
3979 <sect4 id="data-family-overlap">
3980 <title>Overlap of data instances</title>
3982 The instance declarations of a data family used in a single program
3983 may not overlap at all, independent of whether they are associated or
3984 not. In contrast to type class instances, this is not only a matter
3985 of consistency, but one of type safety.
3991 <sect3 id="data-family-import-export">
3992 <title>Import and export</title>
3995 The association of data constructors with type families is more dynamic
3996 than that is the case with standard data and newtype declarations. In
3997 the standard case, the notation <literal>T(..)</literal> in an import or
3998 export list denotes the type constructor and all the data constructors
3999 introduced in its declaration. However, a family declaration never
4000 introduces any data constructors; instead, data constructors are
4001 introduced by family instances. As a result, which data constructors
4002 are associated with a type family depends on the currently visible
4003 instance declarations for that family. Consequently, an import or
4004 export item of the form <literal>T(..)</literal> denotes the family
4005 constructor and all currently visible data constructors - in the case of
4006 an export item, these may be either imported or defined in the current
4007 module. The treatment of import and export items that explicitly list
4008 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4012 <sect4 id="data-family-impexp-assoc">
4013 <title>Associated families</title>
4015 As expected, an import or export item of the
4016 form <literal>C(..)</literal> denotes all of the class' methods and
4017 associated types. However, when associated types are explicitly
4018 listed as subitems of a class, we need some new syntax, as uppercase
4019 identifiers as subitems are usually data constructors, not type
4020 constructors. To clarify that we denote types here, each associated
4021 type name needs to be prefixed by the keyword <literal>type</literal>.
4022 So for example, when explicitly listing the components of
4023 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4024 GMap, empty, lookup, insert)</literal>.
4028 <sect4 id="data-family-impexp-examples">
4029 <title>Examples</title>
4031 Assuming our running <literal>GMapKey</literal> class example, let us
4032 look at some export lists and their meaning:
4035 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4036 just the class name.</para>
4039 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4040 Exports the class, the associated type <literal>GMap</literal>
4042 functions <literal>empty</literal>, <literal>lookup</literal>,
4043 and <literal>insert</literal>. None of the data constructors is
4047 <para><literal>module GMap (GMapKey(..), GMap(..))
4048 where...</literal>: As before, but also exports all the data
4049 constructors <literal>GMapInt</literal>,
4050 <literal>GMapChar</literal>,
4051 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4052 and <literal>GMapUnit</literal>.</para>
4055 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4056 GMap(..)) where...</literal>: As before.</para>
4059 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4060 where...</literal>: As before.</para>
4065 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4066 both the class <literal>GMapKey</literal> as well as its associated
4067 type <literal>GMap</literal>. However, you cannot
4068 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4069 sub-component specifications cannot be nested. To
4070 specify <literal>GMap</literal>'s data constructors, you have to list
4075 <sect4 id="data-family-impexp-instances">
4076 <title>Instances</title>
4078 Family instances are implicitly exported, just like class instances.
4079 However, this applies only to the heads of instances, not to the data
4080 constructors an instance defines.
4088 <sect2 id="synonym-families">
4089 <title>Synonym families</title>
4092 Type families appear in two flavours: (1) they can be defined on the
4093 toplevel or (2) they can appear inside type classes (in which case they
4094 are known as associated type synonyms). The former is the more general
4095 variant, as it lacks the requirement for the type-indexes to coincide with
4096 the class parameters. However, the latter can lead to more clearly
4097 structured code and compiler warnings if some type instances were -
4098 possibly accidentally - omitted. In the following, we always discuss the
4099 general toplevel form first and then cover the additional constraints
4100 placed on associated types.
4103 <sect3 id="type-family-declarations">
4104 <title>Type family declarations</title>
4107 Indexed type families are introduced by a signature, such as
4109 type family Elem c :: *
4111 The special <literal>family</literal> distinguishes family from standard
4112 type declarations. The result kind annotation is optional and, as
4113 usual, defaults to <literal>*</literal> if omitted. An example is
4117 Parameters can also be given explicit kind signatures if needed. We
4118 call the number of parameters in a type family declaration, the family's
4119 arity, and all applications of a type family must be fully saturated
4120 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4121 and it implies that the kind of a type family is not sufficient to
4122 determine a family's arity, and hence in general, also insufficient to
4123 determine whether a type family application is well formed. As an
4124 example, consider the following declaration:
4126 type family F a b :: * -> * -- F's arity is 2,
4127 -- although it's overall kind is * -> * -> * -> *
4129 Given this declaration the following are examples of well-formed and
4132 F Char [Int] -- OK! Kind: * -> *
4133 F Char [Int] Bool -- OK! Kind: *
4134 F IO Bool -- WRONG: kind mismatch in the first argument
4135 F Bool -- WRONG: unsaturated application
4139 <sect4 id="assoc-type-family-decl">
4140 <title>Associated type family declarations</title>
4142 When a type family is declared as part of a type class, we drop
4143 the <literal>family</literal> special. The <literal>Elem</literal>
4144 declaration takes the following form
4146 class Collects ce where
4150 The argument names of the type family must be class parameters. Each
4151 class parameter may only be used at most once per associated type, but
4152 some may be omitted and they may be in an order other than in the
4153 class head. Hence, the following contrived example is admissible:
4158 These rules are exactly as for associated data families.
4163 <sect3 id="type-instance-declarations">
4164 <title>Type instance declarations</title>
4166 Instance declarations of type families are very similar to standard type
4167 synonym declarations. The only two differences are that the
4168 keyword <literal>type</literal> is followed
4169 by <literal>instance</literal> and that some or all of the type
4170 arguments can be non-variable types, but may not contain forall types or
4171 type synonym families. However, data families are generally allowed, and
4172 type synonyms are allowed as long as they are fully applied and expand
4173 to a type that is admissible - these are the exact same requirements as
4174 for data instances. For example, the <literal>[e]</literal> instance
4175 for <literal>Elem</literal> is
4177 type instance Elem [e] = e
4181 Type family instance declarations are only legitimate when an
4182 appropriate family declaration is in scope - just like class instances
4183 require the class declaration to be visible. Moreover, each instance
4184 declaration has to conform to the kind determined by its family
4185 declaration, and the number of type parameters in an instance
4186 declaration must match the number of type parameters in the family
4187 declaration. Finally, the right-hand side of a type instance must be a
4188 monotype (i.e., it may not include foralls) and after the expansion of
4189 all saturated vanilla type synonyms, no synonyms, except family synonyms
4190 may remain. Here are some examples of admissible and illegal type
4193 type family F a :: *
4194 type instance F [Int] = Int -- OK!
4195 type instance F String = Char -- OK!
4196 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4197 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4198 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4200 type family G a b :: * -> *
4201 type instance G Int = (,) -- WRONG: must be two type parameters
4202 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4206 <sect4 id="assoc-type-instance">
4207 <title>Associated type instance declarations</title>
4209 When an associated family instance is declared within a type class
4210 instance, we drop the <literal>instance</literal> keyword in the family
4211 instance. So, the <literal>[e]</literal> instance
4212 for <literal>Elem</literal> becomes:
4214 instance (Eq (Elem [e])) => Collects ([e]) where
4218 The most important point about associated family instances is that the
4219 type indexes corresponding to class parameters must be identical to the
4220 type given in the instance head; here this is <literal>[e]</literal>,
4221 which coincides with the only class parameter.
4224 Instances for an associated family can only appear as part of instances
4225 declarations of the class in which the family was declared - just as
4226 with the equations of the methods of a class. Also in correspondence to
4227 how methods are handled, declarations of associated types can be omitted
4228 in class instances. If an associated family instance is omitted, the
4229 corresponding instance type is not inhabited; i.e., only diverging
4230 expressions, such as <literal>undefined</literal>, can assume the type.
4234 <sect4 id="type-family-overlap">
4235 <title>Overlap of type synonym instances</title>
4237 The instance declarations of a type family used in a single program
4238 may only overlap if the right-hand sides of the overlapping instances
4239 coincide for the overlapping types. More formally, two instance
4240 declarations overlap if there is a substitution that makes the
4241 left-hand sides of the instances syntactically the same. Whenever
4242 that is the case, the right-hand sides of the instances must also be
4243 syntactically equal under the same substitution. This condition is
4244 independent of whether the type family is associated or not, and it is
4245 not only a matter of consistency, but one of type safety.
4248 Here are two example to illustrate the condition under which overlap
4251 type instance F (a, Int) = [a]
4252 type instance F (Int, b) = [b] -- overlap permitted
4254 type instance G (a, Int) = [a]
4255 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4260 <sect4 id="type-family-decidability">
4261 <title>Decidability of type synonym instances</title>
4263 In order to guarantee that type inference in the presence of type
4264 families decidable, we need to place a number of additional
4265 restrictions on the formation of type instance declarations (c.f.,
4266 Definition 5 (Relaxed Conditions) of “<ulink
4267 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4268 Checking with Open Type Functions</ulink>”). Instance
4269 declarations have the general form
4271 type instance F t1 .. tn = t
4273 where we require that for every type family application <literal>(G s1
4274 .. sm)</literal> in <literal>t</literal>,
4277 <para><literal>s1 .. sm</literal> do not contain any type family
4278 constructors,</para>
4281 <para>the total number of symbols (data type constructors and type
4282 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4283 in <literal>t1 .. tn</literal>, and</para>
4286 <para>for every type
4287 variable <literal>a</literal>, <literal>a</literal> occurs
4288 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4289 .. tn</literal>.</para>
4292 These restrictions are easily verified and ensure termination of type
4293 inference. However, they are not sufficient to guarantee completeness
4294 of type inference in the presence of, so called, ''loopy equalities'',
4295 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4296 a type variable is underneath a family application and data
4297 constructor application - see the above mentioned paper for details.
4300 If the option <option>-XUndecidableInstances</option> is passed to the
4301 compiler, the above restrictions are not enforced and it is on the
4302 programmer to ensure termination of the normalisation of type families
4303 during type inference.
4308 <sect3 id-="equality-constraints">
4309 <title>Equality constraints</title>
4311 Type context can include equality constraints of the form <literal>t1 ~
4312 t2</literal>, which denote that the types <literal>t1</literal>
4313 and <literal>t2</literal> need to be the same. In the presence of type
4314 families, whether two types are equal cannot generally be decided
4315 locally. Hence, the contexts of function signatures may include
4316 equality constraints, as in the following example:
4318 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4320 where we require that the element type of <literal>c1</literal>
4321 and <literal>c2</literal> are the same. In general, the
4322 types <literal>t1</literal> and <literal>t2</literal> of an equality
4323 constraint may be arbitrary monotypes; i.e., they may not contain any
4324 quantifiers, independent of whether higher-rank types are otherwise
4328 Equality constraints can also appear in class and instance contexts.
4329 The former enable a simple translation of programs using functional
4330 dependencies into programs using family synonyms instead. The general
4331 idea is to rewrite a class declaration of the form
4333 class C a b | a -> b
4337 class (F a ~ b) => C a b where
4340 That is, we represent every functional dependency (FD) <literal>a1 .. an
4341 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4342 superclass context equality <literal>F a1 .. an ~ b</literal>,
4343 essentially giving a name to the functional dependency. In class
4344 instances, we define the type instances of FD families in accordance
4345 with the class head. Method signatures are not affected by that
4349 NB: Equalities in superclass contexts are not fully implemented in
4354 <sect3 id-="ty-fams-in-instances">
4355 <title>Type families and instance declarations</title>
4356 <para>Type families require us to extend the rules for
4357 the form of instance heads, which are given
4358 in <xref linkend="flexible-instance-head"/>.
4361 <listitem><para>Data type families may appear in an instance head</para></listitem>
4362 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4364 The reason for the latter restriction is that there is no way to check for. Consider
4367 type instance F Bool = Int
4374 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4375 The situation is especially bad because the type instance for <literal>F Bool</literal>
4376 might be in another module, or even in a module that is not yet written.
4383 <sect1 id="other-type-extensions">
4384 <title>Other type system extensions</title>
4386 <sect2 id="type-restrictions">
4387 <title>Type signatures</title>
4389 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4391 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4392 that the type-class constraints in a type signature must have the
4393 form <emphasis>(class type-variable)</emphasis> or
4394 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4395 With <option>-XFlexibleContexts</option>
4396 these type signatures are perfectly OK
4399 g :: Ord (T a ()) => ...
4403 GHC imposes the following restrictions on the constraints in a type signature.
4407 forall tv1..tvn (c1, ...,cn) => type
4410 (Here, we write the "foralls" explicitly, although the Haskell source
4411 language omits them; in Haskell 98, all the free type variables of an
4412 explicit source-language type signature are universally quantified,
4413 except for the class type variables in a class declaration. However,
4414 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4423 <emphasis>Each universally quantified type variable
4424 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4426 A type variable <literal>a</literal> is "reachable" if it appears
4427 in the same constraint as either a type variable free in
4428 <literal>type</literal>, or another reachable type variable.
4429 A value with a type that does not obey
4430 this reachability restriction cannot be used without introducing
4431 ambiguity; that is why the type is rejected.
4432 Here, for example, is an illegal type:
4436 forall a. Eq a => Int
4440 When a value with this type was used, the constraint <literal>Eq tv</literal>
4441 would be introduced where <literal>tv</literal> is a fresh type variable, and
4442 (in the dictionary-translation implementation) the value would be
4443 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4444 can never know which instance of <literal>Eq</literal> to use because we never
4445 get any more information about <literal>tv</literal>.
4449 that the reachability condition is weaker than saying that <literal>a</literal> is
4450 functionally dependent on a type variable free in
4451 <literal>type</literal> (see <xref
4452 linkend="functional-dependencies"/>). The reason for this is there
4453 might be a "hidden" dependency, in a superclass perhaps. So
4454 "reachable" is a conservative approximation to "functionally dependent".
4455 For example, consider:
4457 class C a b | a -> b where ...
4458 class C a b => D a b where ...
4459 f :: forall a b. D a b => a -> a
4461 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4462 but that is not immediately apparent from <literal>f</literal>'s type.
4468 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4469 universally quantified type variables <literal>tvi</literal></emphasis>.
4471 For example, this type is OK because <literal>C a b</literal> mentions the
4472 universally quantified type variable <literal>b</literal>:
4476 forall a. C a b => burble
4480 The next type is illegal because the constraint <literal>Eq b</literal> does not
4481 mention <literal>a</literal>:
4485 forall a. Eq b => burble
4489 The reason for this restriction is milder than the other one. The
4490 excluded types are never useful or necessary (because the offending
4491 context doesn't need to be witnessed at this point; it can be floated
4492 out). Furthermore, floating them out increases sharing. Lastly,
4493 excluding them is a conservative choice; it leaves a patch of
4494 territory free in case we need it later.
4508 <sect2 id="implicit-parameters">
4509 <title>Implicit parameters</title>
4511 <para> Implicit parameters are implemented as described in
4512 "Implicit parameters: dynamic scoping with static types",
4513 J Lewis, MB Shields, E Meijer, J Launchbury,
4514 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4518 <para>(Most of the following, still rather incomplete, documentation is
4519 due to Jeff Lewis.)</para>
4521 <para>Implicit parameter support is enabled with the option
4522 <option>-XImplicitParams</option>.</para>
4525 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4526 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4527 context. In Haskell, all variables are statically bound. Dynamic
4528 binding of variables is a notion that goes back to Lisp, but was later
4529 discarded in more modern incarnations, such as Scheme. Dynamic binding
4530 can be very confusing in an untyped language, and unfortunately, typed
4531 languages, in particular Hindley-Milner typed languages like Haskell,
4532 only support static scoping of variables.
4535 However, by a simple extension to the type class system of Haskell, we
4536 can support dynamic binding. Basically, we express the use of a
4537 dynamically bound variable as a constraint on the type. These
4538 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4539 function uses a dynamically-bound variable <literal>?x</literal>
4540 of type <literal>t'</literal>". For
4541 example, the following expresses the type of a sort function,
4542 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4544 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4546 The dynamic binding constraints are just a new form of predicate in the type class system.
4549 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4550 where <literal>x</literal> is
4551 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4552 Use of this construct also introduces a new
4553 dynamic-binding constraint in the type of the expression.
4554 For example, the following definition
4555 shows how we can define an implicitly parameterized sort function in
4556 terms of an explicitly parameterized <literal>sortBy</literal> function:
4558 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4560 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4566 <title>Implicit-parameter type constraints</title>
4568 Dynamic binding constraints behave just like other type class
4569 constraints in that they are automatically propagated. Thus, when a
4570 function is used, its implicit parameters are inherited by the
4571 function that called it. For example, our <literal>sort</literal> function might be used
4572 to pick out the least value in a list:
4574 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4575 least xs = head (sort xs)
4577 Without lifting a finger, the <literal>?cmp</literal> parameter is
4578 propagated to become a parameter of <literal>least</literal> as well. With explicit
4579 parameters, the default is that parameters must always be explicit
4580 propagated. With implicit parameters, the default is to always
4584 An implicit-parameter type constraint differs from other type class constraints in the
4585 following way: All uses of a particular implicit parameter must have
4586 the same type. This means that the type of <literal>(?x, ?x)</literal>
4587 is <literal>(?x::a) => (a,a)</literal>, and not
4588 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4592 <para> You can't have an implicit parameter in the context of a class or instance
4593 declaration. For example, both these declarations are illegal:
4595 class (?x::Int) => C a where ...
4596 instance (?x::a) => Foo [a] where ...
4598 Reason: exactly which implicit parameter you pick up depends on exactly where
4599 you invoke a function. But the ``invocation'' of instance declarations is done
4600 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4601 Easiest thing is to outlaw the offending types.</para>
4603 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4605 f :: (?x :: [a]) => Int -> Int
4608 g :: (Read a, Show a) => String -> String
4611 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4612 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4613 quite unambiguous, and fixes the type <literal>a</literal>.
4618 <title>Implicit-parameter bindings</title>
4621 An implicit parameter is <emphasis>bound</emphasis> using the standard
4622 <literal>let</literal> or <literal>where</literal> binding forms.
4623 For example, we define the <literal>min</literal> function by binding
4624 <literal>cmp</literal>.
4627 min = let ?cmp = (<=) in least
4631 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4632 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4633 (including in a list comprehension, or do-notation, or pattern guards),
4634 or a <literal>where</literal> clause.
4635 Note the following points:
4638 An implicit-parameter binding group must be a
4639 collection of simple bindings to implicit-style variables (no
4640 function-style bindings, and no type signatures); these bindings are
4641 neither polymorphic or recursive.
4644 You may not mix implicit-parameter bindings with ordinary bindings in a
4645 single <literal>let</literal>
4646 expression; use two nested <literal>let</literal>s instead.
4647 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4651 You may put multiple implicit-parameter bindings in a
4652 single binding group; but they are <emphasis>not</emphasis> treated
4653 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4654 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4655 parameter. The bindings are not nested, and may be re-ordered without changing
4656 the meaning of the program.
4657 For example, consider:
4659 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4661 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4662 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4664 f :: (?x::Int) => Int -> Int
4672 <sect3><title>Implicit parameters and polymorphic recursion</title>
4675 Consider these two definitions:
4678 len1 xs = let ?acc = 0 in len_acc1 xs
4681 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4686 len2 xs = let ?acc = 0 in len_acc2 xs
4688 len_acc2 :: (?acc :: Int) => [a] -> Int
4690 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4692 The only difference between the two groups is that in the second group
4693 <literal>len_acc</literal> is given a type signature.
4694 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4695 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4696 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4697 has a type signature, the recursive call is made to the
4698 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4699 as an implicit parameter. So we get the following results in GHCi:
4706 Adding a type signature dramatically changes the result! This is a rather
4707 counter-intuitive phenomenon, worth watching out for.
4711 <sect3><title>Implicit parameters and monomorphism</title>
4713 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4714 Haskell Report) to implicit parameters. For example, consider:
4722 Since the binding for <literal>y</literal> falls under the Monomorphism
4723 Restriction it is not generalised, so the type of <literal>y</literal> is
4724 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4725 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4726 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4727 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4728 <literal>y</literal> in the body of the <literal>let</literal> will see the
4729 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4730 <literal>14</literal>.
4735 <!-- ======================= COMMENTED OUT ========================
4737 We intend to remove linear implicit parameters, so I'm at least removing
4738 them from the 6.6 user manual
4740 <sect2 id="linear-implicit-parameters">
4741 <title>Linear implicit parameters</title>
4743 Linear implicit parameters are an idea developed by Koen Claessen,
4744 Mark Shields, and Simon PJ. They address the long-standing
4745 problem that monads seem over-kill for certain sorts of problem, notably:
4748 <listitem> <para> distributing a supply of unique names </para> </listitem>
4749 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4750 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4754 Linear implicit parameters are just like ordinary implicit parameters,
4755 except that they are "linear"; that is, they cannot be copied, and
4756 must be explicitly "split" instead. Linear implicit parameters are
4757 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4758 (The '/' in the '%' suggests the split!)
4763 import GHC.Exts( Splittable )
4765 data NameSupply = ...
4767 splitNS :: NameSupply -> (NameSupply, NameSupply)
4768 newName :: NameSupply -> Name
4770 instance Splittable NameSupply where
4774 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4775 f env (Lam x e) = Lam x' (f env e)
4778 env' = extend env x x'
4779 ...more equations for f...
4781 Notice that the implicit parameter %ns is consumed
4783 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4784 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4788 So the translation done by the type checker makes
4789 the parameter explicit:
4791 f :: NameSupply -> Env -> Expr -> Expr
4792 f ns env (Lam x e) = Lam x' (f ns1 env e)
4794 (ns1,ns2) = splitNS ns
4796 env = extend env x x'
4798 Notice the call to 'split' introduced by the type checker.
4799 How did it know to use 'splitNS'? Because what it really did
4800 was to introduce a call to the overloaded function 'split',
4801 defined by the class <literal>Splittable</literal>:
4803 class Splittable a where
4806 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4807 split for name supplies. But we can simply write
4813 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4815 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4816 <literal>GHC.Exts</literal>.
4821 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4822 are entirely distinct implicit parameters: you
4823 can use them together and they won't interfere with each other. </para>
4826 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4828 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4829 in the context of a class or instance declaration. </para></listitem>
4833 <sect3><title>Warnings</title>
4836 The monomorphism restriction is even more important than usual.
4837 Consider the example above:
4839 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4840 f env (Lam x e) = Lam x' (f env e)
4843 env' = extend env x x'
4845 If we replaced the two occurrences of x' by (newName %ns), which is
4846 usually a harmless thing to do, we get:
4848 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4849 f env (Lam x e) = Lam (newName %ns) (f env e)
4851 env' = extend env x (newName %ns)
4853 But now the name supply is consumed in <emphasis>three</emphasis> places
4854 (the two calls to newName,and the recursive call to f), so
4855 the result is utterly different. Urk! We don't even have
4859 Well, this is an experimental change. With implicit
4860 parameters we have already lost beta reduction anyway, and
4861 (as John Launchbury puts it) we can't sensibly reason about
4862 Haskell programs without knowing their typing.
4867 <sect3><title>Recursive functions</title>
4868 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4871 foo :: %x::T => Int -> [Int]
4873 foo n = %x : foo (n-1)
4875 where T is some type in class Splittable.</para>
4877 Do you get a list of all the same T's or all different T's
4878 (assuming that split gives two distinct T's back)?
4880 If you supply the type signature, taking advantage of polymorphic
4881 recursion, you get what you'd probably expect. Here's the
4882 translated term, where the implicit param is made explicit:
4885 foo x n = let (x1,x2) = split x
4886 in x1 : foo x2 (n-1)
4888 But if you don't supply a type signature, GHC uses the Hindley
4889 Milner trick of using a single monomorphic instance of the function
4890 for the recursive calls. That is what makes Hindley Milner type inference
4891 work. So the translation becomes
4895 foom n = x : foom (n-1)
4899 Result: 'x' is not split, and you get a list of identical T's. So the
4900 semantics of the program depends on whether or not foo has a type signature.
4903 You may say that this is a good reason to dislike linear implicit parameters
4904 and you'd be right. That is why they are an experimental feature.
4910 ================ END OF Linear Implicit Parameters commented out -->
4912 <sect2 id="kinding">
4913 <title>Explicitly-kinded quantification</title>
4916 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4917 to give the kind explicitly as (machine-checked) documentation,
4918 just as it is nice to give a type signature for a function. On some occasions,
4919 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4920 John Hughes had to define the data type:
4922 data Set cxt a = Set [a]
4923 | Unused (cxt a -> ())
4925 The only use for the <literal>Unused</literal> constructor was to force the correct
4926 kind for the type variable <literal>cxt</literal>.
4929 GHC now instead allows you to specify the kind of a type variable directly, wherever
4930 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4933 This flag enables kind signatures in the following places:
4935 <listitem><para><literal>data</literal> declarations:
4937 data Set (cxt :: * -> *) a = Set [a]
4938 </screen></para></listitem>
4939 <listitem><para><literal>type</literal> declarations:
4941 type T (f :: * -> *) = f Int
4942 </screen></para></listitem>
4943 <listitem><para><literal>class</literal> declarations:
4945 class (Eq a) => C (f :: * -> *) a where ...
4946 </screen></para></listitem>
4947 <listitem><para><literal>forall</literal>'s in type signatures:
4949 f :: forall (cxt :: * -> *). Set cxt Int
4950 </screen></para></listitem>
4955 The parentheses are required. Some of the spaces are required too, to
4956 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4957 will get a parse error, because "<literal>::*->*</literal>" is a
4958 single lexeme in Haskell.
4962 As part of the same extension, you can put kind annotations in types
4965 f :: (Int :: *) -> Int
4966 g :: forall a. a -> (a :: *)
4970 atype ::= '(' ctype '::' kind ')
4972 The parentheses are required.
4977 <sect2 id="universal-quantification">
4978 <title>Arbitrary-rank polymorphism
4982 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4983 allows us to say exactly what this means. For example:
4991 g :: forall b. (b -> b)
4993 The two are treated identically.
4997 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4998 explicit universal quantification in
5000 For example, all the following types are legal:
5002 f1 :: forall a b. a -> b -> a
5003 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5005 f2 :: (forall a. a->a) -> Int -> Int
5006 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5008 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5010 f4 :: Int -> (forall a. a -> a)
5012 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5013 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5014 The <literal>forall</literal> makes explicit the universal quantification that
5015 is implicitly added by Haskell.
5018 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5019 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5020 shows, the polymorphic type on the left of the function arrow can be overloaded.
5023 The function <literal>f3</literal> has a rank-3 type;
5024 it has rank-2 types on the left of a function arrow.
5027 GHC has three flags to control higher-rank types:
5030 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5033 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5036 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5037 That is, you can nest <literal>forall</literal>s
5038 arbitrarily deep in function arrows.
5039 In particular, a forall-type (also called a "type scheme"),
5040 including an operational type class context, is legal:
5042 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5043 of a function arrow </para> </listitem>
5044 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5045 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5046 field type signatures.</para> </listitem>
5047 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5048 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5052 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5053 a type variable any more!
5062 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5063 the types of the constructor arguments. Here are several examples:
5069 data T a = T1 (forall b. b -> b -> b) a
5071 data MonadT m = MkMonad { return :: forall a. a -> m a,
5072 bind :: forall a b. m a -> (a -> m b) -> m b
5075 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5081 The constructors have rank-2 types:
5087 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5088 MkMonad :: forall m. (forall a. a -> m a)
5089 -> (forall a b. m a -> (a -> m b) -> m b)
5091 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5097 Notice that you don't need to use a <literal>forall</literal> if there's an
5098 explicit context. For example in the first argument of the
5099 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5100 prefixed to the argument type. The implicit <literal>forall</literal>
5101 quantifies all type variables that are not already in scope, and are
5102 mentioned in the type quantified over.
5106 As for type signatures, implicit quantification happens for non-overloaded
5107 types too. So if you write this:
5110 data T a = MkT (Either a b) (b -> b)
5113 it's just as if you had written this:
5116 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5119 That is, since the type variable <literal>b</literal> isn't in scope, it's
5120 implicitly universally quantified. (Arguably, it would be better
5121 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5122 where that is what is wanted. Feedback welcomed.)
5126 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5127 the constructor to suitable values, just as usual. For example,
5138 a3 = MkSwizzle reverse
5141 a4 = let r x = Just x
5148 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5149 mkTs f x y = [T1 f x, T1 f y]
5155 The type of the argument can, as usual, be more general than the type
5156 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5157 does not need the <literal>Ord</literal> constraint.)
5161 When you use pattern matching, the bound variables may now have
5162 polymorphic types. For example:
5168 f :: T a -> a -> (a, Char)
5169 f (T1 w k) x = (w k x, w 'c' 'd')
5171 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5172 g (MkSwizzle s) xs f = s (map f (s xs))
5174 h :: MonadT m -> [m a] -> m [a]
5175 h m [] = return m []
5176 h m (x:xs) = bind m x $ \y ->
5177 bind m (h m xs) $ \ys ->
5184 In the function <function>h</function> we use the record selectors <literal>return</literal>
5185 and <literal>bind</literal> to extract the polymorphic bind and return functions
5186 from the <literal>MonadT</literal> data structure, rather than using pattern
5192 <title>Type inference</title>
5195 In general, type inference for arbitrary-rank types is undecidable.
5196 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5197 to get a decidable algorithm by requiring some help from the programmer.
5198 We do not yet have a formal specification of "some help" but the rule is this:
5201 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5202 provides an explicit polymorphic type for x, or GHC's type inference will assume
5203 that x's type has no foralls in it</emphasis>.
5206 What does it mean to "provide" an explicit type for x? You can do that by
5207 giving a type signature for x directly, using a pattern type signature
5208 (<xref linkend="scoped-type-variables"/>), thus:
5210 \ f :: (forall a. a->a) -> (f True, f 'c')
5212 Alternatively, you can give a type signature to the enclosing
5213 context, which GHC can "push down" to find the type for the variable:
5215 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5217 Here the type signature on the expression can be pushed inwards
5218 to give a type signature for f. Similarly, and more commonly,
5219 one can give a type signature for the function itself:
5221 h :: (forall a. a->a) -> (Bool,Char)
5222 h f = (f True, f 'c')
5224 You don't need to give a type signature if the lambda bound variable
5225 is a constructor argument. Here is an example we saw earlier:
5227 f :: T a -> a -> (a, Char)
5228 f (T1 w k) x = (w k x, w 'c' 'd')
5230 Here we do not need to give a type signature to <literal>w</literal>, because
5231 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5238 <sect3 id="implicit-quant">
5239 <title>Implicit quantification</title>
5242 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5243 user-written types, if and only if there is no explicit <literal>forall</literal>,
5244 GHC finds all the type variables mentioned in the type that are not already
5245 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5249 f :: forall a. a -> a
5256 h :: forall b. a -> b -> b
5262 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5265 f :: (a -> a) -> Int
5267 f :: forall a. (a -> a) -> Int
5269 f :: (forall a. a -> a) -> Int
5272 g :: (Ord a => a -> a) -> Int
5273 -- MEANS the illegal type
5274 g :: forall a. (Ord a => a -> a) -> Int
5276 g :: (forall a. Ord a => a -> a) -> Int
5278 The latter produces an illegal type, which you might think is silly,
5279 but at least the rule is simple. If you want the latter type, you
5280 can write your for-alls explicitly. Indeed, doing so is strongly advised
5287 <sect2 id="impredicative-polymorphism">
5288 <title>Impredicative polymorphism
5290 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5291 enabled with <option>-XImpredicativeTypes</option>.
5293 that you can call a polymorphic function at a polymorphic type, and
5294 parameterise data structures over polymorphic types. For example:
5296 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5297 f (Just g) = Just (g [3], g "hello")
5300 Notice here that the <literal>Maybe</literal> type is parameterised by the
5301 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5304 <para>The technical details of this extension are described in the paper
5305 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5306 type inference for higher-rank types and impredicativity</ulink>,
5307 which appeared at ICFP 2006.
5311 <sect2 id="scoped-type-variables">
5312 <title>Lexically scoped type variables
5316 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5317 which some type signatures are simply impossible to write. For example:
5319 f :: forall a. [a] -> [a]
5325 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5326 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5327 The type variables bound by a <literal>forall</literal> scope over
5328 the entire definition of the accompanying value declaration.
5329 In this example, the type variable <literal>a</literal> scopes over the whole
5330 definition of <literal>f</literal>, including over
5331 the type signature for <varname>ys</varname>.
5332 In Haskell 98 it is not possible to declare
5333 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5334 it becomes possible to do so.
5336 <para>Lexically-scoped type variables are enabled by
5337 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5339 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5340 variables work, compared to earlier releases. Read this section
5344 <title>Overview</title>
5346 <para>The design follows the following principles
5348 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5349 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5350 design.)</para></listitem>
5351 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5352 type variables. This means that every programmer-written type signature
5353 (including one that contains free scoped type variables) denotes a
5354 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5355 checker, and no inference is involved.</para></listitem>
5356 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5357 changing the program.</para></listitem>
5361 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5363 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5364 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5365 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5366 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5370 In Haskell, a programmer-written type signature is implicitly quantified over
5371 its free type variables (<ulink
5372 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5374 of the Haskell Report).
5375 Lexically scoped type variables affect this implicit quantification rules
5376 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5377 quantified. For example, if type variable <literal>a</literal> is in scope,
5380 (e :: a -> a) means (e :: a -> a)
5381 (e :: b -> b) means (e :: forall b. b->b)
5382 (e :: a -> b) means (e :: forall b. a->b)
5390 <sect3 id="decl-type-sigs">
5391 <title>Declaration type signatures</title>
5392 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5393 quantification (using <literal>forall</literal>) brings into scope the
5394 explicitly-quantified
5395 type variables, in the definition of the named function. For example:
5397 f :: forall a. [a] -> [a]
5398 f (x:xs) = xs ++ [ x :: a ]
5400 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5401 the definition of "<literal>f</literal>".
5403 <para>This only happens if:
5405 <listitem><para> The quantification in <literal>f</literal>'s type
5406 signature is explicit. For example:
5409 g (x:xs) = xs ++ [ x :: a ]
5411 This program will be rejected, because "<literal>a</literal>" does not scope
5412 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5413 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5414 quantification rules.
5416 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5417 not a pattern binding.
5420 f1 :: forall a. [a] -> [a]
5421 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5423 f2 :: forall a. [a] -> [a]
5424 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5426 f3 :: forall a. [a] -> [a]
5427 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5429 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5430 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5431 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5432 the type signature brings <literal>a</literal> into scope.
5438 <sect3 id="exp-type-sigs">
5439 <title>Expression type signatures</title>
5441 <para>An expression type signature that has <emphasis>explicit</emphasis>
5442 quantification (using <literal>forall</literal>) brings into scope the
5443 explicitly-quantified
5444 type variables, in the annotated expression. For example:
5446 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5448 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5449 type variable <literal>s</literal> into scope, in the annotated expression
5450 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5455 <sect3 id="pattern-type-sigs">
5456 <title>Pattern type signatures</title>
5458 A type signature may occur in any pattern; this is a <emphasis>pattern type
5459 signature</emphasis>.
5462 -- f and g assume that 'a' is already in scope
5463 f = \(x::Int, y::a) -> x
5465 h ((x,y) :: (Int,Bool)) = (y,x)
5467 In the case where all the type variables in the pattern type signature are
5468 already in scope (i.e. bound by the enclosing context), matters are simple: the
5469 signature simply constrains the type of the pattern in the obvious way.
5472 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5473 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5474 that are already in scope. For example:
5476 f :: forall a. [a] -> (Int, [a])
5479 (ys::[a], n) = (reverse xs, length xs) -- OK
5480 zs::[a] = xs ++ ys -- OK
5482 Just (v::b) = ... -- Not OK; b is not in scope
5484 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5485 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5489 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5490 type signature may mention a type variable that is not in scope; in this case,
5491 <emphasis>the signature brings that type variable into scope</emphasis>.
5492 This is particularly important for existential data constructors. For example:
5494 data T = forall a. MkT [a]
5497 k (MkT [t::a]) = MkT t3
5501 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5502 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5503 because it is bound by the pattern match. GHC's rule is that in this situation
5504 (and only then), a pattern type signature can mention a type variable that is
5505 not already in scope; the effect is to bring it into scope, standing for the
5506 existentially-bound type variable.
5509 When a pattern type signature binds a type variable in this way, GHC insists that the
5510 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5511 This means that any user-written type signature always stands for a completely known type.
5514 If all this seems a little odd, we think so too. But we must have
5515 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5516 could not name existentially-bound type variables in subsequent type signatures.
5519 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5520 signature is allowed to mention a lexical variable that is not already in
5522 For example, both <literal>f</literal> and <literal>g</literal> would be
5523 illegal if <literal>a</literal> was not already in scope.
5529 <!-- ==================== Commented out part about result type signatures
5531 <sect3 id="result-type-sigs">
5532 <title>Result type signatures</title>
5535 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5538 {- f assumes that 'a' is already in scope -}
5539 f x y :: [a] = [x,y,x]
5541 g = \ x :: [Int] -> [3,4]
5543 h :: forall a. [a] -> a
5547 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5548 the result of the function. Similarly, the body of the lambda in the RHS of
5549 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5550 alternative in <literal>h</literal> is <literal>a</literal>.
5552 <para> A result type signature never brings new type variables into scope.</para>
5554 There are a couple of syntactic wrinkles. First, notice that all three
5555 examples would parse quite differently with parentheses:
5557 {- f assumes that 'a' is already in scope -}
5558 f x (y :: [a]) = [x,y,x]
5560 g = \ (x :: [Int]) -> [3,4]
5562 h :: forall a. [a] -> a
5566 Now the signature is on the <emphasis>pattern</emphasis>; and
5567 <literal>h</literal> would certainly be ill-typed (since the pattern
5568 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5570 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5571 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5572 token or a parenthesised type of some sort). To see why,
5573 consider how one would parse this:
5582 <sect3 id="cls-inst-scoped-tyvars">
5583 <title>Class and instance declarations</title>
5586 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5587 scope over the methods defined in the <literal>where</literal> part. For example:
5605 <sect2 id="typing-binds">
5606 <title>Generalised typing of mutually recursive bindings</title>
5609 The Haskell Report specifies that a group of bindings (at top level, or in a
5610 <literal>let</literal> or <literal>where</literal>) should be sorted into
5611 strongly-connected components, and then type-checked in dependency order
5612 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5613 Report, Section 4.5.1</ulink>).
5614 As each group is type-checked, any binders of the group that
5616 an explicit type signature are put in the type environment with the specified
5618 and all others are monomorphic until the group is generalised
5619 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5622 <para>Following a suggestion of Mark Jones, in his paper
5623 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5625 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5627 <emphasis>the dependency analysis ignores references to variables that have an explicit
5628 type signature</emphasis>.
5629 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5630 typecheck. For example, consider:
5632 f :: Eq a => a -> Bool
5633 f x = (x == x) || g True || g "Yes"
5635 g y = (y <= y) || f True
5637 This is rejected by Haskell 98, but under Jones's scheme the definition for
5638 <literal>g</literal> is typechecked first, separately from that for
5639 <literal>f</literal>,
5640 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5641 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5642 type is generalised, to get
5644 g :: Ord a => a -> Bool
5646 Now, the definition for <literal>f</literal> is typechecked, with this type for
5647 <literal>g</literal> in the type environment.
5651 The same refined dependency analysis also allows the type signatures of
5652 mutually-recursive functions to have different contexts, something that is illegal in
5653 Haskell 98 (Section 4.5.2, last sentence). With
5654 <option>-XRelaxedPolyRec</option>
5655 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5656 type signatures; in practice this means that only variables bound by the same
5657 pattern binding must have the same context. For example, this is fine:
5659 f :: Eq a => a -> Bool
5660 f x = (x == x) || g True
5662 g :: Ord a => a -> Bool
5663 g y = (y <= y) || f True
5669 <!-- ==================== End of type system extensions ================= -->
5671 <!-- ====================== TEMPLATE HASKELL ======================= -->
5673 <sect1 id="template-haskell">
5674 <title>Template Haskell</title>
5676 <para>Template Haskell allows you to do compile-time meta-programming in
5679 the main technical innovations is discussed in "<ulink
5680 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5681 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5684 There is a Wiki page about
5685 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5686 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5690 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5691 Haskell library reference material</ulink>
5692 (look for module <literal>Language.Haskell.TH</literal>).
5693 Many changes to the original design are described in
5694 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5695 Notes on Template Haskell version 2</ulink>.
5696 Not all of these changes are in GHC, however.
5699 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5700 as a worked example to help get you started.
5704 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5705 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5710 <title>Syntax</title>
5712 <para> Template Haskell has the following new syntactic
5713 constructions. You need to use the flag
5714 <option>-XTemplateHaskell</option>
5715 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5716 </indexterm>to switch these syntactic extensions on
5717 (<option>-XTemplateHaskell</option> is no longer implied by
5718 <option>-fglasgow-exts</option>).</para>
5722 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5723 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5724 There must be no space between the "$" and the identifier or parenthesis. This use
5725 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5726 of "." as an infix operator. If you want the infix operator, put spaces around it.
5728 <para> A splice can occur in place of
5730 <listitem><para> an expression; the spliced expression must
5731 have type <literal>Q Exp</literal></para></listitem>
5732 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5735 Inside a splice you can can only call functions defined in imported modules,
5736 not functions defined elsewhere in the same module.</listitem>
5740 A expression quotation is written in Oxford brackets, thus:
5742 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5743 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5744 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5745 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5746 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5747 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5748 </itemizedlist></para></listitem>
5751 A quasi-quotation can appear in either a pattern context or an
5752 expression context and is also written in Oxford brackets:
5754 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5755 where the "..." is an arbitrary string; a full description of the
5756 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5757 </itemizedlist></para></listitem>
5760 A name can be quoted with either one or two prefix single quotes:
5762 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5763 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5764 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5766 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5767 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5770 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5771 may also be given as an argument to the <literal>reify</literal> function.
5777 (Compared to the original paper, there are many differences of detail.
5778 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5779 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5780 Type splices are not implemented, and neither are pattern splices or quotations.
5784 <sect2> <title> Using Template Haskell </title>
5788 The data types and monadic constructor functions for Template Haskell are in the library
5789 <literal>Language.Haskell.THSyntax</literal>.
5793 You can only run a function at compile time if it is imported from another module. That is,
5794 you can't define a function in a module, and call it from within a splice in the same module.
5795 (It would make sense to do so, but it's hard to implement.)
5799 You can only run a function at compile time if it is imported
5800 from another module <emphasis>that is not part of a mutually-recursive group of modules
5801 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5802 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5803 splice is to be run.</para>
5805 For example, when compiling module A,
5806 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5807 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5811 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5814 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5815 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5816 compiles and runs a program, and then looks at the result. So it's important that
5817 the program it compiles produces results whose representations are identical to
5818 those of the compiler itself.
5822 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5823 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5828 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5829 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5830 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5837 -- Import our template "pr"
5838 import Printf ( pr )
5840 -- The splice operator $ takes the Haskell source code
5841 -- generated at compile time by "pr" and splices it into
5842 -- the argument of "putStrLn".
5843 main = putStrLn ( $(pr "Hello") )
5849 -- Skeletal printf from the paper.
5850 -- It needs to be in a separate module to the one where
5851 -- you intend to use it.
5853 -- Import some Template Haskell syntax
5854 import Language.Haskell.TH
5856 -- Describe a format string
5857 data Format = D | S | L String
5859 -- Parse a format string. This is left largely to you
5860 -- as we are here interested in building our first ever
5861 -- Template Haskell program and not in building printf.
5862 parse :: String -> [Format]
5865 -- Generate Haskell source code from a parsed representation
5866 -- of the format string. This code will be spliced into
5867 -- the module which calls "pr", at compile time.
5868 gen :: [Format] -> Q Exp
5869 gen [D] = [| \n -> show n |]
5870 gen [S] = [| \s -> s |]
5871 gen [L s] = stringE s
5873 -- Here we generate the Haskell code for the splice
5874 -- from an input format string.
5875 pr :: String -> Q Exp
5876 pr s = gen (parse s)
5879 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5882 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5885 <para>Run "main.exe" and here is your output:</para>
5895 <title>Using Template Haskell with Profiling</title>
5896 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5898 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5899 interpreter to run the splice expressions. The bytecode interpreter
5900 runs the compiled expression on top of the same runtime on which GHC
5901 itself is running; this means that the compiled code referred to by
5902 the interpreted expression must be compatible with this runtime, and
5903 in particular this means that object code that is compiled for
5904 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5905 expression, because profiled object code is only compatible with the
5906 profiling version of the runtime.</para>
5908 <para>This causes difficulties if you have a multi-module program
5909 containing Template Haskell code and you need to compile it for
5910 profiling, because GHC cannot load the profiled object code and use it
5911 when executing the splices. Fortunately GHC provides a workaround.
5912 The basic idea is to compile the program twice:</para>
5916 <para>Compile the program or library first the normal way, without
5917 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5920 <para>Then compile it again with <option>-prof</option>, and
5921 additionally use <option>-osuf
5922 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5923 to name the object files differently (you can choose any suffix
5924 that isn't the normal object suffix here). GHC will automatically
5925 load the object files built in the first step when executing splice
5926 expressions. If you omit the <option>-osuf</option> flag when
5927 building with <option>-prof</option> and Template Haskell is used,
5928 GHC will emit an error message. </para>
5933 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5934 <para>Quasi-quotation allows patterns and expressions to be written using
5935 programmer-defined concrete syntax; the motivation behind the extension and
5936 several examples are documented in
5937 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5938 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5939 2007). The example below shows how to write a quasiquoter for a simple
5940 expression language.</para>
5943 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5944 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5945 functions for quoting expressions and patterns, respectively. The first argument
5946 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5947 context of the quasi-quotation statement determines which of the two parsers is
5948 called: if the quasi-quotation occurs in an expression context, the expression
5949 parser is called, and if it occurs in a pattern context, the pattern parser is
5953 Note that in the example we make use of an antiquoted
5954 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5955 (this syntax for anti-quotation was defined by the parser's
5956 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5957 integer value argument of the constructor <literal>IntExpr</literal> when
5958 pattern matching. Please see the referenced paper for further details regarding
5959 anti-quotation as well as the description of a technique that uses SYB to
5960 leverage a single parser of type <literal>String -> a</literal> to generate both
5961 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5962 pattern parser that returns a value of type <literal>Q Pat</literal>.
5965 <para>In general, a quasi-quote has the form
5966 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5967 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5968 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5969 can be arbitrary, and may contain newlines.
5972 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5973 the example, <literal>expr</literal> cannot be defined
5974 in <literal>Main.hs</literal> where it is used, but must be imported.
5985 main = do { print $ eval [$expr|1 + 2|]
5987 { [$expr|'int:n|] -> print n
5996 import qualified Language.Haskell.TH as TH
5997 import Language.Haskell.TH.Quasi
5999 data Expr = IntExpr Integer
6000 | AntiIntExpr String
6001 | BinopExpr BinOp Expr Expr
6003 deriving(Show, Typeable, Data)
6009 deriving(Show, Typeable, Data)
6011 eval :: Expr -> Integer
6012 eval (IntExpr n) = n
6013 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6020 expr = QuasiQuoter parseExprExp parseExprPat
6022 -- Parse an Expr, returning its representation as
6023 -- either a Q Exp or a Q Pat. See the referenced paper
6024 -- for how to use SYB to do this by writing a single
6025 -- parser of type String -> Expr instead of two
6026 -- separate parsers.
6028 parseExprExp :: String -> Q Exp
6031 parseExprPat :: String -> Q Pat
6035 <para>Now run the compiler:
6038 $ ghc --make -XQuasiQuotes Main.hs -o main
6041 <para>Run "main" and here is your output:</para>
6053 <!-- ===================== Arrow notation =================== -->
6055 <sect1 id="arrow-notation">
6056 <title>Arrow notation
6059 <para>Arrows are a generalization of monads introduced by John Hughes.
6060 For more details, see
6065 “Generalising Monads to Arrows”,
6066 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6067 pp67–111, May 2000.
6068 The paper that introduced arrows: a friendly introduction, motivated with
6069 programming examples.
6075 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6076 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6077 Introduced the notation described here.
6083 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6084 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6091 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6092 John Hughes, in <citetitle>5th International Summer School on
6093 Advanced Functional Programming</citetitle>,
6094 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6096 This paper includes another introduction to the notation,
6097 with practical examples.
6103 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6104 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6105 A terse enumeration of the formal rules used
6106 (extracted from comments in the source code).
6112 The arrows web page at
6113 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6118 With the <option>-XArrows</option> flag, GHC supports the arrow
6119 notation described in the second of these papers,
6120 translating it using combinators from the
6121 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6123 What follows is a brief introduction to the notation;
6124 it won't make much sense unless you've read Hughes's paper.
6127 <para>The extension adds a new kind of expression for defining arrows:
6129 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6130 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6132 where <literal>proc</literal> is a new keyword.
6133 The variables of the pattern are bound in the body of the
6134 <literal>proc</literal>-expression,
6135 which is a new sort of thing called a <firstterm>command</firstterm>.
6136 The syntax of commands is as follows:
6138 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6139 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6140 | <replaceable>cmd</replaceable><superscript>0</superscript>
6142 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6143 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6144 infix operators as for expressions, and
6146 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6147 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6148 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6149 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6150 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6151 | <replaceable>fcmd</replaceable>
6153 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6154 | ( <replaceable>cmd</replaceable> )
6155 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6157 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6158 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6159 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6160 | <replaceable>cmd</replaceable>
6162 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6163 except that the bodies are commands instead of expressions.
6167 Commands produce values, but (like monadic computations)
6168 may yield more than one value,
6169 or none, and may do other things as well.
6170 For the most part, familiarity with monadic notation is a good guide to
6172 However the values of expressions, even monadic ones,
6173 are determined by the values of the variables they contain;
6174 this is not necessarily the case for commands.
6178 A simple example of the new notation is the expression
6180 proc x -> f -< x+1
6182 We call this a <firstterm>procedure</firstterm> or
6183 <firstterm>arrow abstraction</firstterm>.
6184 As with a lambda expression, the variable <literal>x</literal>
6185 is a new variable bound within the <literal>proc</literal>-expression.
6186 It refers to the input to the arrow.
6187 In the above example, <literal>-<</literal> is not an identifier but an
6188 new reserved symbol used for building commands from an expression of arrow
6189 type and an expression to be fed as input to that arrow.
6190 (The weird look will make more sense later.)
6191 It may be read as analogue of application for arrows.
6192 The above example is equivalent to the Haskell expression
6194 arr (\ x -> x+1) >>> f
6196 That would make no sense if the expression to the left of
6197 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6198 More generally, the expression to the left of <literal>-<</literal>
6199 may not involve any <firstterm>local variable</firstterm>,
6200 i.e. a variable bound in the current arrow abstraction.
6201 For such a situation there is a variant <literal>-<<</literal>, as in
6203 proc x -> f x -<< x+1
6205 which is equivalent to
6207 arr (\ x -> (f x, x+1)) >>> app
6209 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6211 Such an arrow is equivalent to a monad, so if you're using this form
6212 you may find a monadic formulation more convenient.
6216 <title>do-notation for commands</title>
6219 Another form of command is a form of <literal>do</literal>-notation.
6220 For example, you can write
6229 You can read this much like ordinary <literal>do</literal>-notation,
6230 but with commands in place of monadic expressions.
6231 The first line sends the value of <literal>x+1</literal> as an input to
6232 the arrow <literal>f</literal>, and matches its output against
6233 <literal>y</literal>.
6234 In the next line, the output is discarded.
6235 The arrow <function>returnA</function> is defined in the
6236 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6237 module as <literal>arr id</literal>.
6238 The above example is treated as an abbreviation for
6240 arr (\ x -> (x, x)) >>>
6241 first (arr (\ x -> x+1) >>> f) >>>
6242 arr (\ (y, x) -> (y, (x, y))) >>>
6243 first (arr (\ y -> 2*y) >>> g) >>>
6245 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6246 first (arr (\ (x, z) -> x*z) >>> h) >>>
6247 arr (\ (t, z) -> t+z) >>>
6250 Note that variables not used later in the composition are projected out.
6251 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6253 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6254 module, this reduces to
6256 arr (\ x -> (x+1, x)) >>>
6258 arr (\ (y, x) -> (2*y, (x, y))) >>>
6260 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6262 arr (\ (t, z) -> t+z)
6264 which is what you might have written by hand.
6265 With arrow notation, GHC keeps track of all those tuples of variables for you.
6269 Note that although the above translation suggests that
6270 <literal>let</literal>-bound variables like <literal>z</literal> must be
6271 monomorphic, the actual translation produces Core,
6272 so polymorphic variables are allowed.
6276 It's also possible to have mutually recursive bindings,
6277 using the new <literal>rec</literal> keyword, as in the following example:
6279 counter :: ArrowCircuit a => a Bool Int
6280 counter = proc reset -> do
6281 rec output <- returnA -< if reset then 0 else next
6282 next <- delay 0 -< output+1
6283 returnA -< output
6285 The translation of such forms uses the <function>loop</function> combinator,
6286 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6292 <title>Conditional commands</title>
6295 In the previous example, we used a conditional expression to construct the
6297 Sometimes we want to conditionally execute different commands, as in
6304 which is translated to
6306 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6307 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6309 Since the translation uses <function>|||</function>,
6310 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6314 There are also <literal>case</literal> commands, like
6320 y <- h -< (x1, x2)
6324 The syntax is the same as for <literal>case</literal> expressions,
6325 except that the bodies of the alternatives are commands rather than expressions.
6326 The translation is similar to that of <literal>if</literal> commands.
6332 <title>Defining your own control structures</title>
6335 As we're seen, arrow notation provides constructs,
6336 modelled on those for expressions,
6337 for sequencing, value recursion and conditionals.
6338 But suitable combinators,
6339 which you can define in ordinary Haskell,
6340 may also be used to build new commands out of existing ones.
6341 The basic idea is that a command defines an arrow from environments to values.
6342 These environments assign values to the free local variables of the command.
6343 Thus combinators that produce arrows from arrows
6344 may also be used to build commands from commands.
6345 For example, the <literal>ArrowChoice</literal> class includes a combinator
6347 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6349 so we can use it to build commands:
6351 expr' = proc x -> do
6354 symbol Plus -< ()
6355 y <- term -< ()
6358 symbol Minus -< ()
6359 y <- term -< ()
6362 (The <literal>do</literal> on the first line is needed to prevent the first
6363 <literal><+> ...</literal> from being interpreted as part of the
6364 expression on the previous line.)
6365 This is equivalent to
6367 expr' = (proc x -> returnA -< x)
6368 <+> (proc x -> do
6369 symbol Plus -< ()
6370 y <- term -< ()
6372 <+> (proc x -> do
6373 symbol Minus -< ()
6374 y <- term -< ()
6377 It is essential that this operator be polymorphic in <literal>e</literal>
6378 (representing the environment input to the command
6379 and thence to its subcommands)
6380 and satisfy the corresponding naturality property
6382 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6384 at least for strict <literal>k</literal>.
6385 (This should be automatic if you're not using <function>seq</function>.)
6386 This ensures that environments seen by the subcommands are environments
6387 of the whole command,
6388 and also allows the translation to safely trim these environments.
6389 The operator must also not use any variable defined within the current
6394 We could define our own operator
6396 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6397 untilA body cond = proc x ->
6398 b <- cond -< x
6399 if b then returnA -< ()
6402 untilA body cond -< x
6404 and use it in the same way.
6405 Of course this infix syntax only makes sense for binary operators;
6406 there is also a more general syntax involving special brackets:
6410 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6417 <title>Primitive constructs</title>
6420 Some operators will need to pass additional inputs to their subcommands.
6421 For example, in an arrow type supporting exceptions,
6422 the operator that attaches an exception handler will wish to pass the
6423 exception that occurred to the handler.
6424 Such an operator might have a type
6426 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6428 where <literal>Ex</literal> is the type of exceptions handled.
6429 You could then use this with arrow notation by writing a command
6431 body `handleA` \ ex -> handler
6433 so that if an exception is raised in the command <literal>body</literal>,
6434 the variable <literal>ex</literal> is bound to the value of the exception
6435 and the command <literal>handler</literal>,
6436 which typically refers to <literal>ex</literal>, is entered.
6437 Though the syntax here looks like a functional lambda,
6438 we are talking about commands, and something different is going on.
6439 The input to the arrow represented by a command consists of values for
6440 the free local variables in the command, plus a stack of anonymous values.
6441 In all the prior examples, this stack was empty.
6442 In the second argument to <function>handleA</function>,
6443 this stack consists of one value, the value of the exception.
6444 The command form of lambda merely gives this value a name.
6449 the values on the stack are paired to the right of the environment.
6450 So operators like <function>handleA</function> that pass
6451 extra inputs to their subcommands can be designed for use with the notation
6452 by pairing the values with the environment in this way.
6453 More precisely, the type of each argument of the operator (and its result)
6454 should have the form
6456 a (...(e,t1), ... tn) t
6458 where <replaceable>e</replaceable> is a polymorphic variable
6459 (representing the environment)
6460 and <replaceable>ti</replaceable> are the types of the values on the stack,
6461 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6462 The polymorphic variable <replaceable>e</replaceable> must not occur in
6463 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6464 <replaceable>t</replaceable>.
6465 However the arrows involved need not be the same.
6466 Here are some more examples of suitable operators:
6468 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6469 runReader :: ... => a e c -> a' (e,State) c
6470 runState :: ... => a e c -> a' (e,State) (c,State)
6472 We can supply the extra input required by commands built with the last two
6473 by applying them to ordinary expressions, as in
6477 (|runReader (do { ... })|) s
6479 which adds <literal>s</literal> to the stack of inputs to the command
6480 built using <function>runReader</function>.
6484 The command versions of lambda abstraction and application are analogous to
6485 the expression versions.
6486 In particular, the beta and eta rules describe equivalences of commands.
6487 These three features (operators, lambda abstraction and application)
6488 are the core of the notation; everything else can be built using them,
6489 though the results would be somewhat clumsy.
6490 For example, we could simulate <literal>do</literal>-notation by defining
6492 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6493 u `bind` f = returnA &&& u >>> f
6495 bind_ :: Arrow a => a e b -> a e c -> a e c
6496 u `bind_` f = u `bind` (arr fst >>> f)
6498 We could simulate <literal>if</literal> by defining
6500 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6501 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6508 <title>Differences with the paper</title>
6513 <para>Instead of a single form of arrow application (arrow tail) with two
6514 translations, the implementation provides two forms
6515 <quote><literal>-<</literal></quote> (first-order)
6516 and <quote><literal>-<<</literal></quote> (higher-order).
6521 <para>User-defined operators are flagged with banana brackets instead of
6522 a new <literal>form</literal> keyword.
6531 <title>Portability</title>
6534 Although only GHC implements arrow notation directly,
6535 there is also a preprocessor
6537 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6538 that translates arrow notation into Haskell 98
6539 for use with other Haskell systems.
6540 You would still want to check arrow programs with GHC;
6541 tracing type errors in the preprocessor output is not easy.
6542 Modules intended for both GHC and the preprocessor must observe some
6543 additional restrictions:
6548 The module must import
6549 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6555 The preprocessor cannot cope with other Haskell extensions.
6556 These would have to go in separate modules.
6562 Because the preprocessor targets Haskell (rather than Core),
6563 <literal>let</literal>-bound variables are monomorphic.
6574 <!-- ==================== BANG PATTERNS ================= -->
6576 <sect1 id="bang-patterns">
6577 <title>Bang patterns
6578 <indexterm><primary>Bang patterns</primary></indexterm>
6580 <para>GHC supports an extension of pattern matching called <emphasis>bang
6581 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
6583 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6584 prime feature description</ulink> contains more discussion and examples
6585 than the material below.
6588 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6591 <sect2 id="bang-patterns-informal">
6592 <title>Informal description of bang patterns
6595 The main idea is to add a single new production to the syntax of patterns:
6599 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6600 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6605 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6606 whereas without the bang it would be lazy.
6607 Bang patterns can be nested of course:
6611 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6612 <literal>y</literal>.
6613 A bang only really has an effect if it precedes a variable or wild-card pattern:
6618 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
6619 forces evaluation anyway does nothing.
6621 Bang patterns work in <literal>case</literal> expressions too, of course:
6623 g5 x = let y = f x in body
6624 g6 x = case f x of { y -> body }
6625 g7 x = case f x of { !y -> body }
6627 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6628 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6629 result, and then evaluates <literal>body</literal>.
6631 Bang patterns work in <literal>let</literal> and <literal>where</literal>
6632 definitions too. For example:
6636 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
6637 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
6638 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
6639 in a function argument <literal>![x,y]</literal> means the
6640 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
6641 is part of the syntax of <literal>let</literal> bindings.
6646 <sect2 id="bang-patterns-sem">
6647 <title>Syntax and semantics
6651 We add a single new production to the syntax of patterns:
6655 There is one problem with syntactic ambiguity. Consider:
6659 Is this a definition of the infix function "<literal>(!)</literal>",
6660 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6661 ambiguity in favour of the latter. If you want to define
6662 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6667 The semantics of Haskell pattern matching is described in <ulink
6668 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6669 Section 3.17.2</ulink> of the Haskell Report. To this description add
6670 one extra item 10, saying:
6671 <itemizedlist><listitem><para>Matching
6672 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6673 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6674 <listitem><para>otherwise, <literal>pat</literal> is matched against
6675 <literal>v</literal></para></listitem>
6677 </para></listitem></itemizedlist>
6678 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6679 Section 3.17.3</ulink>, add a new case (t):
6681 case v of { !pat -> e; _ -> e' }
6682 = v `seq` case v of { pat -> e; _ -> e' }
6685 That leaves let expressions, whose translation is given in
6686 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6688 of the Haskell Report.
6689 In the translation box, first apply
6690 the following transformation: for each pattern <literal>pi</literal> that is of
6691 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6692 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6693 have a bang at the top, apply the rules in the existing box.
6695 <para>The effect of the let rule is to force complete matching of the pattern
6696 <literal>qi</literal> before evaluation of the body is begun. The bang is
6697 retained in the translated form in case <literal>qi</literal> is a variable,
6705 The let-binding can be recursive. However, it is much more common for
6706 the let-binding to be non-recursive, in which case the following law holds:
6707 <literal>(let !p = rhs in body)</literal>
6709 <literal>(case rhs of !p -> body)</literal>
6712 A pattern with a bang at the outermost level is not allowed at the top level of
6718 <!-- ==================== ASSERTIONS ================= -->
6720 <sect1 id="assertions">
6722 <indexterm><primary>Assertions</primary></indexterm>
6726 If you want to make use of assertions in your standard Haskell code, you
6727 could define a function like the following:
6733 assert :: Bool -> a -> a
6734 assert False x = error "assertion failed!"
6741 which works, but gives you back a less than useful error message --
6742 an assertion failed, but which and where?
6746 One way out is to define an extended <function>assert</function> function which also
6747 takes a descriptive string to include in the error message and
6748 perhaps combine this with the use of a pre-processor which inserts
6749 the source location where <function>assert</function> was used.
6753 Ghc offers a helping hand here, doing all of this for you. For every
6754 use of <function>assert</function> in the user's source:
6760 kelvinToC :: Double -> Double
6761 kelvinToC k = assert (k >= 0.0) (k+273.15)
6767 Ghc will rewrite this to also include the source location where the
6774 assert pred val ==> assertError "Main.hs|15" pred val
6780 The rewrite is only performed by the compiler when it spots
6781 applications of <function>Control.Exception.assert</function>, so you
6782 can still define and use your own versions of
6783 <function>assert</function>, should you so wish. If not, import
6784 <literal>Control.Exception</literal> to make use
6785 <function>assert</function> in your code.
6789 GHC ignores assertions when optimisation is turned on with the
6790 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6791 <literal>assert pred e</literal> will be rewritten to
6792 <literal>e</literal>. You can also disable assertions using the
6793 <option>-fignore-asserts</option>
6794 option<indexterm><primary><option>-fignore-asserts</option></primary>
6795 </indexterm>.</para>
6798 Assertion failures can be caught, see the documentation for the
6799 <literal>Control.Exception</literal> library for the details.
6805 <!-- =============================== PRAGMAS =========================== -->
6807 <sect1 id="pragmas">
6808 <title>Pragmas</title>
6810 <indexterm><primary>pragma</primary></indexterm>
6812 <para>GHC supports several pragmas, or instructions to the
6813 compiler placed in the source code. Pragmas don't normally affect
6814 the meaning of the program, but they might affect the efficiency
6815 of the generated code.</para>
6817 <para>Pragmas all take the form
6819 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6821 where <replaceable>word</replaceable> indicates the type of
6822 pragma, and is followed optionally by information specific to that
6823 type of pragma. Case is ignored in
6824 <replaceable>word</replaceable>. The various values for
6825 <replaceable>word</replaceable> that GHC understands are described
6826 in the following sections; any pragma encountered with an
6827 unrecognised <replaceable>word</replaceable> is (silently)
6828 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6829 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6831 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6832 pragma must precede the <literal>module</literal> keyword in the file.
6833 There can be as many file-header pragmas as you please, and they can be
6834 preceded or followed by comments.</para>
6836 <sect2 id="language-pragma">
6837 <title>LANGUAGE pragma</title>
6839 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6840 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6842 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6844 It is the intention that all Haskell compilers support the
6845 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6846 all extensions are supported by all compilers, of
6847 course. The <literal>LANGUAGE</literal> pragma should be used instead
6848 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6850 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6852 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6854 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6856 <para>Every language extension can also be turned into a command-line flag
6857 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6858 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6861 <para>A list of all supported language extensions can be obtained by invoking
6862 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6864 <para>Any extension from the <literal>Extension</literal> type defined in
6866 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6867 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6871 <sect2 id="options-pragma">
6872 <title>OPTIONS_GHC pragma</title>
6873 <indexterm><primary>OPTIONS_GHC</primary>
6875 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6878 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6879 additional options that are given to the compiler when compiling
6880 this source file. See <xref linkend="source-file-options"/> for
6883 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6884 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6887 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6889 <sect2 id="include-pragma">
6890 <title>INCLUDE pragma</title>
6892 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6893 of C header files that should be <literal>#include</literal>'d into
6894 the C source code generated by the compiler for the current module (if
6895 compiling via C). For example:</para>
6898 {-# INCLUDE "foo.h" #-}
6899 {-# INCLUDE <stdio.h> #-}</programlisting>
6901 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6903 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6904 to the <option>-#include</option> option (<xref
6905 linkend="options-C-compiler" />), because the
6906 <literal>INCLUDE</literal> pragma is understood by other
6907 compilers. Yet another alternative is to add the include file to each
6908 <literal>foreign import</literal> declaration in your code, but we
6909 don't recommend using this approach with GHC.</para>
6912 <sect2 id="warning-deprecated-pragma">
6913 <title>WARNING and DEPRECATED pragmas</title>
6914 <indexterm><primary>WARNING</primary></indexterm>
6915 <indexterm><primary>DEPRECATED</primary></indexterm>
6917 <para>The WARNING pragma allows you to attach an arbitrary warning
6918 to a particular function, class, or type.
6919 A DEPRECATED pragma lets you specify that
6920 a particular function, class, or type is deprecated.
6921 There are two ways of using these pragmas.
6925 <para>You can work on an entire module thus:</para>
6927 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6932 module Wibble {-# WARNING "This is an unstable interface." #-} where
6935 <para>When you compile any module that import
6936 <literal>Wibble</literal>, GHC will print the specified
6941 <para>You can attach a warning to a function, class, type, or data constructor, with the
6942 following top-level declarations:</para>
6944 {-# DEPRECATED f, C, T "Don't use these" #-}
6945 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6947 <para>When you compile any module that imports and uses any
6948 of the specified entities, GHC will print the specified
6950 <para> You can only attach to entities declared at top level in the module
6951 being compiled, and you can only use unqualified names in the list of
6952 entities. A capitalised name, such as <literal>T</literal>
6953 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6954 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6955 both are in scope. If both are in scope, there is currently no way to
6956 specify one without the other (c.f. fixities
6957 <xref linkend="infix-tycons"/>).</para>
6960 Warnings and deprecations are not reported for
6961 (a) uses within the defining module, and
6962 (b) uses in an export list.
6963 The latter reduces spurious complaints within a library
6964 in which one module gathers together and re-exports
6965 the exports of several others.
6967 <para>You can suppress the warnings with the flag
6968 <option>-fno-warn-warnings-deprecations</option>.</para>
6971 <sect2 id="inline-noinline-pragma">
6972 <title>INLINE and NOINLINE pragmas</title>
6974 <para>These pragmas control the inlining of function
6977 <sect3 id="inline-pragma">
6978 <title>INLINE pragma</title>
6979 <indexterm><primary>INLINE</primary></indexterm>
6981 <para>GHC (with <option>-O</option>, as always) tries to
6982 inline (or “unfold”) functions/values that are
6983 “small enough,” thus avoiding the call overhead
6984 and possibly exposing other more-wonderful optimisations.
6985 Normally, if GHC decides a function is “too
6986 expensive” to inline, it will not do so, nor will it
6987 export that unfolding for other modules to use.</para>
6989 <para>The sledgehammer you can bring to bear is the
6990 <literal>INLINE</literal><indexterm><primary>INLINE
6991 pragma</primary></indexterm> pragma, used thusly:</para>
6994 key_function :: Int -> String -> (Bool, Double)
6995 {-# INLINE key_function #-}
6998 <para>The major effect of an <literal>INLINE</literal> pragma
6999 is to declare a function's “cost” to be very low.
7000 The normal unfolding machinery will then be very keen to
7001 inline it. However, an <literal>INLINE</literal> pragma for a
7002 function "<literal>f</literal>" has a number of other effects:
7005 No functions are inlined into <literal>f</literal>. Otherwise
7006 GHC might inline a big function into <literal>f</literal>'s right hand side,
7007 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7010 The float-in, float-out, and common-sub-expression transformations are not
7011 applied to the body of <literal>f</literal>.
7014 An INLINE function is not worker/wrappered by strictness analysis.
7015 It's going to be inlined wholesale instead.
7018 All of these effects are aimed at ensuring that what gets inlined is
7019 exactly what you asked for, no more and no less.
7021 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7022 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7023 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7024 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7025 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7026 when there is no choice even an INLINE function can be selected, in which case
7027 the INLINE pragma is ignored.
7028 For example, for a self-recursive function, the loop breaker can only be the function
7029 itself, so an INLINE pragma is always ignored.</para>
7031 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7032 function can be put anywhere its type signature could be
7035 <para><literal>INLINE</literal> pragmas are a particularly
7037 <literal>then</literal>/<literal>return</literal> (or
7038 <literal>bind</literal>/<literal>unit</literal>) functions in
7039 a monad. For example, in GHC's own
7040 <literal>UniqueSupply</literal> monad code, we have:</para>
7043 {-# INLINE thenUs #-}
7044 {-# INLINE returnUs #-}
7047 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7048 linkend="noinline-pragma"/>).</para>
7050 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7051 so if you want your code to be HBC-compatible you'll have to surround
7052 the pragma with C pre-processor directives
7053 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7057 <sect3 id="noinline-pragma">
7058 <title>NOINLINE pragma</title>
7060 <indexterm><primary>NOINLINE</primary></indexterm>
7061 <indexterm><primary>NOTINLINE</primary></indexterm>
7063 <para>The <literal>NOINLINE</literal> pragma does exactly what
7064 you'd expect: it stops the named function from being inlined
7065 by the compiler. You shouldn't ever need to do this, unless
7066 you're very cautious about code size.</para>
7068 <para><literal>NOTINLINE</literal> is a synonym for
7069 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7070 specified by Haskell 98 as the standard way to disable
7071 inlining, so it should be used if you want your code to be
7075 <sect3 id="phase-control">
7076 <title>Phase control</title>
7078 <para> Sometimes you want to control exactly when in GHC's
7079 pipeline the INLINE pragma is switched on. Inlining happens
7080 only during runs of the <emphasis>simplifier</emphasis>. Each
7081 run of the simplifier has a different <emphasis>phase
7082 number</emphasis>; the phase number decreases towards zero.
7083 If you use <option>-dverbose-core2core</option> you'll see the
7084 sequence of phase numbers for successive runs of the
7085 simplifier. In an INLINE pragma you can optionally specify a
7089 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7090 <literal>f</literal>
7091 until phase <literal>k</literal>, but from phase
7092 <literal>k</literal> onwards be very keen to inline it.
7095 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7096 <literal>f</literal>
7097 until phase <literal>k</literal>, but from phase
7098 <literal>k</literal> onwards do not inline it.
7101 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7102 <literal>f</literal>
7103 until phase <literal>k</literal>, but from phase
7104 <literal>k</literal> onwards be willing to inline it (as if
7105 there was no pragma).
7108 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7109 <literal>f</literal>
7110 until phase <literal>k</literal>, but from phase
7111 <literal>k</literal> onwards do not inline it.
7114 The same information is summarised here:
7116 -- Before phase 2 Phase 2 and later
7117 {-# INLINE [2] f #-} -- No Yes
7118 {-# INLINE [~2] f #-} -- Yes No
7119 {-# NOINLINE [2] f #-} -- No Maybe
7120 {-# NOINLINE [~2] f #-} -- Maybe No
7122 {-# INLINE f #-} -- Yes Yes
7123 {-# NOINLINE f #-} -- No No
7125 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7126 function body is small, or it is applied to interesting-looking arguments etc).
7127 Another way to understand the semantics is this:
7129 <listitem><para>For both INLINE and NOINLINE, the phase number says
7130 when inlining is allowed at all.</para></listitem>
7131 <listitem><para>The INLINE pragma has the additional effect of making the
7132 function body look small, so that when inlining is allowed it is very likely to
7137 <para>The same phase-numbering control is available for RULES
7138 (<xref linkend="rewrite-rules"/>).</para>
7142 <sect2 id="annotation-pragmas">
7143 <title>ANN pragmas</title>
7145 <para>GHC offers the ability to annotate various code constructs with additional
7146 data by using three pragmas. This data can then be inspected at a later date by
7147 using GHC-as-a-library.</para>
7149 <sect3 id="ann-pragma">
7150 <title>Annotating values</title>
7152 <indexterm><primary>ANN</primary></indexterm>
7154 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7155 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7156 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7157 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7158 you would do this:</para>
7161 {-# ANN foo (Just "Hello") #-}
7166 A number of restrictions apply to use of annotations:
7168 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7169 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7170 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7171 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7172 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7174 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7175 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7178 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7179 please give the GHC team a shout</ulink>.
7182 <para>However, apart from these restrictions, many things are allowed, including expressions which not fully evaluated!
7183 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7186 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7191 <sect3 id="typeann-pragma">
7192 <title>Annotating types</title>
7194 <indexterm><primary>ANN type</primary></indexterm>
7195 <indexterm><primary>ANN</primary></indexterm>
7197 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7200 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7205 <sect3 id="modann-pragma">
7206 <title>Annotating modules</title>
7208 <indexterm><primary>ANN module</primary></indexterm>
7209 <indexterm><primary>ANN</primary></indexterm>
7211 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7214 {-# ANN module (Just "A `Maybe String' annotation") #-}
7219 <sect2 id="line-pragma">
7220 <title>LINE pragma</title>
7222 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7223 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7224 <para>This pragma is similar to C's <literal>#line</literal>
7225 pragma, and is mainly for use in automatically generated Haskell
7226 code. It lets you specify the line number and filename of the
7227 original code; for example</para>
7229 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7231 <para>if you'd generated the current file from something called
7232 <filename>Foo.vhs</filename> and this line corresponds to line
7233 42 in the original. GHC will adjust its error messages to refer
7234 to the line/file named in the <literal>LINE</literal>
7239 <title>RULES pragma</title>
7241 <para>The RULES pragma lets you specify rewrite rules. It is
7242 described in <xref linkend="rewrite-rules"/>.</para>
7245 <sect2 id="specialize-pragma">
7246 <title>SPECIALIZE pragma</title>
7248 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7249 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7250 <indexterm><primary>overloading, death to</primary></indexterm>
7252 <para>(UK spelling also accepted.) For key overloaded
7253 functions, you can create extra versions (NB: more code space)
7254 specialised to particular types. Thus, if you have an
7255 overloaded function:</para>
7258 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7261 <para>If it is heavily used on lists with
7262 <literal>Widget</literal> keys, you could specialise it as
7266 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7269 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7270 be put anywhere its type signature could be put.</para>
7272 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7273 (a) a specialised version of the function and (b) a rewrite rule
7274 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7275 un-specialised function into a call to the specialised one.</para>
7277 <para>The type in a SPECIALIZE pragma can be any type that is less
7278 polymorphic than the type of the original function. In concrete terms,
7279 if the original function is <literal>f</literal> then the pragma
7281 {-# SPECIALIZE f :: <type> #-}
7283 is valid if and only if the definition
7285 f_spec :: <type>
7288 is valid. Here are some examples (where we only give the type signature
7289 for the original function, not its code):
7291 f :: Eq a => a -> b -> b
7292 {-# SPECIALISE f :: Int -> b -> b #-}
7294 g :: (Eq a, Ix b) => a -> b -> b
7295 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7297 h :: Eq a => a -> a -> a
7298 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7300 The last of these examples will generate a
7301 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7302 well. If you use this kind of specialisation, let us know how well it works.
7305 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7306 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7307 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7308 The <literal>INLINE</literal> pragma affects the specialised version of the
7309 function (only), and applies even if the function is recursive. The motivating
7312 -- A GADT for arrays with type-indexed representation
7314 ArrInt :: !Int -> ByteArray# -> Arr Int
7315 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7317 (!:) :: Arr e -> Int -> e
7318 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7319 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7320 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7321 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7323 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7324 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7325 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7326 the specialised function will be inlined. It has two calls to
7327 <literal>(!:)</literal>,
7328 both at type <literal>Int</literal>. Both these calls fire the first
7329 specialisation, whose body is also inlined. The result is a type-based
7330 unrolling of the indexing function.</para>
7331 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7332 on an ordinarily-recursive function.</para>
7334 <para>Note: In earlier versions of GHC, it was possible to provide your own
7335 specialised function for a given type:
7338 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7341 This feature has been removed, as it is now subsumed by the
7342 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7346 <sect2 id="specialize-instance-pragma">
7347 <title>SPECIALIZE instance pragma
7351 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7352 <indexterm><primary>overloading, death to</primary></indexterm>
7353 Same idea, except for instance declarations. For example:
7356 instance (Eq a) => Eq (Foo a) where {
7357 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7361 The pragma must occur inside the <literal>where</literal> part
7362 of the instance declaration.
7365 Compatible with HBC, by the way, except perhaps in the placement
7371 <sect2 id="unpack-pragma">
7372 <title>UNPACK pragma</title>
7374 <indexterm><primary>UNPACK</primary></indexterm>
7376 <para>The <literal>UNPACK</literal> indicates to the compiler
7377 that it should unpack the contents of a constructor field into
7378 the constructor itself, removing a level of indirection. For
7382 data T = T {-# UNPACK #-} !Float
7383 {-# UNPACK #-} !Float
7386 <para>will create a constructor <literal>T</literal> containing
7387 two unboxed floats. This may not always be an optimisation: if
7388 the <function>T</function> constructor is scrutinised and the
7389 floats passed to a non-strict function for example, they will
7390 have to be reboxed (this is done automatically by the
7393 <para>Unpacking constructor fields should only be used in
7394 conjunction with <option>-O</option>, in order to expose
7395 unfoldings to the compiler so the reboxing can be removed as
7396 often as possible. For example:</para>
7400 f (T f1 f2) = f1 + f2
7403 <para>The compiler will avoid reboxing <function>f1</function>
7404 and <function>f2</function> by inlining <function>+</function>
7405 on floats, but only when <option>-O</option> is on.</para>
7407 <para>Any single-constructor data is eligible for unpacking; for
7411 data T = T {-# UNPACK #-} !(Int,Int)
7414 <para>will store the two <literal>Int</literal>s directly in the
7415 <function>T</function> constructor, by flattening the pair.
7416 Multi-level unpacking is also supported:
7419 data T = T {-# UNPACK #-} !S
7420 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7423 will store two unboxed <literal>Int#</literal>s
7424 directly in the <function>T</function> constructor. The
7425 unpacker can see through newtypes, too.</para>
7427 <para>If a field cannot be unpacked, you will not get a warning,
7428 so it might be an idea to check the generated code with
7429 <option>-ddump-simpl</option>.</para>
7431 <para>See also the <option>-funbox-strict-fields</option> flag,
7432 which essentially has the effect of adding
7433 <literal>{-# UNPACK #-}</literal> to every strict
7434 constructor field.</para>
7437 <sect2 id="source-pragma">
7438 <title>SOURCE pragma</title>
7440 <indexterm><primary>SOURCE</primary></indexterm>
7441 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7442 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7448 <!-- ======================= REWRITE RULES ======================== -->
7450 <sect1 id="rewrite-rules">
7451 <title>Rewrite rules
7453 <indexterm><primary>RULES pragma</primary></indexterm>
7454 <indexterm><primary>pragma, RULES</primary></indexterm>
7455 <indexterm><primary>rewrite rules</primary></indexterm></title>
7458 The programmer can specify rewrite rules as part of the source program
7464 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7469 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7470 If you need more information, then <option>-ddump-rule-firings</option> shows you
7471 each individual rule firing in detail.
7475 <title>Syntax</title>
7478 From a syntactic point of view:
7484 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7485 may be generated by the layout rule).
7491 The layout rule applies in a pragma.
7492 Currently no new indentation level
7493 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7494 you must lay out the starting in the same column as the enclosing definitions.
7497 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7498 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7501 Furthermore, the closing <literal>#-}</literal>
7502 should start in a column to the right of the opening <literal>{-#</literal>.
7508 Each rule has a name, enclosed in double quotes. The name itself has
7509 no significance at all. It is only used when reporting how many times the rule fired.
7515 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7516 immediately after the name of the rule. Thus:
7519 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7522 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7523 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7532 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7533 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7534 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7535 by spaces, just like in a type <literal>forall</literal>.
7541 A pattern variable may optionally have a type signature.
7542 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7543 For example, here is the <literal>foldr/build</literal> rule:
7546 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7547 foldr k z (build g) = g k z
7550 Since <function>g</function> has a polymorphic type, it must have a type signature.
7557 The left hand side of a rule must consist of a top-level variable applied
7558 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7561 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7562 "wrong2" forall f. f True = True
7565 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7572 A rule does not need to be in the same module as (any of) the
7573 variables it mentions, though of course they need to be in scope.
7579 All rules are implicitly exported from the module, and are therefore
7580 in force in any module that imports the module that defined the rule, directly
7581 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7582 in force when compiling A.) The situation is very similar to that for instance
7590 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7591 any other flag settings. Furthermore, inside a RULE, the language extension
7592 <option>-XScopedTypeVariables</option> is automatically enabled; see
7593 <xref linkend="scoped-type-variables"/>.
7599 Like other pragmas, RULE pragmas are always checked for scope errors, and
7600 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7601 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7602 if the <option>-fenable-rewrite-rules</option> flag is
7603 on (see <xref linkend="rule-semantics"/>).
7612 <sect2 id="rule-semantics">
7613 <title>Semantics</title>
7616 From a semantic point of view:
7621 Rules are enabled (that is, used during optimisation)
7622 by the <option>-fenable-rewrite-rules</option> flag.
7623 This flag is implied by <option>-O</option>, and may be switched
7624 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7625 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7626 may not do what you expect, though, because without <option>-O</option> GHC
7627 ignores all optimisation information in interface files;
7628 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7629 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7630 has no effect on parsing or typechecking.
7636 Rules are regarded as left-to-right rewrite rules.
7637 When GHC finds an expression that is a substitution instance of the LHS
7638 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7639 By "a substitution instance" we mean that the LHS can be made equal to the
7640 expression by substituting for the pattern variables.
7647 GHC makes absolutely no attempt to verify that the LHS and RHS
7648 of a rule have the same meaning. That is undecidable in general, and
7649 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7656 GHC makes no attempt to make sure that the rules are confluent or
7657 terminating. For example:
7660 "loop" forall x y. f x y = f y x
7663 This rule will cause the compiler to go into an infinite loop.
7670 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7676 GHC currently uses a very simple, syntactic, matching algorithm
7677 for matching a rule LHS with an expression. It seeks a substitution
7678 which makes the LHS and expression syntactically equal modulo alpha
7679 conversion. The pattern (rule), but not the expression, is eta-expanded if
7680 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7681 But not beta conversion (that's called higher-order matching).
7685 Matching is carried out on GHC's intermediate language, which includes
7686 type abstractions and applications. So a rule only matches if the
7687 types match too. See <xref linkend="rule-spec"/> below.
7693 GHC keeps trying to apply the rules as it optimises the program.
7694 For example, consider:
7703 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7704 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7705 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7706 not be substituted, and the rule would not fire.
7713 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7714 results. Consider this (artificial) example
7717 {-# RULES "f" f True = False #-}
7723 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7728 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7730 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7731 would have been a better chance that <literal>f</literal>'s RULE might fire.
7734 The way to get predictable behaviour is to use a NOINLINE
7735 pragma on <literal>f</literal>, to ensure
7736 that it is not inlined until its RULEs have had a chance to fire.
7746 <title>List fusion</title>
7749 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7750 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7751 intermediate list should be eliminated entirely.
7755 The following are good producers:
7767 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7773 Explicit lists (e.g. <literal>[True, False]</literal>)
7779 The cons constructor (e.g <literal>3:4:[]</literal>)
7785 <function>++</function>
7791 <function>map</function>
7797 <function>take</function>, <function>filter</function>
7803 <function>iterate</function>, <function>repeat</function>
7809 <function>zip</function>, <function>zipWith</function>
7818 The following are good consumers:
7830 <function>array</function> (on its second argument)
7836 <function>++</function> (on its first argument)
7842 <function>foldr</function>
7848 <function>map</function>
7854 <function>take</function>, <function>filter</function>
7860 <function>concat</function>
7866 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7872 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7873 will fuse with one but not the other)
7879 <function>partition</function>
7885 <function>head</function>
7891 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7897 <function>sequence_</function>
7903 <function>msum</function>
7909 <function>sortBy</function>
7918 So, for example, the following should generate no intermediate lists:
7921 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7927 This list could readily be extended; if there are Prelude functions that you use
7928 a lot which are not included, please tell us.
7932 If you want to write your own good consumers or producers, look at the
7933 Prelude definitions of the above functions to see how to do so.
7938 <sect2 id="rule-spec">
7939 <title>Specialisation
7943 Rewrite rules can be used to get the same effect as a feature
7944 present in earlier versions of GHC.
7945 For example, suppose that:
7948 genericLookup :: Ord a => Table a b -> a -> b
7949 intLookup :: Table Int b -> Int -> b
7952 where <function>intLookup</function> is an implementation of
7953 <function>genericLookup</function> that works very fast for
7954 keys of type <literal>Int</literal>. You might wish
7955 to tell GHC to use <function>intLookup</function> instead of
7956 <function>genericLookup</function> whenever the latter was called with
7957 type <literal>Table Int b -> Int -> b</literal>.
7958 It used to be possible to write
7961 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7964 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7967 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7970 This slightly odd-looking rule instructs GHC to replace
7971 <function>genericLookup</function> by <function>intLookup</function>
7972 <emphasis>whenever the types match</emphasis>.
7973 What is more, this rule does not need to be in the same
7974 file as <function>genericLookup</function>, unlike the
7975 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7976 have an original definition available to specialise).
7979 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7980 <function>intLookup</function> really behaves as a specialised version
7981 of <function>genericLookup</function>!!!</para>
7983 <para>An example in which using <literal>RULES</literal> for
7984 specialisation will Win Big:
7987 toDouble :: Real a => a -> Double
7988 toDouble = fromRational . toRational
7990 {-# RULES "toDouble/Int" toDouble = i2d #-}
7991 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7994 The <function>i2d</function> function is virtually one machine
7995 instruction; the default conversion—via an intermediate
7996 <literal>Rational</literal>—is obscenely expensive by
8003 <title>Controlling what's going on</title>
8011 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8017 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8018 If you add <option>-dppr-debug</option> you get a more detailed listing.
8024 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8027 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8028 {-# INLINE build #-}
8032 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8033 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8034 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8035 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8042 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8043 see how to write rules that will do fusion and yet give an efficient
8044 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8054 <sect2 id="core-pragma">
8055 <title>CORE pragma</title>
8057 <indexterm><primary>CORE pragma</primary></indexterm>
8058 <indexterm><primary>pragma, CORE</primary></indexterm>
8059 <indexterm><primary>core, annotation</primary></indexterm>
8062 The external core format supports <quote>Note</quote> annotations;
8063 the <literal>CORE</literal> pragma gives a way to specify what these
8064 should be in your Haskell source code. Syntactically, core
8065 annotations are attached to expressions and take a Haskell string
8066 literal as an argument. The following function definition shows an
8070 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8073 Semantically, this is equivalent to:
8081 However, when external core is generated (via
8082 <option>-fext-core</option>), there will be Notes attached to the
8083 expressions <function>show</function> and <varname>x</varname>.
8084 The core function declaration for <function>f</function> is:
8088 f :: %forall a . GHCziShow.ZCTShow a ->
8089 a -> GHCziBase.ZMZN GHCziBase.Char =
8090 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8092 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8094 (tpl1::GHCziBase.Int ->
8096 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8098 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8099 (tpl3::GHCziBase.ZMZN a ->
8100 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8108 Here, we can see that the function <function>show</function> (which
8109 has been expanded out to a case expression over the Show dictionary)
8110 has a <literal>%note</literal> attached to it, as does the
8111 expression <varname>eta</varname> (which used to be called
8112 <varname>x</varname>).
8119 <sect1 id="special-ids">
8120 <title>Special built-in functions</title>
8121 <para>GHC has a few built-in functions with special behaviour. These
8122 are now described in the module <ulink
8123 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8124 in the library documentation.</para>
8128 <sect1 id="generic-classes">
8129 <title>Generic classes</title>
8132 The ideas behind this extension are described in detail in "Derivable type classes",
8133 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8134 An example will give the idea:
8142 fromBin :: [Int] -> (a, [Int])
8144 toBin {| Unit |} Unit = []
8145 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8146 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8147 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8149 fromBin {| Unit |} bs = (Unit, bs)
8150 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8151 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8152 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8153 (y,bs'') = fromBin bs'
8156 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8157 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8158 which are defined thus in the library module <literal>Generics</literal>:
8162 data a :+: b = Inl a | Inr b
8163 data a :*: b = a :*: b
8166 Now you can make a data type into an instance of Bin like this:
8168 instance (Bin a, Bin b) => Bin (a,b)
8169 instance Bin a => Bin [a]
8171 That is, just leave off the "where" clause. Of course, you can put in the
8172 where clause and over-ride whichever methods you please.
8176 <title> Using generics </title>
8177 <para>To use generics you need to</para>
8180 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8181 <option>-XGenerics</option> (to generate extra per-data-type code),
8182 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8186 <para>Import the module <literal>Generics</literal> from the
8187 <literal>lang</literal> package. This import brings into
8188 scope the data types <literal>Unit</literal>,
8189 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8190 don't need this import if you don't mention these types
8191 explicitly; for example, if you are simply giving instance
8192 declarations.)</para>
8197 <sect2> <title> Changes wrt the paper </title>
8199 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8200 can be written infix (indeed, you can now use
8201 any operator starting in a colon as an infix type constructor). Also note that
8202 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8203 Finally, note that the syntax of the type patterns in the class declaration
8204 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8205 alone would ambiguous when they appear on right hand sides (an extension we
8206 anticipate wanting).
8210 <sect2> <title>Terminology and restrictions</title>
8212 Terminology. A "generic default method" in a class declaration
8213 is one that is defined using type patterns as above.
8214 A "polymorphic default method" is a default method defined as in Haskell 98.
8215 A "generic class declaration" is a class declaration with at least one
8216 generic default method.
8224 Alas, we do not yet implement the stuff about constructor names and
8231 A generic class can have only one parameter; you can't have a generic
8232 multi-parameter class.
8238 A default method must be defined entirely using type patterns, or entirely
8239 without. So this is illegal:
8242 op :: a -> (a, Bool)
8243 op {| Unit |} Unit = (Unit, True)
8246 However it is perfectly OK for some methods of a generic class to have
8247 generic default methods and others to have polymorphic default methods.
8253 The type variable(s) in the type pattern for a generic method declaration
8254 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:
8258 op {| p :*: q |} (x :*: y) = op (x :: p)
8266 The type patterns in a generic default method must take one of the forms:
8272 where "a" and "b" are type variables. Furthermore, all the type patterns for
8273 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8274 must use the same type variables. So this is illegal:
8278 op {| a :+: b |} (Inl x) = True
8279 op {| p :+: q |} (Inr y) = False
8281 The type patterns must be identical, even in equations for different methods of the class.
8282 So this too is illegal:
8286 op1 {| a :*: b |} (x :*: y) = True
8289 op2 {| p :*: q |} (x :*: y) = False
8291 (The reason for this restriction is that we gather all the equations for a particular type constructor
8292 into a single generic instance declaration.)
8298 A generic method declaration must give a case for each of the three type constructors.
8304 The type for a generic method can be built only from:
8306 <listitem> <para> Function arrows </para> </listitem>
8307 <listitem> <para> Type variables </para> </listitem>
8308 <listitem> <para> Tuples </para> </listitem>
8309 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8311 Here are some example type signatures for generic methods:
8314 op2 :: Bool -> (a,Bool)
8315 op3 :: [Int] -> a -> a
8318 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8322 This restriction is an implementation restriction: we just haven't got around to
8323 implementing the necessary bidirectional maps over arbitrary type constructors.
8324 It would be relatively easy to add specific type constructors, such as Maybe and list,
8325 to the ones that are allowed.</para>
8330 In an instance declaration for a generic class, the idea is that the compiler
8331 will fill in the methods for you, based on the generic templates. However it can only
8336 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8341 No constructor of the instance type has unboxed fields.
8345 (Of course, these things can only arise if you are already using GHC extensions.)
8346 However, you can still give an instance declarations for types which break these rules,
8347 provided you give explicit code to override any generic default methods.
8355 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8356 what the compiler does with generic declarations.
8361 <sect2> <title> Another example </title>
8363 Just to finish with, here's another example I rather like:
8367 nCons {| Unit |} _ = 1
8368 nCons {| a :*: b |} _ = 1
8369 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8372 tag {| Unit |} _ = 1
8373 tag {| a :*: b |} _ = 1
8374 tag {| a :+: b |} (Inl x) = tag x
8375 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8381 <sect1 id="monomorphism">
8382 <title>Control over monomorphism</title>
8384 <para>GHC supports two flags that control the way in which generalisation is
8385 carried out at let and where bindings.
8389 <title>Switching off the dreaded Monomorphism Restriction</title>
8390 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8392 <para>Haskell's monomorphism restriction (see
8393 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8395 of the Haskell Report)
8396 can be completely switched off by
8397 <option>-XNoMonomorphismRestriction</option>.
8402 <title>Monomorphic pattern bindings</title>
8403 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8404 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8406 <para> As an experimental change, we are exploring the possibility of
8407 making pattern bindings monomorphic; that is, not generalised at all.
8408 A pattern binding is a binding whose LHS has no function arguments,
8409 and is not a simple variable. For example:
8411 f x = x -- Not a pattern binding
8412 f = \x -> x -- Not a pattern binding
8413 f :: Int -> Int = \x -> x -- Not a pattern binding
8415 (g,h) = e -- A pattern binding
8416 (f) = e -- A pattern binding
8417 [x] = e -- A pattern binding
8419 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8420 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8429 ;;; Local Variables: ***
8431 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8432 ;;; ispell-local-dictionary: "british" ***
projects / ghc-hetmet.git / blob