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 <options>-fglasgow-exts</options>.
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>
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 GHC allows a small extension to the syntax of left operator sections, which
1180 allows you to define postfix operators. The extension is this: the left section
1184 is equivalent (from the point of view of both type checking and execution) to the expression
1188 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1189 The strict Haskell 98 interpretation is that the section is equivalent to
1193 That is, the operator must be a function of two arguments. GHC allows it to
1194 take only one argument, and that in turn allows you to write the function
1197 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1198 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1199 change their behaviour, of course.)
1201 <para>The extension does not extend to the left-hand side of function
1202 definitions; you must define such a function in prefix form.</para>
1206 <sect2 id="disambiguate-fields">
1207 <title>Record field disambiguation</title>
1209 In record construction and record pattern matching
1210 it is entirely unambiguous which field is referred to, even if there are two different
1211 data types in scope with a common field name. For example:
1214 data S = MkS { x :: Int, y :: Bool }
1219 data T = MkT { x :: Int }
1221 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1223 ok2 n = MkT { x = n+1 } -- Unambiguous
1225 bad1 k = k { x = 3 } -- Ambiguous
1226 bad2 k = x k -- Ambiguous
1228 Even though there are two <literal>x</literal>'s in scope,
1229 it is clear that the <literal>x</literal> in the pattern in the
1230 definition of <literal>ok1</literal> can only mean the field
1231 <literal>x</literal> from type <literal>S</literal>. Similarly for
1232 the function <literal>ok2</literal>. However, in the record update
1233 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1234 it is not clear which of the two types is intended.
1237 Haskell 98 regards all four as ambiguous, but with the
1238 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1239 the former two. The rules are precisely the same as those for instance
1240 declarations in Haskell 98, where the method names on the left-hand side
1241 of the method bindings in an instance declaration refer unambiguously
1242 to the method of that class (provided they are in scope at all), even
1243 if there are other variables in scope with the same name.
1244 This reduces the clutter of qualified names when you import two
1245 records from different modules that use the same field name.
1249 <!-- ===================== Record puns =================== -->
1251 <sect2 id="record-puns">
1256 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1260 When using records, it is common to write a pattern that binds a
1261 variable with the same name as a record field, such as:
1264 data C = C {a :: Int}
1270 Record punning permits the variable name to be elided, so one can simply
1277 to mean the same pattern as above. That is, in a record pattern, the
1278 pattern <literal>a</literal> expands into the pattern <literal>a =
1279 a</literal> for the same name <literal>a</literal>.
1283 Note that puns and other patterns can be mixed in the same record:
1285 data C = C {a :: Int, b :: Int}
1286 f (C {a, b = 4}) = a
1288 and that puns can be used wherever record patterns occur (e.g. in
1289 <literal>let</literal> bindings or at the top-level).
1293 Record punning can also be used in an expression, writing, for example,
1299 let a = 1 in C {a = a}
1302 Note that this expansion is purely syntactic, so the record pun
1303 expression refers to the nearest enclosing variable that is spelled the
1304 same as the field name.
1309 <!-- ===================== Record wildcards =================== -->
1311 <sect2 id="record-wildcards">
1312 <title>Record wildcards
1316 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1320 For records with many fields, it can be tiresome to write out each field
1321 individually in a record pattern, as in
1323 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1324 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1329 Record wildcard syntax permits a (<literal>..</literal>) in a record
1330 pattern, where each elided field <literal>f</literal> is replaced by the
1331 pattern <literal>f = f</literal>. For example, the above pattern can be
1334 f (C {a = 1, ..}) = b + c + d
1339 Note that wildcards can be mixed with other patterns, including puns
1340 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1341 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1342 wherever record patterns occur, including in <literal>let</literal>
1343 bindings and at the top-level. For example, the top-level binding
1347 defines <literal>b</literal>, <literal>c</literal>, and
1348 <literal>d</literal>.
1352 Record wildcards can also be used in expressions, writing, for example,
1355 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1361 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1364 Note that this expansion is purely syntactic, so the record wildcard
1365 expression refers to the nearest enclosing variables that are spelled
1366 the same as the omitted field names.
1371 <!-- ===================== Local fixity declarations =================== -->
1373 <sect2 id="local-fixity-declarations">
1374 <title>Local Fixity Declarations
1377 <para>A careful reading of the Haskell 98 Report reveals that fixity
1378 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1379 <literal>infixr</literal>) are permitted to appear inside local bindings
1380 such those introduced by <literal>let</literal> and
1381 <literal>where</literal>. However, the Haskell Report does not specify
1382 the semantics of such bindings very precisely.
1385 <para>In GHC, a fixity declaration may accompany a local binding:
1392 and the fixity declaration applies wherever the binding is in scope.
1393 For example, in a <literal>let</literal>, it applies in the right-hand
1394 sides of other <literal>let</literal>-bindings and the body of the
1395 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1396 expressions (<xref linkend="mdo-notation"/>), the local fixity
1397 declarations of a <literal>let</literal> statement scope over other
1398 statements in the group, just as the bound name does.
1402 Moreover, a local fixity declaration *must* accompany a local binding of
1403 that name: it is not possible to revise the fixity of name bound
1406 let infixr 9 $ in ...
1409 Because local fixity declarations are technically Haskell 98, no flag is
1410 necessary to enable them.
1414 <sect2 id="package-imports">
1415 <title>Package-qualified imports</title>
1417 <para>With the <option>-XPackageImports</option> flag, GHC allows
1418 import declarations to be qualified by the package name that the
1419 module is intended to be imported from. For example:</para>
1422 import "network" Network.Socket
1425 <para>would import the module <literal>Network.Socket</literal> from
1426 the package <literal>network</literal> (any version). This may
1427 be used to disambiguate an import when the same module is
1428 available from multiple packages, or is present in both the
1429 current package being built and an external package.</para>
1431 <para>Note: you probably don't need to use this feature, it was
1432 added mainly so that we can build backwards-compatible versions of
1433 packages when APIs change. It can lead to fragile dependencies in
1434 the common case: modules occasionally move from one package to
1435 another, rendering any package-qualified imports broken.</para>
1438 <sect2 id="syntax-stolen">
1439 <title>Summary of stolen syntax</title>
1441 <para>Turning on an option that enables special syntax
1442 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1443 to compile, perhaps because it uses a variable name which has
1444 become a reserved word. This section lists the syntax that is
1445 "stolen" by language extensions.
1447 notation and nonterminal names from the Haskell 98 lexical syntax
1448 (see the Haskell 98 Report).
1449 We only list syntax changes here that might affect
1450 existing working programs (i.e. "stolen" syntax). Many of these
1451 extensions will also enable new context-free syntax, but in all
1452 cases programs written to use the new syntax would not be
1453 compilable without the option enabled.</para>
1455 <para>There are two classes of special
1460 <para>New reserved words and symbols: character sequences
1461 which are no longer available for use as identifiers in the
1465 <para>Other special syntax: sequences of characters that have
1466 a different meaning when this particular option is turned
1471 The following syntax is stolen:
1476 <literal>forall</literal>
1477 <indexterm><primary><literal>forall</literal></primary></indexterm>
1480 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1481 <option>-XLiberalTypeSynonyms</option>,
1482 <option>-XRank2Types</option>,
1483 <option>-XRankNTypes</option>,
1484 <option>-XPolymorphicComponents</option>,
1485 <option>-XExistentialQuantification</option>
1491 <literal>mdo</literal>
1492 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1495 Stolen by: <option>-XRecursiveDo</option>,
1501 <literal>foreign</literal>
1502 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1505 Stolen by: <option>-XForeignFunctionInterface</option>,
1511 <literal>rec</literal>,
1512 <literal>proc</literal>, <literal>-<</literal>,
1513 <literal>>-</literal>, <literal>-<<</literal>,
1514 <literal>>>-</literal>, and <literal>(|</literal>,
1515 <literal>|)</literal> brackets
1516 <indexterm><primary><literal>proc</literal></primary></indexterm>
1519 Stolen by: <option>-XArrows</option>,
1525 <literal>?<replaceable>varid</replaceable></literal>,
1526 <literal>%<replaceable>varid</replaceable></literal>
1527 <indexterm><primary>implicit parameters</primary></indexterm>
1530 Stolen by: <option>-XImplicitParams</option>,
1536 <literal>[|</literal>,
1537 <literal>[e|</literal>, <literal>[p|</literal>,
1538 <literal>[d|</literal>, <literal>[t|</literal>,
1539 <literal>$(</literal>,
1540 <literal>$<replaceable>varid</replaceable></literal>
1541 <indexterm><primary>Template Haskell</primary></indexterm>
1544 Stolen by: <option>-XTemplateHaskell</option>,
1550 <literal>[:<replaceable>varid</replaceable>|</literal>
1551 <indexterm><primary>quasi-quotation</primary></indexterm>
1554 Stolen by: <option>-XQuasiQuotes</option>,
1560 <replaceable>varid</replaceable>{<literal>#</literal>},
1561 <replaceable>char</replaceable><literal>#</literal>,
1562 <replaceable>string</replaceable><literal>#</literal>,
1563 <replaceable>integer</replaceable><literal>#</literal>,
1564 <replaceable>float</replaceable><literal>#</literal>,
1565 <replaceable>float</replaceable><literal>##</literal>,
1566 <literal>(#</literal>, <literal>#)</literal>,
1569 Stolen by: <option>-XMagicHash</option>,
1578 <!-- TYPE SYSTEM EXTENSIONS -->
1579 <sect1 id="data-type-extensions">
1580 <title>Extensions to data types and type synonyms</title>
1582 <sect2 id="nullary-types">
1583 <title>Data types with no constructors</title>
1585 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1586 a data type with no constructors. For example:</para>
1590 data T a -- T :: * -> *
1593 <para>Syntactically, the declaration lacks the "= constrs" part. The
1594 type can be parameterised over types of any kind, but if the kind is
1595 not <literal>*</literal> then an explicit kind annotation must be used
1596 (see <xref linkend="kinding"/>).</para>
1598 <para>Such data types have only one value, namely bottom.
1599 Nevertheless, they can be useful when defining "phantom types".</para>
1602 <sect2 id="infix-tycons">
1603 <title>Infix type constructors, classes, and type variables</title>
1606 GHC allows type constructors, classes, and type variables to be operators, and
1607 to be written infix, very much like expressions. More specifically:
1610 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1611 The lexical syntax is the same as that for data constructors.
1614 Data type and type-synonym declarations can be written infix, parenthesised
1615 if you want further arguments. E.g.
1617 data a :*: b = Foo a b
1618 type a :+: b = Either a b
1619 class a :=: b where ...
1621 data (a :**: b) x = Baz a b x
1622 type (a :++: b) y = Either (a,b) y
1626 Types, and class constraints, can be written infix. For example
1629 f :: (a :=: b) => a -> b
1633 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1634 The lexical syntax is the same as that for variable operators, excluding "(.)",
1635 "(!)", and "(*)". In a binding position, the operator must be
1636 parenthesised. For example:
1638 type T (+) = Int + Int
1642 liftA2 :: Arrow (~>)
1643 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1649 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1650 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1653 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1654 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1655 sets the fixity for a data constructor and the corresponding type constructor. For example:
1659 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1660 and similarly for <literal>:*:</literal>.
1661 <literal>Int `a` Bool</literal>.
1664 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1671 <sect2 id="type-synonyms">
1672 <title>Liberalised type synonyms</title>
1675 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1676 on individual synonym declarations.
1677 With the <option>-XLiberalTypeSynonyms</option> extension,
1678 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1679 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1682 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1683 in a type synonym, thus:
1685 type Discard a = forall b. Show b => a -> b -> (a, String)
1690 g :: Discard Int -> (Int,String) -- A rank-2 type
1697 If you also use <option>-XUnboxedTuples</option>,
1698 you can write an unboxed tuple in a type synonym:
1700 type Pr = (# Int, Int #)
1708 You can apply a type synonym to a forall type:
1710 type Foo a = a -> a -> Bool
1712 f :: Foo (forall b. b->b)
1714 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1716 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1721 You can apply a type synonym to a partially applied type synonym:
1723 type Generic i o = forall x. i x -> o x
1726 foo :: Generic Id []
1728 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1730 foo :: forall x. x -> [x]
1738 GHC currently does kind checking before expanding synonyms (though even that
1742 After expanding type synonyms, GHC does validity checking on types, looking for
1743 the following mal-formedness which isn't detected simply by kind checking:
1746 Type constructor applied to a type involving for-alls.
1749 Unboxed tuple on left of an arrow.
1752 Partially-applied type synonym.
1756 this will be rejected:
1758 type Pr = (# Int, Int #)
1763 because GHC does not allow unboxed tuples on the left of a function arrow.
1768 <sect2 id="existential-quantification">
1769 <title>Existentially quantified data constructors
1773 The idea of using existential quantification in data type declarations
1774 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1775 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1776 London, 1991). It was later formalised by Laufer and Odersky
1777 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1778 TOPLAS, 16(5), pp1411-1430, 1994).
1779 It's been in Lennart
1780 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1781 proved very useful. Here's the idea. Consider the declaration:
1787 data Foo = forall a. MkFoo a (a -> Bool)
1794 The data type <literal>Foo</literal> has two constructors with types:
1800 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1807 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1808 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1809 For example, the following expression is fine:
1815 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1821 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1822 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1823 isUpper</function> packages a character with a compatible function. These
1824 two things are each of type <literal>Foo</literal> and can be put in a list.
1828 What can we do with a value of type <literal>Foo</literal>?. In particular,
1829 what happens when we pattern-match on <function>MkFoo</function>?
1835 f (MkFoo val fn) = ???
1841 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1842 are compatible, the only (useful) thing we can do with them is to
1843 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1850 f (MkFoo val fn) = fn val
1856 What this allows us to do is to package heterogeneous values
1857 together with a bunch of functions that manipulate them, and then treat
1858 that collection of packages in a uniform manner. You can express
1859 quite a bit of object-oriented-like programming this way.
1862 <sect3 id="existential">
1863 <title>Why existential?
1867 What has this to do with <emphasis>existential</emphasis> quantification?
1868 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1874 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1880 But Haskell programmers can safely think of the ordinary
1881 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1882 adding a new existential quantification construct.
1887 <sect3 id="existential-with-context">
1888 <title>Existentials and type classes</title>
1891 An easy extension is to allow
1892 arbitrary contexts before the constructor. For example:
1898 data Baz = forall a. Eq a => Baz1 a a
1899 | forall b. Show b => Baz2 b (b -> b)
1905 The two constructors have the types you'd expect:
1911 Baz1 :: forall a. Eq a => a -> a -> Baz
1912 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1918 But when pattern matching on <function>Baz1</function> the matched values can be compared
1919 for equality, and when pattern matching on <function>Baz2</function> the first matched
1920 value can be converted to a string (as well as applying the function to it).
1921 So this program is legal:
1928 f (Baz1 p q) | p == q = "Yes"
1930 f (Baz2 v fn) = show (fn v)
1936 Operationally, in a dictionary-passing implementation, the
1937 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1938 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1939 extract it on pattern matching.
1944 <sect3 id="existential-records">
1945 <title>Record Constructors</title>
1948 GHC allows existentials to be used with records syntax as well. For example:
1951 data Counter a = forall self. NewCounter
1953 , _inc :: self -> self
1954 , _display :: self -> IO ()
1958 Here <literal>tag</literal> is a public field, with a well-typed selector
1959 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1960 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1961 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1962 compile-time error. In other words, <emphasis>GHC defines a record selector function
1963 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1964 (This example used an underscore in the fields for which record selectors
1965 will not be defined, but that is only programming style; GHC ignores them.)
1969 To make use of these hidden fields, we need to create some helper functions:
1972 inc :: Counter a -> Counter a
1973 inc (NewCounter x i d t) = NewCounter
1974 { _this = i x, _inc = i, _display = d, tag = t }
1976 display :: Counter a -> IO ()
1977 display NewCounter{ _this = x, _display = d } = d x
1980 Now we can define counters with different underlying implementations:
1983 counterA :: Counter String
1984 counterA = NewCounter
1985 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1987 counterB :: Counter String
1988 counterB = NewCounter
1989 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1992 display (inc counterA) -- prints "1"
1993 display (inc (inc counterB)) -- prints "##"
1996 At the moment, record update syntax is only supported for Haskell 98 data types,
1997 so the following function does <emphasis>not</emphasis> work:
2000 -- This is invalid; use explicit NewCounter instead for now
2001 setTag :: Counter a -> a -> Counter a
2002 setTag obj t = obj{ tag = t }
2011 <title>Restrictions</title>
2014 There are several restrictions on the ways in which existentially-quantified
2015 constructors can be use.
2024 When pattern matching, each pattern match introduces a new,
2025 distinct, type for each existential type variable. These types cannot
2026 be unified with any other type, nor can they escape from the scope of
2027 the pattern match. For example, these fragments are incorrect:
2035 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2036 is the result of <function>f1</function>. One way to see why this is wrong is to
2037 ask what type <function>f1</function> has:
2041 f1 :: Foo -> a -- Weird!
2045 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2050 f1 :: forall a. Foo -> a -- Wrong!
2054 The original program is just plain wrong. Here's another sort of error
2058 f2 (Baz1 a b) (Baz1 p q) = a==q
2062 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2063 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2064 from the two <function>Baz1</function> constructors.
2072 You can't pattern-match on an existentially quantified
2073 constructor in a <literal>let</literal> or <literal>where</literal> group of
2074 bindings. So this is illegal:
2078 f3 x = a==b where { Baz1 a b = x }
2081 Instead, use a <literal>case</literal> expression:
2084 f3 x = case x of Baz1 a b -> a==b
2087 In general, you can only pattern-match
2088 on an existentially-quantified constructor in a <literal>case</literal> expression or
2089 in the patterns of a function definition.
2091 The reason for this restriction is really an implementation one.
2092 Type-checking binding groups is already a nightmare without
2093 existentials complicating the picture. Also an existential pattern
2094 binding at the top level of a module doesn't make sense, because it's
2095 not clear how to prevent the existentially-quantified type "escaping".
2096 So for now, there's a simple-to-state restriction. We'll see how
2104 You can't use existential quantification for <literal>newtype</literal>
2105 declarations. So this is illegal:
2109 newtype T = forall a. Ord a => MkT a
2113 Reason: a value of type <literal>T</literal> must be represented as a
2114 pair of a dictionary for <literal>Ord t</literal> and a value of type
2115 <literal>t</literal>. That contradicts the idea that
2116 <literal>newtype</literal> should have no concrete representation.
2117 You can get just the same efficiency and effect by using
2118 <literal>data</literal> instead of <literal>newtype</literal>. If
2119 there is no overloading involved, then there is more of a case for
2120 allowing an existentially-quantified <literal>newtype</literal>,
2121 because the <literal>data</literal> version does carry an
2122 implementation cost, but single-field existentially quantified
2123 constructors aren't much use. So the simple restriction (no
2124 existential stuff on <literal>newtype</literal>) stands, unless there
2125 are convincing reasons to change it.
2133 You can't use <literal>deriving</literal> to define instances of a
2134 data type with existentially quantified data constructors.
2136 Reason: in most cases it would not make sense. For example:;
2139 data T = forall a. MkT [a] deriving( Eq )
2142 To derive <literal>Eq</literal> in the standard way we would need to have equality
2143 between the single component of two <function>MkT</function> constructors:
2147 (MkT a) == (MkT b) = ???
2150 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2151 It's just about possible to imagine examples in which the derived instance
2152 would make sense, but it seems altogether simpler simply to prohibit such
2153 declarations. Define your own instances!
2164 <!-- ====================== Generalised algebraic data types ======================= -->
2166 <sect2 id="gadt-style">
2167 <title>Declaring data types with explicit constructor signatures</title>
2169 <para>GHC allows you to declare an algebraic data type by
2170 giving the type signatures of constructors explicitly. For example:
2174 Just :: a -> Maybe a
2176 The form is called a "GADT-style declaration"
2177 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2178 can only be declared using this form.</para>
2179 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2180 For example, these two declarations are equivalent:
2182 data Foo = forall a. MkFoo a (a -> Bool)
2183 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2186 <para>Any data type that can be declared in standard Haskell-98 syntax
2187 can also be declared using GADT-style syntax.
2188 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2189 they treat class constraints on the data constructors differently.
2190 Specifically, if the constructor is given a type-class context, that
2191 context is made available by pattern matching. For example:
2194 MkSet :: Eq a => [a] -> Set a
2196 makeSet :: Eq a => [a] -> Set a
2197 makeSet xs = MkSet (nub xs)
2199 insert :: a -> Set a -> Set a
2200 insert a (MkSet as) | a `elem` as = MkSet as
2201 | otherwise = MkSet (a:as)
2203 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2204 gives rise to a <literal>(Eq a)</literal>
2205 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2206 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2207 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2208 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2209 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2210 In the example, the equality dictionary is used to satisfy the equality constraint
2211 generated by the call to <literal>elem</literal>, so that the type of
2212 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2215 For example, one possible application is to reify dictionaries:
2217 data NumInst a where
2218 MkNumInst :: Num a => NumInst a
2220 intInst :: NumInst Int
2223 plus :: NumInst a -> a -> a -> a
2224 plus MkNumInst p q = p + q
2226 Here, a value of type <literal>NumInst a</literal> is equivalent
2227 to an explicit <literal>(Num a)</literal> dictionary.
2230 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2231 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2235 = Num a => MkNumInst (NumInst a)
2237 Notice that, unlike the situation when declaring an existential, there is
2238 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2239 data type's universally quantified type variable <literal>a</literal>.
2240 A constructor may have both universal and existential type variables: for example,
2241 the following two declarations are equivalent:
2244 = forall b. (Num a, Eq b) => MkT1 a b
2246 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2249 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2250 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2251 In Haskell 98 the definition
2253 data Eq a => Set' a = MkSet' [a]
2255 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2256 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2257 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2258 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2259 GHC's behaviour is much more useful, as well as much more intuitive.
2263 The rest of this section gives further details about GADT-style data
2268 The result type of each data constructor must begin with the type constructor being defined.
2269 If the result type of all constructors
2270 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2271 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2272 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2276 The type signature of
2277 each constructor is independent, and is implicitly universally quantified as usual.
2278 Different constructors may have different universally-quantified type variables
2279 and different type-class constraints.
2280 For example, this is fine:
2283 T1 :: Eq b => b -> T b
2284 T2 :: (Show c, Ix c) => c -> [c] -> T c
2289 Unlike a Haskell-98-style
2290 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2291 have no scope. Indeed, one can write a kind signature instead:
2293 data Set :: * -> * where ...
2295 or even a mixture of the two:
2297 data Foo a :: (* -> *) -> * where ...
2299 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2302 data Foo a (b :: * -> *) where ...
2308 You can use strictness annotations, in the obvious places
2309 in the constructor type:
2312 Lit :: !Int -> Term Int
2313 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2314 Pair :: Term a -> Term b -> Term (a,b)
2319 You can use a <literal>deriving</literal> clause on a GADT-style data type
2320 declaration. For example, these two declarations are equivalent
2322 data Maybe1 a where {
2323 Nothing1 :: Maybe1 a ;
2324 Just1 :: a -> Maybe1 a
2325 } deriving( Eq, Ord )
2327 data Maybe2 a = Nothing2 | Just2 a
2333 You can use record syntax on a GADT-style data type declaration:
2337 Adult { name :: String, children :: [Person] } :: Person
2338 Child { name :: String } :: Person
2340 As usual, for every constructor that has a field <literal>f</literal>, the type of
2341 field <literal>f</literal> must be the same (modulo alpha conversion).
2344 At the moment, record updates are not yet possible with GADT-style declarations,
2345 so support is limited to record construction, selection and pattern matching.
2348 aPerson = Adult { name = "Fred", children = [] }
2350 shortName :: Person -> Bool
2351 hasChildren (Adult { children = kids }) = not (null kids)
2352 hasChildren (Child {}) = False
2357 As in the case of existentials declared using the Haskell-98-like record syntax
2358 (<xref linkend="existential-records"/>),
2359 record-selector functions are generated only for those fields that have well-typed
2361 Here is the example of that section, in GADT-style syntax:
2363 data Counter a where
2364 NewCounter { _this :: self
2365 , _inc :: self -> self
2366 , _display :: self -> IO ()
2371 As before, only one selector function is generated here, that for <literal>tag</literal>.
2372 Nevertheless, you can still use all the field names in pattern matching and record construction.
2374 </itemizedlist></para>
2378 <title>Generalised Algebraic Data Types (GADTs)</title>
2380 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2381 by allowing constructors to have richer return types. Here is an example:
2384 Lit :: Int -> Term Int
2385 Succ :: Term Int -> Term Int
2386 IsZero :: Term Int -> Term Bool
2387 If :: Term Bool -> Term a -> Term a -> Term a
2388 Pair :: Term a -> Term b -> Term (a,b)
2390 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2391 case with ordinary data types. This generality allows us to
2392 write a well-typed <literal>eval</literal> function
2393 for these <literal>Terms</literal>:
2397 eval (Succ t) = 1 + eval t
2398 eval (IsZero t) = eval t == 0
2399 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2400 eval (Pair e1 e2) = (eval e1, eval e2)
2402 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2403 For example, in the right hand side of the equation
2408 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2409 A precise specification of the type rules is beyond what this user manual aspires to,
2410 but the design closely follows that described in
2412 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2413 unification-based type inference for GADTs</ulink>,
2415 The general principle is this: <emphasis>type refinement is only carried out
2416 based on user-supplied type annotations</emphasis>.
2417 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2418 and lots of obscure error messages will
2419 occur. However, the refinement is quite general. For example, if we had:
2421 eval :: Term a -> a -> a
2422 eval (Lit i) j = i+j
2424 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2425 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2426 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2429 These and many other examples are given in papers by Hongwei Xi, and
2430 Tim Sheard. There is a longer introduction
2431 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2433 <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
2434 may use different notation to that implemented in GHC.
2437 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2438 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2441 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2442 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2443 The result type of each constructor must begin with the type constructor being defined,
2444 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2445 For example, in the <literal>Term</literal> data
2446 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2447 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2452 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2453 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2454 whose result type is not just <literal>T a b</literal>.
2458 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2459 an ordinary data type.
2463 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2467 Lit { val :: Int } :: Term Int
2468 Succ { num :: Term Int } :: Term Int
2469 Pred { num :: Term Int } :: Term Int
2470 IsZero { arg :: Term Int } :: Term Bool
2471 Pair { arg1 :: Term a
2474 If { cnd :: Term Bool
2479 However, for GADTs there is the following additional constraint:
2480 every constructor that has a field <literal>f</literal> must have
2481 the same result type (modulo alpha conversion)
2482 Hence, in the above example, we cannot merge the <literal>num</literal>
2483 and <literal>arg</literal> fields above into a
2484 single name. Although their field types are both <literal>Term Int</literal>,
2485 their selector functions actually have different types:
2488 num :: Term Int -> Term Int
2489 arg :: Term Bool -> Term Int
2494 When pattern-matching against data constructors drawn from a GADT,
2495 for example in a <literal>case</literal> expression, the following rules apply:
2497 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2498 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2499 <listitem><para>The type of any free variable mentioned in any of
2500 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2502 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2503 way to ensure that a variable a rigid type is to give it a type signature.
2504 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2505 Simple unification-based type inference for GADTs
2506 </ulink>. The criteria implemented by GHC are given in the Appendix.
2516 <!-- ====================== End of Generalised algebraic data types ======================= -->
2518 <sect1 id="deriving">
2519 <title>Extensions to the "deriving" mechanism</title>
2521 <sect2 id="deriving-inferred">
2522 <title>Inferred context for deriving clauses</title>
2525 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2528 data T0 f a = MkT0 a deriving( Eq )
2529 data T1 f a = MkT1 (f a) deriving( Eq )
2530 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2532 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2534 instance Eq a => Eq (T0 f a) where ...
2535 instance Eq (f a) => Eq (T1 f a) where ...
2536 instance Eq (f (f a)) => Eq (T2 f a) where ...
2538 The first of these is obviously fine. The second is still fine, although less obviously.
2539 The third is not Haskell 98, and risks losing termination of instances.
2542 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2543 each constraint in the inferred instance context must consist only of type variables,
2544 with no repetitions.
2547 This rule is applied regardless of flags. If you want a more exotic context, you can write
2548 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2552 <sect2 id="stand-alone-deriving">
2553 <title>Stand-alone deriving declarations</title>
2556 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2558 data Foo a = Bar a | Baz String
2560 deriving instance Eq a => Eq (Foo a)
2562 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2563 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2564 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2565 exactly as you would in an ordinary instance declaration.
2566 (In contrast the context is inferred in a <literal>deriving</literal> clause
2567 attached to a data type declaration.)
2569 A <literal>deriving instance</literal> declaration
2570 must obey the same rules concerning form and termination as ordinary instance declarations,
2571 controlled by the same flags; see <xref linkend="instance-decls"/>.
2574 Unlike a <literal>deriving</literal>
2575 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2576 than the data type (assuming you also use
2577 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2580 data Foo a = Bar a | Baz String
2582 deriving instance Eq a => Eq (Foo [a])
2583 deriving instance Eq a => Eq (Foo (Maybe a))
2585 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2586 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2589 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2590 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2593 newtype Foo a = MkFoo (State Int a)
2595 deriving instance MonadState Int Foo
2597 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2598 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2604 <sect2 id="deriving-typeable">
2605 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2608 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2609 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2610 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2611 classes <literal>Eq</literal>, <literal>Ord</literal>,
2612 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2615 GHC extends this list with two more classes that may be automatically derived
2616 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2617 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2618 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2619 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2621 <para>An instance of <literal>Typeable</literal> can only be derived if the
2622 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2623 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2625 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2626 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2628 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2629 are used, and only <literal>Typeable1</literal> up to
2630 <literal>Typeable7</literal> are provided in the library.)
2631 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2632 class, whose kind suits that of the data type constructor, and
2633 then writing the data type instance by hand.
2637 <sect2 id="newtype-deriving">
2638 <title>Generalised derived instances for newtypes</title>
2641 When you define an abstract type using <literal>newtype</literal>, you may want
2642 the new type to inherit some instances from its representation. In
2643 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2644 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2645 other classes you have to write an explicit instance declaration. For
2646 example, if you define
2649 newtype Dollars = Dollars Int
2652 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2653 explicitly define an instance of <literal>Num</literal>:
2656 instance Num Dollars where
2657 Dollars a + Dollars b = Dollars (a+b)
2660 All the instance does is apply and remove the <literal>newtype</literal>
2661 constructor. It is particularly galling that, since the constructor
2662 doesn't appear at run-time, this instance declaration defines a
2663 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2664 dictionary, only slower!
2668 <sect3> <title> Generalising the deriving clause </title>
2670 GHC now permits such instances to be derived instead,
2671 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2674 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2677 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2678 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2679 derives an instance declaration of the form
2682 instance Num Int => Num Dollars
2685 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2689 We can also derive instances of constructor classes in a similar
2690 way. For example, suppose we have implemented state and failure monad
2691 transformers, such that
2694 instance Monad m => Monad (State s m)
2695 instance Monad m => Monad (Failure m)
2697 In Haskell 98, we can define a parsing monad by
2699 type Parser tok m a = State [tok] (Failure m) a
2702 which is automatically a monad thanks to the instance declarations
2703 above. With the extension, we can make the parser type abstract,
2704 without needing to write an instance of class <literal>Monad</literal>, via
2707 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2710 In this case the derived instance declaration is of the form
2712 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2715 Notice that, since <literal>Monad</literal> is a constructor class, the
2716 instance is a <emphasis>partial application</emphasis> of the new type, not the
2717 entire left hand side. We can imagine that the type declaration is
2718 "eta-converted" to generate the context of the instance
2723 We can even derive instances of multi-parameter classes, provided the
2724 newtype is the last class parameter. In this case, a ``partial
2725 application'' of the class appears in the <literal>deriving</literal>
2726 clause. For example, given the class
2729 class StateMonad s m | m -> s where ...
2730 instance Monad m => StateMonad s (State s m) where ...
2732 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2734 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2735 deriving (Monad, StateMonad [tok])
2738 The derived instance is obtained by completing the application of the
2739 class to the new type:
2742 instance StateMonad [tok] (State [tok] (Failure m)) =>
2743 StateMonad [tok] (Parser tok m)
2748 As a result of this extension, all derived instances in newtype
2749 declarations are treated uniformly (and implemented just by reusing
2750 the dictionary for the representation type), <emphasis>except</emphasis>
2751 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2752 the newtype and its representation.
2756 <sect3> <title> A more precise specification </title>
2758 Derived instance declarations are constructed as follows. Consider the
2759 declaration (after expansion of any type synonyms)
2762 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2768 The <literal>ci</literal> are partial applications of
2769 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2770 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2773 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2776 The type <literal>t</literal> is an arbitrary type.
2779 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2780 nor in the <literal>ci</literal>, and
2783 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2784 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2785 should not "look through" the type or its constructor. You can still
2786 derive these classes for a newtype, but it happens in the usual way, not
2787 via this new mechanism.
2790 Then, for each <literal>ci</literal>, the derived instance
2793 instance ci t => ci (T v1...vk)
2795 As an example which does <emphasis>not</emphasis> work, consider
2797 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2799 Here we cannot derive the instance
2801 instance Monad (State s m) => Monad (NonMonad m)
2804 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2805 and so cannot be "eta-converted" away. It is a good thing that this
2806 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2807 not, in fact, a monad --- for the same reason. Try defining
2808 <literal>>>=</literal> with the correct type: you won't be able to.
2812 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2813 important, since we can only derive instances for the last one. If the
2814 <literal>StateMonad</literal> class above were instead defined as
2817 class StateMonad m s | m -> s where ...
2820 then we would not have been able to derive an instance for the
2821 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2822 classes usually have one "main" parameter for which deriving new
2823 instances is most interesting.
2825 <para>Lastly, all of this applies only for classes other than
2826 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2827 and <literal>Data</literal>, for which the built-in derivation applies (section
2828 4.3.3. of the Haskell Report).
2829 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2830 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2831 the standard method is used or the one described here.)
2838 <!-- TYPE SYSTEM EXTENSIONS -->
2839 <sect1 id="type-class-extensions">
2840 <title>Class and instances declarations</title>
2842 <sect2 id="multi-param-type-classes">
2843 <title>Class declarations</title>
2846 This section, and the next one, documents GHC's type-class extensions.
2847 There's lots of background in the paper <ulink
2848 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2849 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2850 Jones, Erik Meijer).
2853 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2857 <title>Multi-parameter type classes</title>
2859 Multi-parameter type classes are permitted. For example:
2863 class Collection c a where
2864 union :: c a -> c a -> c a
2872 <title>The superclasses of a class declaration</title>
2875 There are no restrictions on the context in a class declaration
2876 (which introduces superclasses), except that the class hierarchy must
2877 be acyclic. So these class declarations are OK:
2881 class Functor (m k) => FiniteMap m k where
2884 class (Monad m, Monad (t m)) => Transform t m where
2885 lift :: m a -> (t m) a
2891 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2892 of "acyclic" involves only the superclass relationships. For example,
2898 op :: D b => a -> b -> b
2901 class C a => D a where { ... }
2905 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2906 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2907 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2914 <sect3 id="class-method-types">
2915 <title>Class method types</title>
2918 Haskell 98 prohibits class method types to mention constraints on the
2919 class type variable, thus:
2922 fromList :: [a] -> s a
2923 elem :: Eq a => a -> s a -> Bool
2925 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2926 contains the constraint <literal>Eq a</literal>, constrains only the
2927 class type variable (in this case <literal>a</literal>).
2928 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2935 <sect2 id="functional-dependencies">
2936 <title>Functional dependencies
2939 <para> Functional dependencies are implemented as described by Mark Jones
2940 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2941 In Proceedings of the 9th European Symposium on Programming,
2942 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2946 Functional dependencies are introduced by a vertical bar in the syntax of a
2947 class declaration; e.g.
2949 class (Monad m) => MonadState s m | m -> s where ...
2951 class Foo a b c | a b -> c where ...
2953 There should be more documentation, but there isn't (yet). Yell if you need it.
2956 <sect3><title>Rules for functional dependencies </title>
2958 In a class declaration, all of the class type variables must be reachable (in the sense
2959 mentioned in <xref linkend="type-restrictions"/>)
2960 from the free variables of each method type.
2964 class Coll s a where
2966 insert :: s -> a -> s
2969 is not OK, because the type of <literal>empty</literal> doesn't mention
2970 <literal>a</literal>. Functional dependencies can make the type variable
2973 class Coll s a | s -> a where
2975 insert :: s -> a -> s
2978 Alternatively <literal>Coll</literal> might be rewritten
2981 class Coll s a where
2983 insert :: s a -> a -> s a
2987 which makes the connection between the type of a collection of
2988 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2989 Occasionally this really doesn't work, in which case you can split the
2997 class CollE s => Coll s a where
2998 insert :: s -> a -> s
3005 <title>Background on functional dependencies</title>
3007 <para>The following description of the motivation and use of functional dependencies is taken
3008 from the Hugs user manual, reproduced here (with minor changes) by kind
3009 permission of Mark Jones.
3012 Consider the following class, intended as part of a
3013 library for collection types:
3015 class Collects e ce where
3017 insert :: e -> ce -> ce
3018 member :: e -> ce -> Bool
3020 The type variable e used here represents the element type, while ce is the type
3021 of the container itself. Within this framework, we might want to define
3022 instances of this class for lists or characteristic functions (both of which
3023 can be used to represent collections of any equality type), bit sets (which can
3024 be used to represent collections of characters), or hash tables (which can be
3025 used to represent any collection whose elements have a hash function). Omitting
3026 standard implementation details, this would lead to the following declarations:
3028 instance Eq e => Collects e [e] where ...
3029 instance Eq e => Collects e (e -> Bool) where ...
3030 instance Collects Char BitSet where ...
3031 instance (Hashable e, Collects a ce)
3032 => Collects e (Array Int ce) where ...
3034 All this looks quite promising; we have a class and a range of interesting
3035 implementations. Unfortunately, there are some serious problems with the class
3036 declaration. First, the empty function has an ambiguous type:
3038 empty :: Collects e ce => ce
3040 By "ambiguous" we mean that there is a type variable e that appears on the left
3041 of the <literal>=></literal> symbol, but not on the right. The problem with
3042 this is that, according to the theoretical foundations of Haskell overloading,
3043 we cannot guarantee a well-defined semantics for any term with an ambiguous
3047 We can sidestep this specific problem by removing the empty member from the
3048 class declaration. However, although the remaining members, insert and member,
3049 do not have ambiguous types, we still run into problems when we try to use
3050 them. For example, consider the following two functions:
3052 f x y = insert x . insert y
3055 for which GHC infers the following types:
3057 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3058 g :: (Collects Bool c, Collects Char c) => c -> c
3060 Notice that the type for f allows the two parameters x and y to be assigned
3061 different types, even though it attempts to insert each of the two values, one
3062 after the other, into the same collection. If we're trying to model collections
3063 that contain only one type of value, then this is clearly an inaccurate
3064 type. Worse still, the definition for g is accepted, without causing a type
3065 error. As a result, the error in this code will not be flagged at the point
3066 where it appears. Instead, it will show up only when we try to use g, which
3067 might even be in a different module.
3070 <sect4><title>An attempt to use constructor classes</title>
3073 Faced with the problems described above, some Haskell programmers might be
3074 tempted to use something like the following version of the class declaration:
3076 class Collects e c where
3078 insert :: e -> c e -> c e
3079 member :: e -> c e -> Bool
3081 The key difference here is that we abstract over the type constructor c that is
3082 used to form the collection type c e, and not over that collection type itself,
3083 represented by ce in the original class declaration. This avoids the immediate
3084 problems that we mentioned above: empty has type <literal>Collects e c => c
3085 e</literal>, which is not ambiguous.
3088 The function f from the previous section has a more accurate type:
3090 f :: (Collects e c) => e -> e -> c e -> c e
3092 The function g from the previous section is now rejected with a type error as
3093 we would hope because the type of f does not allow the two arguments to have
3095 This, then, is an example of a multiple parameter class that does actually work
3096 quite well in practice, without ambiguity problems.
3097 There is, however, a catch. This version of the Collects class is nowhere near
3098 as general as the original class seemed to be: only one of the four instances
3099 for <literal>Collects</literal>
3100 given above can be used with this version of Collects because only one of
3101 them---the instance for lists---has a collection type that can be written in
3102 the form c e, for some type constructor c, and element type e.
3106 <sect4><title>Adding functional dependencies</title>
3109 To get a more useful version of the Collects class, Hugs provides a mechanism
3110 that allows programmers to specify dependencies between the parameters of a
3111 multiple parameter class (For readers with an interest in theoretical
3112 foundations and previous work: The use of dependency information can be seen
3113 both as a generalization of the proposal for `parametric type classes' that was
3114 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3115 later framework for "improvement" of qualified types. The
3116 underlying ideas are also discussed in a more theoretical and abstract setting
3117 in a manuscript [implparam], where they are identified as one point in a
3118 general design space for systems of implicit parameterization.).
3120 To start with an abstract example, consider a declaration such as:
3122 class C a b where ...
3124 which tells us simply that C can be thought of as a binary relation on types
3125 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3126 included in the definition of classes to add information about dependencies
3127 between parameters, as in the following examples:
3129 class D a b | a -> b where ...
3130 class E a b | a -> b, b -> a where ...
3132 The notation <literal>a -> b</literal> used here between the | and where
3133 symbols --- not to be
3134 confused with a function type --- indicates that the a parameter uniquely
3135 determines the b parameter, and might be read as "a determines b." Thus D is
3136 not just a relation, but actually a (partial) function. Similarly, from the two
3137 dependencies that are included in the definition of E, we can see that E
3138 represents a (partial) one-one mapping between types.
3141 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3142 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3143 m>=0, meaning that the y parameters are uniquely determined by the x
3144 parameters. Spaces can be used as separators if more than one variable appears
3145 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3146 annotated with multiple dependencies using commas as separators, as in the
3147 definition of E above. Some dependencies that we can write in this notation are
3148 redundant, and will be rejected because they don't serve any useful
3149 purpose, and may instead indicate an error in the program. Examples of
3150 dependencies like this include <literal>a -> a </literal>,
3151 <literal>a -> a a </literal>,
3152 <literal>a -> </literal>, etc. There can also be
3153 some redundancy if multiple dependencies are given, as in
3154 <literal>a->b</literal>,
3155 <literal>b->c </literal>, <literal>a->c </literal>, and
3156 in which some subset implies the remaining dependencies. Examples like this are
3157 not treated as errors. Note that dependencies appear only in class
3158 declarations, and not in any other part of the language. In particular, the
3159 syntax for instance declarations, class constraints, and types is completely
3163 By including dependencies in a class declaration, we provide a mechanism for
3164 the programmer to specify each multiple parameter class more precisely. The
3165 compiler, on the other hand, is responsible for ensuring that the set of
3166 instances that are in scope at any given point in the program is consistent
3167 with any declared dependencies. For example, the following pair of instance
3168 declarations cannot appear together in the same scope because they violate the
3169 dependency for D, even though either one on its own would be acceptable:
3171 instance D Bool Int where ...
3172 instance D Bool Char where ...
3174 Note also that the following declaration is not allowed, even by itself:
3176 instance D [a] b where ...
3178 The problem here is that this instance would allow one particular choice of [a]
3179 to be associated with more than one choice for b, which contradicts the
3180 dependency specified in the definition of D. More generally, this means that,
3181 in any instance of the form:
3183 instance D t s where ...
3185 for some particular types t and s, the only variables that can appear in s are
3186 the ones that appear in t, and hence, if the type t is known, then s will be
3187 uniquely determined.
3190 The benefit of including dependency information is that it allows us to define
3191 more general multiple parameter classes, without ambiguity problems, and with
3192 the benefit of more accurate types. To illustrate this, we return to the
3193 collection class example, and annotate the original definition of <literal>Collects</literal>
3194 with a simple dependency:
3196 class Collects e ce | ce -> e where
3198 insert :: e -> ce -> ce
3199 member :: e -> ce -> Bool
3201 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3202 determined by the type of the collection ce. Note that both parameters of
3203 Collects are of kind *; there are no constructor classes here. Note too that
3204 all of the instances of Collects that we gave earlier can be used
3205 together with this new definition.
3208 What about the ambiguity problems that we encountered with the original
3209 definition? The empty function still has type Collects e ce => ce, but it is no
3210 longer necessary to regard that as an ambiguous type: Although the variable e
3211 does not appear on the right of the => symbol, the dependency for class
3212 Collects tells us that it is uniquely determined by ce, which does appear on
3213 the right of the => symbol. Hence the context in which empty is used can still
3214 give enough information to determine types for both ce and e, without
3215 ambiguity. More generally, we need only regard a type as ambiguous if it
3216 contains a variable on the left of the => that is not uniquely determined
3217 (either directly or indirectly) by the variables on the right.
3220 Dependencies also help to produce more accurate types for user defined
3221 functions, and hence to provide earlier detection of errors, and less cluttered
3222 types for programmers to work with. Recall the previous definition for a
3225 f x y = insert x y = insert x . insert y
3227 for which we originally obtained a type:
3229 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3231 Given the dependency information that we have for Collects, however, we can
3232 deduce that a and b must be equal because they both appear as the second
3233 parameter in a Collects constraint with the same first parameter c. Hence we
3234 can infer a shorter and more accurate type for f:
3236 f :: (Collects a c) => a -> a -> c -> c
3238 In a similar way, the earlier definition of g will now be flagged as a type error.
3241 Although we have given only a few examples here, it should be clear that the
3242 addition of dependency information can help to make multiple parameter classes
3243 more useful in practice, avoiding ambiguity problems, and allowing more general
3244 sets of instance declarations.
3250 <sect2 id="instance-decls">
3251 <title>Instance declarations</title>
3253 <sect3 id="instance-rules">
3254 <title>Relaxed rules for instance declarations</title>
3256 <para>An instance declaration has the form
3258 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 ...
3260 The part before the "<literal>=></literal>" is the
3261 <emphasis>context</emphasis>, while the part after the
3262 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3266 In Haskell 98 the head of an instance declaration
3267 must be of the form <literal>C (T a1 ... an)</literal>, where
3268 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3269 and the <literal>a1 ... an</literal> are distinct type variables.
3270 Furthermore, the assertions in the context of the instance declaration
3271 must be of the form <literal>C a</literal> where <literal>a</literal>
3272 is a type variable that occurs in the head.
3275 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3276 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3277 the context and head of the instance declaration can each consist of arbitrary
3278 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3282 The Paterson Conditions: for each assertion in the context
3284 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3285 <listitem><para>The assertion has fewer constructors and variables (taken together
3286 and counting repetitions) than the head</para></listitem>
3290 <listitem><para>The Coverage Condition. For each functional dependency,
3291 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3292 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3293 every type variable in
3294 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3295 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3296 substitution mapping each type variable in the class declaration to the
3297 corresponding type in the instance declaration.
3300 These restrictions ensure that context reduction terminates: each reduction
3301 step makes the problem smaller by at least one
3302 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3303 if you give the <option>-XUndecidableInstances</option>
3304 flag (<xref linkend="undecidable-instances"/>).
3305 You can find lots of background material about the reason for these
3306 restrictions in the paper <ulink
3307 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3308 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3311 For example, these are OK:
3313 instance C Int [a] -- Multiple parameters
3314 instance Eq (S [a]) -- Structured type in head
3316 -- Repeated type variable in head
3317 instance C4 a a => C4 [a] [a]
3318 instance Stateful (ST s) (MutVar s)
3320 -- Head can consist of type variables only
3322 instance (Eq a, Show b) => C2 a b
3324 -- Non-type variables in context
3325 instance Show (s a) => Show (Sized s a)
3326 instance C2 Int a => C3 Bool [a]
3327 instance C2 Int a => C3 [a] b
3331 -- Context assertion no smaller than head
3332 instance C a => C a where ...
3333 -- (C b b) has more more occurrences of b than the head
3334 instance C b b => Foo [b] where ...
3339 The same restrictions apply to instances generated by
3340 <literal>deriving</literal> clauses. Thus the following is accepted:
3342 data MinHeap h a = H a (h a)
3345 because the derived instance
3347 instance (Show a, Show (h a)) => Show (MinHeap h a)
3349 conforms to the above rules.
3353 A useful idiom permitted by the above rules is as follows.
3354 If one allows overlapping instance declarations then it's quite
3355 convenient to have a "default instance" declaration that applies if
3356 something more specific does not:
3364 <sect3 id="undecidable-instances">
3365 <title>Undecidable instances</title>
3368 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3369 For example, sometimes you might want to use the following to get the
3370 effect of a "class synonym":
3372 class (C1 a, C2 a, C3 a) => C a where { }
3374 instance (C1 a, C2 a, C3 a) => C a where { }
3376 This allows you to write shorter signatures:
3382 f :: (C1 a, C2 a, C3 a) => ...
3384 The restrictions on functional dependencies (<xref
3385 linkend="functional-dependencies"/>) are particularly troublesome.
3386 It is tempting to introduce type variables in the context that do not appear in
3387 the head, something that is excluded by the normal rules. For example:
3389 class HasConverter a b | a -> b where
3392 data Foo a = MkFoo a
3394 instance (HasConverter a b,Show b) => Show (Foo a) where
3395 show (MkFoo value) = show (convert value)
3397 This is dangerous territory, however. Here, for example, is a program that would make the
3402 instance F [a] [[a]]
3403 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3405 Similarly, it can be tempting to lift the coverage condition:
3407 class Mul a b c | a b -> c where
3408 (.*.) :: a -> b -> c
3410 instance Mul Int Int Int where (.*.) = (*)
3411 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3412 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3414 The third instance declaration does not obey the coverage condition;
3415 and indeed the (somewhat strange) definition:
3417 f = \ b x y -> if b then x .*. [y] else y
3419 makes instance inference go into a loop, because it requires the constraint
3420 <literal>(Mul a [b] b)</literal>.
3423 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3424 the experimental flag <option>-XUndecidableInstances</option>
3425 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3426 both the Paterson Conditions and the Coverage Condition
3427 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3428 fixed-depth recursion stack. If you exceed the stack depth you get a
3429 sort of backtrace, and the opportunity to increase the stack depth
3430 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3436 <sect3 id="instance-overlap">
3437 <title>Overlapping instances</title>
3439 In general, <emphasis>GHC requires that that it be unambiguous which instance
3441 should be used to resolve a type-class constraint</emphasis>. This behaviour
3442 can be modified by two flags: <option>-XOverlappingInstances</option>
3443 <indexterm><primary>-XOverlappingInstances
3444 </primary></indexterm>
3445 and <option>-XIncoherentInstances</option>
3446 <indexterm><primary>-XIncoherentInstances
3447 </primary></indexterm>, as this section discusses. Both these
3448 flags are dynamic flags, and can be set on a per-module basis, using
3449 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3451 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3452 it tries to match every instance declaration against the
3454 by instantiating the head of the instance declaration. For example, consider
3457 instance context1 => C Int a where ... -- (A)
3458 instance context2 => C a Bool where ... -- (B)
3459 instance context3 => C Int [a] where ... -- (C)
3460 instance context4 => C Int [Int] where ... -- (D)
3462 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3463 but (C) and (D) do not. When matching, GHC takes
3464 no account of the context of the instance declaration
3465 (<literal>context1</literal> etc).
3466 GHC's default behaviour is that <emphasis>exactly one instance must match the
3467 constraint it is trying to resolve</emphasis>.
3468 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3469 including both declarations (A) and (B), say); an error is only reported if a
3470 particular constraint matches more than one.
3474 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3475 more than one instance to match, provided there is a most specific one. For
3476 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3477 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3478 most-specific match, the program is rejected.
3481 However, GHC is conservative about committing to an overlapping instance. For example:
3486 Suppose that from the RHS of <literal>f</literal> we get the constraint
3487 <literal>C Int [b]</literal>. But
3488 GHC does not commit to instance (C), because in a particular
3489 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3490 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3491 So GHC rejects the program.
3492 (If you add the flag <option>-XIncoherentInstances</option>,
3493 GHC will instead pick (C), without complaining about
3494 the problem of subsequent instantiations.)
3497 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3498 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3499 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3500 it instead. In this case, GHC will refrain from
3501 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3502 as before) but, rather than rejecting the program, it will infer the type
3504 f :: C Int [b] => [b] -> [b]
3506 That postpones the question of which instance to pick to the
3507 call site for <literal>f</literal>
3508 by which time more is known about the type <literal>b</literal>.
3509 You can write this type signature yourself if you use the
3510 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3514 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3518 instance Foo [b] where
3521 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3522 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3523 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3524 declaration. The solution is to postpone the choice by adding the constraint to the context
3525 of the instance declaration, thus:
3527 instance C Int [b] => Foo [b] where
3530 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3533 The willingness to be overlapped or incoherent is a property of
3534 the <emphasis>instance declaration</emphasis> itself, controlled by the
3535 presence or otherwise of the <option>-XOverlappingInstances</option>
3536 and <option>-XIncoherentInstances</option> flags when that module is
3537 being defined. Neither flag is required in a module that imports and uses the
3538 instance declaration. Specifically, during the lookup process:
3541 An instance declaration is ignored during the lookup process if (a) a more specific
3542 match is found, and (b) the instance declaration was compiled with
3543 <option>-XOverlappingInstances</option>. The flag setting for the
3544 more-specific instance does not matter.
3547 Suppose an instance declaration does not match the constraint being looked up, but
3548 does unify with it, so that it might match when the constraint is further
3549 instantiated. Usually GHC will regard this as a reason for not committing to
3550 some other constraint. But if the instance declaration was compiled with
3551 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3552 check for that declaration.
3555 These rules make it possible for a library author to design a library that relies on
3556 overlapping instances without the library client having to know.
3559 If an instance declaration is compiled without
3560 <option>-XOverlappingInstances</option>,
3561 then that instance can never be overlapped. This could perhaps be
3562 inconvenient. Perhaps the rule should instead say that the
3563 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3564 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3565 at a usage site should be permitted regardless of how the instance declarations
3566 are compiled, if the <option>-XOverlappingInstances</option> flag is
3567 used at the usage site. (Mind you, the exact usage site can occasionally be
3568 hard to pin down.) We are interested to receive feedback on these points.
3570 <para>The <option>-XIncoherentInstances</option> flag implies the
3571 <option>-XOverlappingInstances</option> flag, but not vice versa.
3576 <title>Type synonyms in the instance head</title>
3579 <emphasis>Unlike Haskell 98, instance heads may use type
3580 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3581 As always, using a type synonym is just shorthand for
3582 writing the RHS of the type synonym definition. For example:
3586 type Point = (Int,Int)
3587 instance C Point where ...
3588 instance C [Point] where ...
3592 is legal. However, if you added
3596 instance C (Int,Int) where ...
3600 as well, then the compiler will complain about the overlapping
3601 (actually, identical) instance declarations. As always, type synonyms
3602 must be fully applied. You cannot, for example, write:
3607 instance Monad P where ...
3611 This design decision is independent of all the others, and easily
3612 reversed, but it makes sense to me.
3620 <sect2 id="overloaded-strings">
3621 <title>Overloaded string literals
3625 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3626 string literal has type <literal>String</literal>, but with overloaded string
3627 literals enabled (with <literal>-XOverloadedStrings</literal>)
3628 a string literal has type <literal>(IsString a) => a</literal>.
3631 This means that the usual string syntax can be used, e.g., for packed strings
3632 and other variations of string like types. String literals behave very much
3633 like integer literals, i.e., they can be used in both expressions and patterns.
3634 If used in a pattern the literal with be replaced by an equality test, in the same
3635 way as an integer literal is.
3638 The class <literal>IsString</literal> is defined as:
3640 class IsString a where
3641 fromString :: String -> a
3643 The only predefined instance is the obvious one to make strings work as usual:
3645 instance IsString [Char] where
3648 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3649 it explicitly (for example, to give an instance declaration for it), you can import it
3650 from module <literal>GHC.Exts</literal>.
3653 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3657 Each type in a default declaration must be an
3658 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3662 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3663 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3664 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3665 <emphasis>or</emphasis> <literal>IsString</literal>.
3674 import GHC.Exts( IsString(..) )
3676 newtype MyString = MyString String deriving (Eq, Show)
3677 instance IsString MyString where
3678 fromString = MyString
3680 greet :: MyString -> MyString
3681 greet "hello" = "world"
3685 print $ greet "hello"
3686 print $ greet "fool"
3690 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3691 to work since it gets translated into an equality comparison.
3697 <sect1 id="other-type-extensions">
3698 <title>Other type system extensions</title>
3700 <sect2 id="type-restrictions">
3701 <title>Type signatures</title>
3703 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3705 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
3706 that the type-class constraints in a type signature must have the
3707 form <emphasis>(class type-variable)</emphasis> or
3708 <emphasis>(class (type-variable type-variable ...))</emphasis>.
3709 With <option>-XFlexibleContexts</option>
3710 these type signatures are perfectly OK
3713 g :: Ord (T a ()) => ...
3717 GHC imposes the following restrictions on the constraints in a type signature.
3721 forall tv1..tvn (c1, ...,cn) => type
3724 (Here, we write the "foralls" explicitly, although the Haskell source
3725 language omits them; in Haskell 98, all the free type variables of an
3726 explicit source-language type signature are universally quantified,
3727 except for the class type variables in a class declaration. However,
3728 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3737 <emphasis>Each universally quantified type variable
3738 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3740 A type variable <literal>a</literal> is "reachable" if it appears
3741 in the same constraint as either a type variable free in
3742 <literal>type</literal>, or another reachable type variable.
3743 A value with a type that does not obey
3744 this reachability restriction cannot be used without introducing
3745 ambiguity; that is why the type is rejected.
3746 Here, for example, is an illegal type:
3750 forall a. Eq a => Int
3754 When a value with this type was used, the constraint <literal>Eq tv</literal>
3755 would be introduced where <literal>tv</literal> is a fresh type variable, and
3756 (in the dictionary-translation implementation) the value would be
3757 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3758 can never know which instance of <literal>Eq</literal> to use because we never
3759 get any more information about <literal>tv</literal>.
3763 that the reachability condition is weaker than saying that <literal>a</literal> is
3764 functionally dependent on a type variable free in
3765 <literal>type</literal> (see <xref
3766 linkend="functional-dependencies"/>). The reason for this is there
3767 might be a "hidden" dependency, in a superclass perhaps. So
3768 "reachable" is a conservative approximation to "functionally dependent".
3769 For example, consider:
3771 class C a b | a -> b where ...
3772 class C a b => D a b where ...
3773 f :: forall a b. D a b => a -> a
3775 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3776 but that is not immediately apparent from <literal>f</literal>'s type.
3782 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3783 universally quantified type variables <literal>tvi</literal></emphasis>.
3785 For example, this type is OK because <literal>C a b</literal> mentions the
3786 universally quantified type variable <literal>b</literal>:
3790 forall a. C a b => burble
3794 The next type is illegal because the constraint <literal>Eq b</literal> does not
3795 mention <literal>a</literal>:
3799 forall a. Eq b => burble
3803 The reason for this restriction is milder than the other one. The
3804 excluded types are never useful or necessary (because the offending
3805 context doesn't need to be witnessed at this point; it can be floated
3806 out). Furthermore, floating them out increases sharing. Lastly,
3807 excluding them is a conservative choice; it leaves a patch of
3808 territory free in case we need it later.
3822 <sect2 id="implicit-parameters">
3823 <title>Implicit parameters</title>
3825 <para> Implicit parameters are implemented as described in
3826 "Implicit parameters: dynamic scoping with static types",
3827 J Lewis, MB Shields, E Meijer, J Launchbury,
3828 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3832 <para>(Most of the following, still rather incomplete, documentation is
3833 due to Jeff Lewis.)</para>
3835 <para>Implicit parameter support is enabled with the option
3836 <option>-XImplicitParams</option>.</para>
3839 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3840 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3841 context. In Haskell, all variables are statically bound. Dynamic
3842 binding of variables is a notion that goes back to Lisp, but was later
3843 discarded in more modern incarnations, such as Scheme. Dynamic binding
3844 can be very confusing in an untyped language, and unfortunately, typed
3845 languages, in particular Hindley-Milner typed languages like Haskell,
3846 only support static scoping of variables.
3849 However, by a simple extension to the type class system of Haskell, we
3850 can support dynamic binding. Basically, we express the use of a
3851 dynamically bound variable as a constraint on the type. These
3852 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3853 function uses a dynamically-bound variable <literal>?x</literal>
3854 of type <literal>t'</literal>". For
3855 example, the following expresses the type of a sort function,
3856 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3858 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3860 The dynamic binding constraints are just a new form of predicate in the type class system.
3863 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3864 where <literal>x</literal> is
3865 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3866 Use of this construct also introduces a new
3867 dynamic-binding constraint in the type of the expression.
3868 For example, the following definition
3869 shows how we can define an implicitly parameterized sort function in
3870 terms of an explicitly parameterized <literal>sortBy</literal> function:
3872 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3874 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3880 <title>Implicit-parameter type constraints</title>
3882 Dynamic binding constraints behave just like other type class
3883 constraints in that they are automatically propagated. Thus, when a
3884 function is used, its implicit parameters are inherited by the
3885 function that called it. For example, our <literal>sort</literal> function might be used
3886 to pick out the least value in a list:
3888 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3889 least xs = head (sort xs)
3891 Without lifting a finger, the <literal>?cmp</literal> parameter is
3892 propagated to become a parameter of <literal>least</literal> as well. With explicit
3893 parameters, the default is that parameters must always be explicit
3894 propagated. With implicit parameters, the default is to always
3898 An implicit-parameter type constraint differs from other type class constraints in the
3899 following way: All uses of a particular implicit parameter must have
3900 the same type. This means that the type of <literal>(?x, ?x)</literal>
3901 is <literal>(?x::a) => (a,a)</literal>, and not
3902 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3906 <para> You can't have an implicit parameter in the context of a class or instance
3907 declaration. For example, both these declarations are illegal:
3909 class (?x::Int) => C a where ...
3910 instance (?x::a) => Foo [a] where ...
3912 Reason: exactly which implicit parameter you pick up depends on exactly where
3913 you invoke a function. But the ``invocation'' of instance declarations is done
3914 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3915 Easiest thing is to outlaw the offending types.</para>
3917 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3919 f :: (?x :: [a]) => Int -> Int
3922 g :: (Read a, Show a) => String -> String
3925 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3926 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3927 quite unambiguous, and fixes the type <literal>a</literal>.
3932 <title>Implicit-parameter bindings</title>
3935 An implicit parameter is <emphasis>bound</emphasis> using the standard
3936 <literal>let</literal> or <literal>where</literal> binding forms.
3937 For example, we define the <literal>min</literal> function by binding
3938 <literal>cmp</literal>.
3941 min = let ?cmp = (<=) in least
3945 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3946 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3947 (including in a list comprehension, or do-notation, or pattern guards),
3948 or a <literal>where</literal> clause.
3949 Note the following points:
3952 An implicit-parameter binding group must be a
3953 collection of simple bindings to implicit-style variables (no
3954 function-style bindings, and no type signatures); these bindings are
3955 neither polymorphic or recursive.
3958 You may not mix implicit-parameter bindings with ordinary bindings in a
3959 single <literal>let</literal>
3960 expression; use two nested <literal>let</literal>s instead.
3961 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3965 You may put multiple implicit-parameter bindings in a
3966 single binding group; but they are <emphasis>not</emphasis> treated
3967 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3968 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3969 parameter. The bindings are not nested, and may be re-ordered without changing
3970 the meaning of the program.
3971 For example, consider:
3973 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3975 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3976 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3978 f :: (?x::Int) => Int -> Int
3986 <sect3><title>Implicit parameters and polymorphic recursion</title>
3989 Consider these two definitions:
3992 len1 xs = let ?acc = 0 in len_acc1 xs
3995 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4000 len2 xs = let ?acc = 0 in len_acc2 xs
4002 len_acc2 :: (?acc :: Int) => [a] -> Int
4004 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4006 The only difference between the two groups is that in the second group
4007 <literal>len_acc</literal> is given a type signature.
4008 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4009 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4010 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4011 has a type signature, the recursive call is made to the
4012 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4013 as an implicit parameter. So we get the following results in GHCi:
4020 Adding a type signature dramatically changes the result! This is a rather
4021 counter-intuitive phenomenon, worth watching out for.
4025 <sect3><title>Implicit parameters and monomorphism</title>
4027 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4028 Haskell Report) to implicit parameters. For example, consider:
4036 Since the binding for <literal>y</literal> falls under the Monomorphism
4037 Restriction it is not generalised, so the type of <literal>y</literal> is
4038 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4039 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4040 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4041 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4042 <literal>y</literal> in the body of the <literal>let</literal> will see the
4043 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4044 <literal>14</literal>.
4049 <!-- ======================= COMMENTED OUT ========================
4051 We intend to remove linear implicit parameters, so I'm at least removing
4052 them from the 6.6 user manual
4054 <sect2 id="linear-implicit-parameters">
4055 <title>Linear implicit parameters</title>
4057 Linear implicit parameters are an idea developed by Koen Claessen,
4058 Mark Shields, and Simon PJ. They address the long-standing
4059 problem that monads seem over-kill for certain sorts of problem, notably:
4062 <listitem> <para> distributing a supply of unique names </para> </listitem>
4063 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4064 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4068 Linear implicit parameters are just like ordinary implicit parameters,
4069 except that they are "linear"; that is, they cannot be copied, and
4070 must be explicitly "split" instead. Linear implicit parameters are
4071 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4072 (The '/' in the '%' suggests the split!)
4077 import GHC.Exts( Splittable )
4079 data NameSupply = ...
4081 splitNS :: NameSupply -> (NameSupply, NameSupply)
4082 newName :: NameSupply -> Name
4084 instance Splittable NameSupply where
4088 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4089 f env (Lam x e) = Lam x' (f env e)
4092 env' = extend env x x'
4093 ...more equations for f...
4095 Notice that the implicit parameter %ns is consumed
4097 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4098 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4102 So the translation done by the type checker makes
4103 the parameter explicit:
4105 f :: NameSupply -> Env -> Expr -> Expr
4106 f ns env (Lam x e) = Lam x' (f ns1 env e)
4108 (ns1,ns2) = splitNS ns
4110 env = extend env x x'
4112 Notice the call to 'split' introduced by the type checker.
4113 How did it know to use 'splitNS'? Because what it really did
4114 was to introduce a call to the overloaded function 'split',
4115 defined by the class <literal>Splittable</literal>:
4117 class Splittable a where
4120 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4121 split for name supplies. But we can simply write
4127 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4129 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4130 <literal>GHC.Exts</literal>.
4135 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4136 are entirely distinct implicit parameters: you
4137 can use them together and they won't interfere with each other. </para>
4140 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4142 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4143 in the context of a class or instance declaration. </para></listitem>
4147 <sect3><title>Warnings</title>
4150 The monomorphism restriction is even more important than usual.
4151 Consider the example above:
4153 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4154 f env (Lam x e) = Lam x' (f env e)
4157 env' = extend env x x'
4159 If we replaced the two occurrences of x' by (newName %ns), which is
4160 usually a harmless thing to do, we get:
4162 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4163 f env (Lam x e) = Lam (newName %ns) (f env e)
4165 env' = extend env x (newName %ns)
4167 But now the name supply is consumed in <emphasis>three</emphasis> places
4168 (the two calls to newName,and the recursive call to f), so
4169 the result is utterly different. Urk! We don't even have
4173 Well, this is an experimental change. With implicit
4174 parameters we have already lost beta reduction anyway, and
4175 (as John Launchbury puts it) we can't sensibly reason about
4176 Haskell programs without knowing their typing.
4181 <sect3><title>Recursive functions</title>
4182 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4185 foo :: %x::T => Int -> [Int]
4187 foo n = %x : foo (n-1)
4189 where T is some type in class Splittable.</para>
4191 Do you get a list of all the same T's or all different T's
4192 (assuming that split gives two distinct T's back)?
4194 If you supply the type signature, taking advantage of polymorphic
4195 recursion, you get what you'd probably expect. Here's the
4196 translated term, where the implicit param is made explicit:
4199 foo x n = let (x1,x2) = split x
4200 in x1 : foo x2 (n-1)
4202 But if you don't supply a type signature, GHC uses the Hindley
4203 Milner trick of using a single monomorphic instance of the function
4204 for the recursive calls. That is what makes Hindley Milner type inference
4205 work. So the translation becomes
4209 foom n = x : foom (n-1)
4213 Result: 'x' is not split, and you get a list of identical T's. So the
4214 semantics of the program depends on whether or not foo has a type signature.
4217 You may say that this is a good reason to dislike linear implicit parameters
4218 and you'd be right. That is why they are an experimental feature.
4224 ================ END OF Linear Implicit Parameters commented out -->
4226 <sect2 id="kinding">
4227 <title>Explicitly-kinded quantification</title>
4230 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4231 to give the kind explicitly as (machine-checked) documentation,
4232 just as it is nice to give a type signature for a function. On some occasions,
4233 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4234 John Hughes had to define the data type:
4236 data Set cxt a = Set [a]
4237 | Unused (cxt a -> ())
4239 The only use for the <literal>Unused</literal> constructor was to force the correct
4240 kind for the type variable <literal>cxt</literal>.
4243 GHC now instead allows you to specify the kind of a type variable directly, wherever
4244 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4247 This flag enables kind signatures in the following places:
4249 <listitem><para><literal>data</literal> declarations:
4251 data Set (cxt :: * -> *) a = Set [a]
4252 </screen></para></listitem>
4253 <listitem><para><literal>type</literal> declarations:
4255 type T (f :: * -> *) = f Int
4256 </screen></para></listitem>
4257 <listitem><para><literal>class</literal> declarations:
4259 class (Eq a) => C (f :: * -> *) a where ...
4260 </screen></para></listitem>
4261 <listitem><para><literal>forall</literal>'s in type signatures:
4263 f :: forall (cxt :: * -> *). Set cxt Int
4264 </screen></para></listitem>
4269 The parentheses are required. Some of the spaces are required too, to
4270 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4271 will get a parse error, because "<literal>::*->*</literal>" is a
4272 single lexeme in Haskell.
4276 As part of the same extension, you can put kind annotations in types
4279 f :: (Int :: *) -> Int
4280 g :: forall a. a -> (a :: *)
4284 atype ::= '(' ctype '::' kind ')
4286 The parentheses are required.
4291 <sect2 id="universal-quantification">
4292 <title>Arbitrary-rank polymorphism
4296 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4297 allows us to say exactly what this means. For example:
4305 g :: forall b. (b -> b)
4307 The two are treated identically.
4311 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4312 explicit universal quantification in
4314 For example, all the following types are legal:
4316 f1 :: forall a b. a -> b -> a
4317 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4319 f2 :: (forall a. a->a) -> Int -> Int
4320 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4322 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4324 f4 :: Int -> (forall a. a -> a)
4326 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4327 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4328 The <literal>forall</literal> makes explicit the universal quantification that
4329 is implicitly added by Haskell.
4332 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4333 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4334 shows, the polymorphic type on the left of the function arrow can be overloaded.
4337 The function <literal>f3</literal> has a rank-3 type;
4338 it has rank-2 types on the left of a function arrow.
4341 GHC has three flags to control higher-rank types:
4344 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4347 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4350 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4351 That is, you can nest <literal>forall</literal>s
4352 arbitrarily deep in function arrows.
4353 In particular, a forall-type (also called a "type scheme"),
4354 including an operational type class context, is legal:
4356 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4357 of a function arrow </para> </listitem>
4358 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4359 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4360 field type signatures.</para> </listitem>
4361 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4362 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4366 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4367 a type variable any more!
4376 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4377 the types of the constructor arguments. Here are several examples:
4383 data T a = T1 (forall b. b -> b -> b) a
4385 data MonadT m = MkMonad { return :: forall a. a -> m a,
4386 bind :: forall a b. m a -> (a -> m b) -> m b
4389 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4395 The constructors have rank-2 types:
4401 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4402 MkMonad :: forall m. (forall a. a -> m a)
4403 -> (forall a b. m a -> (a -> m b) -> m b)
4405 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4411 Notice that you don't need to use a <literal>forall</literal> if there's an
4412 explicit context. For example in the first argument of the
4413 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4414 prefixed to the argument type. The implicit <literal>forall</literal>
4415 quantifies all type variables that are not already in scope, and are
4416 mentioned in the type quantified over.
4420 As for type signatures, implicit quantification happens for non-overloaded
4421 types too. So if you write this:
4424 data T a = MkT (Either a b) (b -> b)
4427 it's just as if you had written this:
4430 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4433 That is, since the type variable <literal>b</literal> isn't in scope, it's
4434 implicitly universally quantified. (Arguably, it would be better
4435 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4436 where that is what is wanted. Feedback welcomed.)
4440 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4441 the constructor to suitable values, just as usual. For example,
4452 a3 = MkSwizzle reverse
4455 a4 = let r x = Just x
4462 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4463 mkTs f x y = [T1 f x, T1 f y]
4469 The type of the argument can, as usual, be more general than the type
4470 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4471 does not need the <literal>Ord</literal> constraint.)
4475 When you use pattern matching, the bound variables may now have
4476 polymorphic types. For example:
4482 f :: T a -> a -> (a, Char)
4483 f (T1 w k) x = (w k x, w 'c' 'd')
4485 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4486 g (MkSwizzle s) xs f = s (map f (s xs))
4488 h :: MonadT m -> [m a] -> m [a]
4489 h m [] = return m []
4490 h m (x:xs) = bind m x $ \y ->
4491 bind m (h m xs) $ \ys ->
4498 In the function <function>h</function> we use the record selectors <literal>return</literal>
4499 and <literal>bind</literal> to extract the polymorphic bind and return functions
4500 from the <literal>MonadT</literal> data structure, rather than using pattern
4506 <title>Type inference</title>
4509 In general, type inference for arbitrary-rank types is undecidable.
4510 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4511 to get a decidable algorithm by requiring some help from the programmer.
4512 We do not yet have a formal specification of "some help" but the rule is this:
4515 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4516 provides an explicit polymorphic type for x, or GHC's type inference will assume
4517 that x's type has no foralls in it</emphasis>.
4520 What does it mean to "provide" an explicit type for x? You can do that by
4521 giving a type signature for x directly, using a pattern type signature
4522 (<xref linkend="scoped-type-variables"/>), thus:
4524 \ f :: (forall a. a->a) -> (f True, f 'c')
4526 Alternatively, you can give a type signature to the enclosing
4527 context, which GHC can "push down" to find the type for the variable:
4529 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4531 Here the type signature on the expression can be pushed inwards
4532 to give a type signature for f. Similarly, and more commonly,
4533 one can give a type signature for the function itself:
4535 h :: (forall a. a->a) -> (Bool,Char)
4536 h f = (f True, f 'c')
4538 You don't need to give a type signature if the lambda bound variable
4539 is a constructor argument. Here is an example we saw earlier:
4541 f :: T a -> a -> (a, Char)
4542 f (T1 w k) x = (w k x, w 'c' 'd')
4544 Here we do not need to give a type signature to <literal>w</literal>, because
4545 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4552 <sect3 id="implicit-quant">
4553 <title>Implicit quantification</title>
4556 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4557 user-written types, if and only if there is no explicit <literal>forall</literal>,
4558 GHC finds all the type variables mentioned in the type that are not already
4559 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4563 f :: forall a. a -> a
4570 h :: forall b. a -> b -> b
4576 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4579 f :: (a -> a) -> Int
4581 f :: forall a. (a -> a) -> Int
4583 f :: (forall a. a -> a) -> Int
4586 g :: (Ord a => a -> a) -> Int
4587 -- MEANS the illegal type
4588 g :: forall a. (Ord a => a -> a) -> Int
4590 g :: (forall a. Ord a => a -> a) -> Int
4592 The latter produces an illegal type, which you might think is silly,
4593 but at least the rule is simple. If you want the latter type, you
4594 can write your for-alls explicitly. Indeed, doing so is strongly advised
4601 <sect2 id="impredicative-polymorphism">
4602 <title>Impredicative polymorphism
4604 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4605 enabled with <option>-XImpredicativeTypes</option>.
4607 that you can call a polymorphic function at a polymorphic type, and
4608 parameterise data structures over polymorphic types. For example:
4610 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4611 f (Just g) = Just (g [3], g "hello")
4614 Notice here that the <literal>Maybe</literal> type is parameterised by the
4615 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4618 <para>The technical details of this extension are described in the paper
4619 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4620 type inference for higher-rank types and impredicativity</ulink>,
4621 which appeared at ICFP 2006.
4625 <sect2 id="scoped-type-variables">
4626 <title>Lexically scoped type variables
4630 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4631 which some type signatures are simply impossible to write. For example:
4633 f :: forall a. [a] -> [a]
4639 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4640 the entire definition of <literal>f</literal>.
4641 In particular, it is in scope at the type signature for <varname>ys</varname>.
4642 In Haskell 98 it is not possible to declare
4643 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4644 it becomes possible to do so.
4646 <para>Lexically-scoped type variables are enabled by
4647 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4649 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4650 variables work, compared to earlier releases. Read this section
4654 <title>Overview</title>
4656 <para>The design follows the following principles
4658 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4659 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4660 design.)</para></listitem>
4661 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4662 type variables. This means that every programmer-written type signature
4663 (including one that contains free scoped type variables) denotes a
4664 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4665 checker, and no inference is involved.</para></listitem>
4666 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4667 changing the program.</para></listitem>
4671 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4673 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4674 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4675 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4676 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4680 In Haskell, a programmer-written type signature is implicitly quantified over
4681 its free type variables (<ulink
4682 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4684 of the Haskell Report).
4685 Lexically scoped type variables affect this implicit quantification rules
4686 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4687 quantified. For example, if type variable <literal>a</literal> is in scope,
4690 (e :: a -> a) means (e :: a -> a)
4691 (e :: b -> b) means (e :: forall b. b->b)
4692 (e :: a -> b) means (e :: forall b. a->b)
4700 <sect3 id="decl-type-sigs">
4701 <title>Declaration type signatures</title>
4702 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4703 quantification (using <literal>forall</literal>) brings into scope the
4704 explicitly-quantified
4705 type variables, in the definition of the named function. For example:
4707 f :: forall a. [a] -> [a]
4708 f (x:xs) = xs ++ [ x :: a ]
4710 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4711 the definition of "<literal>f</literal>".
4713 <para>This only happens if:
4715 <listitem><para> The quantification in <literal>f</literal>'s type
4716 signature is explicit. For example:
4719 g (x:xs) = xs ++ [ x :: a ]
4721 This program will be rejected, because "<literal>a</literal>" does not scope
4722 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4723 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4724 quantification rules.
4726 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4727 not a pattern binding.
4730 f1 :: forall a. [a] -> [a]
4731 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4733 f2 :: forall a. [a] -> [a]
4734 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4736 f3 :: forall a. [a] -> [a]
4737 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4739 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4740 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4741 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4742 the type signature brings <literal>a</literal> into scope.
4748 <sect3 id="exp-type-sigs">
4749 <title>Expression type signatures</title>
4751 <para>An expression type signature that has <emphasis>explicit</emphasis>
4752 quantification (using <literal>forall</literal>) brings into scope the
4753 explicitly-quantified
4754 type variables, in the annotated expression. For example:
4756 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4758 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4759 type variable <literal>s</literal> into scope, in the annotated expression
4760 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4765 <sect3 id="pattern-type-sigs">
4766 <title>Pattern type signatures</title>
4768 A type signature may occur in any pattern; this is a <emphasis>pattern type
4769 signature</emphasis>.
4772 -- f and g assume that 'a' is already in scope
4773 f = \(x::Int, y::a) -> x
4775 h ((x,y) :: (Int,Bool)) = (y,x)
4777 In the case where all the type variables in the pattern type signature are
4778 already in scope (i.e. bound by the enclosing context), matters are simple: the
4779 signature simply constrains the type of the pattern in the obvious way.
4782 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4783 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4784 that are already in scope. For example:
4786 f :: forall a. [a] -> (Int, [a])
4789 (ys::[a], n) = (reverse xs, length xs) -- OK
4790 zs::[a] = xs ++ ys -- OK
4792 Just (v::b) = ... -- Not OK; b is not in scope
4794 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4795 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4799 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4800 type signature may mention a type variable that is not in scope; in this case,
4801 <emphasis>the signature brings that type variable into scope</emphasis>.
4802 This is particularly important for existential data constructors. For example:
4804 data T = forall a. MkT [a]
4807 k (MkT [t::a]) = MkT t3
4811 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4812 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4813 because it is bound by the pattern match. GHC's rule is that in this situation
4814 (and only then), a pattern type signature can mention a type variable that is
4815 not already in scope; the effect is to bring it into scope, standing for the
4816 existentially-bound type variable.
4819 When a pattern type signature binds a type variable in this way, GHC insists that the
4820 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4821 This means that any user-written type signature always stands for a completely known type.
4824 If all this seems a little odd, we think so too. But we must have
4825 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4826 could not name existentially-bound type variables in subsequent type signatures.
4829 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4830 signature is allowed to mention a lexical variable that is not already in
4832 For example, both <literal>f</literal> and <literal>g</literal> would be
4833 illegal if <literal>a</literal> was not already in scope.
4839 <!-- ==================== Commented out part about result type signatures
4841 <sect3 id="result-type-sigs">
4842 <title>Result type signatures</title>
4845 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4848 {- f assumes that 'a' is already in scope -}
4849 f x y :: [a] = [x,y,x]
4851 g = \ x :: [Int] -> [3,4]
4853 h :: forall a. [a] -> a
4857 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4858 the result of the function. Similarly, the body of the lambda in the RHS of
4859 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4860 alternative in <literal>h</literal> is <literal>a</literal>.
4862 <para> A result type signature never brings new type variables into scope.</para>
4864 There are a couple of syntactic wrinkles. First, notice that all three
4865 examples would parse quite differently with parentheses:
4867 {- f assumes that 'a' is already in scope -}
4868 f x (y :: [a]) = [x,y,x]
4870 g = \ (x :: [Int]) -> [3,4]
4872 h :: forall a. [a] -> a
4876 Now the signature is on the <emphasis>pattern</emphasis>; and
4877 <literal>h</literal> would certainly be ill-typed (since the pattern
4878 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4880 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4881 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4882 token or a parenthesised type of some sort). To see why,
4883 consider how one would parse this:
4892 <sect3 id="cls-inst-scoped-tyvars">
4893 <title>Class and instance declarations</title>
4896 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4897 scope over the methods defined in the <literal>where</literal> part. For example:
4915 <sect2 id="typing-binds">
4916 <title>Generalised typing of mutually recursive bindings</title>
4919 The Haskell Report specifies that a group of bindings (at top level, or in a
4920 <literal>let</literal> or <literal>where</literal>) should be sorted into
4921 strongly-connected components, and then type-checked in dependency order
4922 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4923 Report, Section 4.5.1</ulink>).
4924 As each group is type-checked, any binders of the group that
4926 an explicit type signature are put in the type environment with the specified
4928 and all others are monomorphic until the group is generalised
4929 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4932 <para>Following a suggestion of Mark Jones, in his paper
4933 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4935 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4937 <emphasis>the dependency analysis ignores references to variables that have an explicit
4938 type signature</emphasis>.
4939 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4940 typecheck. For example, consider:
4942 f :: Eq a => a -> Bool
4943 f x = (x == x) || g True || g "Yes"
4945 g y = (y <= y) || f True
4947 This is rejected by Haskell 98, but under Jones's scheme the definition for
4948 <literal>g</literal> is typechecked first, separately from that for
4949 <literal>f</literal>,
4950 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4951 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4952 type is generalised, to get
4954 g :: Ord a => a -> Bool
4956 Now, the definition for <literal>f</literal> is typechecked, with this type for
4957 <literal>g</literal> in the type environment.
4961 The same refined dependency analysis also allows the type signatures of
4962 mutually-recursive functions to have different contexts, something that is illegal in
4963 Haskell 98 (Section 4.5.2, last sentence). With
4964 <option>-XRelaxedPolyRec</option>
4965 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4966 type signatures; in practice this means that only variables bound by the same
4967 pattern binding must have the same context. For example, this is fine:
4969 f :: Eq a => a -> Bool
4970 f x = (x == x) || g True
4972 g :: Ord a => a -> Bool
4973 g y = (y <= y) || f True
4978 <sect2 id="type-families">
4979 <title>Type families
4983 GHC supports the definition of type families indexed by types. They may be
4984 seen as an extension of Haskell 98's class-based overloading of values to
4985 types. When type families are declared in classes, they are also known as
4989 There are two forms of type families: data families and type synonym families.
4990 Currently, only the former are fully implemented, while we are still working
4991 on the latter. As a result, the specification of the language extension is
4992 also still to some degree in flux. Hence, a more detailed description of
4993 the language extension and its use is currently available
4994 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4995 wiki page on type families</ulink>. The material will be moved to this user's
4996 guide when it has stabilised.
4999 Type families are enabled by the flag <option>-XTypeFamilies</option>.
5006 <!-- ==================== End of type system extensions ================= -->
5008 <!-- ====================== TEMPLATE HASKELL ======================= -->
5010 <sect1 id="template-haskell">
5011 <title>Template Haskell</title>
5013 <para>Template Haskell allows you to do compile-time meta-programming in
5016 the main technical innovations is discussed in "<ulink
5017 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5018 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5021 There is a Wiki page about
5022 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5023 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5027 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5028 Haskell library reference material</ulink>
5029 (look for module <literal>Language.Haskell.TH</literal>).
5030 Many changes to the original design are described in
5031 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5032 Notes on Template Haskell version 2</ulink>.
5033 Not all of these changes are in GHC, however.
5036 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5037 as a worked example to help get you started.
5041 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5042 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5047 <title>Syntax</title>
5049 <para> Template Haskell has the following new syntactic
5050 constructions. You need to use the flag
5051 <option>-XTemplateHaskell</option>
5052 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5053 </indexterm>to switch these syntactic extensions on
5054 (<option>-XTemplateHaskell</option> is no longer implied by
5055 <option>-fglasgow-exts</option>).</para>
5059 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5060 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5061 There must be no space between the "$" and the identifier or parenthesis. This use
5062 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5063 of "." as an infix operator. If you want the infix operator, put spaces around it.
5065 <para> A splice can occur in place of
5067 <listitem><para> an expression; the spliced expression must
5068 have type <literal>Q Exp</literal></para></listitem>
5069 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5072 Inside a splice you can can only call functions defined in imported modules,
5073 not functions defined elsewhere in the same module.</listitem>
5077 A expression quotation is written in Oxford brackets, thus:
5079 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5080 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5081 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5082 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5083 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5084 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5085 </itemizedlist></para></listitem>
5088 A quasi-quotation can appear in either a pattern context or an
5089 expression context and is also written in Oxford brackets:
5091 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5092 where the "..." is an arbitrary string; a full description of the
5093 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5094 </itemizedlist></para></listitem>
5097 A name can be quoted with either one or two prefix single quotes:
5099 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5100 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5101 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5103 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5104 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5107 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5108 may also be given as an argument to the <literal>reify</literal> function.
5114 (Compared to the original paper, there are many differences of detail.
5115 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5116 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5117 Type splices are not implemented, and neither are pattern splices or quotations.
5121 <sect2> <title> Using Template Haskell </title>
5125 The data types and monadic constructor functions for Template Haskell are in the library
5126 <literal>Language.Haskell.THSyntax</literal>.
5130 You can only run a function at compile time if it is imported from another module. That is,
5131 you can't define a function in a module, and call it from within a splice in the same module.
5132 (It would make sense to do so, but it's hard to implement.)
5136 You can only run a function at compile time if it is imported
5137 from another module <emphasis>that is not part of a mutually-recursive group of modules
5138 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5139 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5140 splice is to be run.</para>
5142 For example, when compiling module A,
5143 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5144 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5148 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5151 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5152 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5153 compiles and runs a program, and then looks at the result. So it's important that
5154 the program it compiles produces results whose representations are identical to
5155 those of the compiler itself.
5159 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5160 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5165 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5166 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5167 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5174 -- Import our template "pr"
5175 import Printf ( pr )
5177 -- The splice operator $ takes the Haskell source code
5178 -- generated at compile time by "pr" and splices it into
5179 -- the argument of "putStrLn".
5180 main = putStrLn ( $(pr "Hello") )
5186 -- Skeletal printf from the paper.
5187 -- It needs to be in a separate module to the one where
5188 -- you intend to use it.
5190 -- Import some Template Haskell syntax
5191 import Language.Haskell.TH
5193 -- Describe a format string
5194 data Format = D | S | L String
5196 -- Parse a format string. This is left largely to you
5197 -- as we are here interested in building our first ever
5198 -- Template Haskell program and not in building printf.
5199 parse :: String -> [Format]
5202 -- Generate Haskell source code from a parsed representation
5203 -- of the format string. This code will be spliced into
5204 -- the module which calls "pr", at compile time.
5205 gen :: [Format] -> Q Exp
5206 gen [D] = [| \n -> show n |]
5207 gen [S] = [| \s -> s |]
5208 gen [L s] = stringE s
5210 -- Here we generate the Haskell code for the splice
5211 -- from an input format string.
5212 pr :: String -> Q Exp
5213 pr s = gen (parse s)
5216 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5219 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5222 <para>Run "main.exe" and here is your output:</para>
5232 <title>Using Template Haskell with Profiling</title>
5233 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5235 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5236 interpreter to run the splice expressions. The bytecode interpreter
5237 runs the compiled expression on top of the same runtime on which GHC
5238 itself is running; this means that the compiled code referred to by
5239 the interpreted expression must be compatible with this runtime, and
5240 in particular this means that object code that is compiled for
5241 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5242 expression, because profiled object code is only compatible with the
5243 profiling version of the runtime.</para>
5245 <para>This causes difficulties if you have a multi-module program
5246 containing Template Haskell code and you need to compile it for
5247 profiling, because GHC cannot load the profiled object code and use it
5248 when executing the splices. Fortunately GHC provides a workaround.
5249 The basic idea is to compile the program twice:</para>
5253 <para>Compile the program or library first the normal way, without
5254 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5257 <para>Then compile it again with <option>-prof</option>, and
5258 additionally use <option>-osuf
5259 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5260 to name the object files differently (you can choose any suffix
5261 that isn't the normal object suffix here). GHC will automatically
5262 load the object files built in the first step when executing splice
5263 expressions. If you omit the <option>-osuf</option> flag when
5264 building with <option>-prof</option> and Template Haskell is used,
5265 GHC will emit an error message. </para>
5270 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5271 <para>Quasi-quotation allows patterns and expressions to be written using
5272 programmer-defined concrete syntax; the motivation behind the extension and
5273 several examples are documented in
5274 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5275 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5276 2007). The example below shows how to write a quasiquoter for a simple
5277 expression language.</para>
5280 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5281 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5282 functions for quoting expressions and patterns, respectively. The first argument
5283 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5284 context of the quasi-quotation statement determines which of the two parsers is
5285 called: if the quasi-quotation occurs in an expression context, the expression
5286 parser is called, and if it occurs in a pattern context, the pattern parser is
5290 Note that in the example we make use of an antiquoted
5291 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5292 (this syntax for anti-quotation was defined by the parser's
5293 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5294 integer value argument of the constructor <literal>IntExpr</literal> when
5295 pattern matching. Please see the referenced paper for further details regarding
5296 anti-quotation as well as the description of a technique that uses SYB to
5297 leverage a single parser of type <literal>String -> a</literal> to generate both
5298 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5299 pattern parser that returns a value of type <literal>Q Pat</literal>.
5302 <para>In general, a quasi-quote has the form
5303 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5304 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5305 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5306 can be arbitrary, and may contain newlines.
5309 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5310 the example, <literal>expr</literal> cannot be defined
5311 in <literal>Main.hs</literal> where it is used, but must be imported.
5322 main = do { print $ eval [$expr|1 + 2|]
5324 { [$expr|'int:n|] -> print n
5333 import qualified Language.Haskell.TH as TH
5334 import Language.Haskell.TH.Quasi
5336 data Expr = IntExpr Integer
5337 | AntiIntExpr String
5338 | BinopExpr BinOp Expr Expr
5340 deriving(Show, Typeable, Data)
5346 deriving(Show, Typeable, Data)
5348 eval :: Expr -> Integer
5349 eval (IntExpr n) = n
5350 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5357 expr = QuasiQuoter parseExprExp parseExprPat
5359 -- Parse an Expr, returning its representation as
5360 -- either a Q Exp or a Q Pat. See the referenced paper
5361 -- for how to use SYB to do this by writing a single
5362 -- parser of type String -> Expr instead of two
5363 -- separate parsers.
5365 parseExprExp :: String -> Q Exp
5368 parseExprPat :: String -> Q Pat
5372 <para>Now run the compiler:
5375 $ ghc --make -XQuasiQuotes Main.hs -o main
5378 <para>Run "main" and here is your output:</para>
5390 <!-- ===================== Arrow notation =================== -->
5392 <sect1 id="arrow-notation">
5393 <title>Arrow notation
5396 <para>Arrows are a generalization of monads introduced by John Hughes.
5397 For more details, see
5402 “Generalising Monads to Arrows”,
5403 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5404 pp67–111, May 2000.
5405 The paper that introduced arrows: a friendly introduction, motivated with
5406 programming examples.
5412 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5413 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5414 Introduced the notation described here.
5420 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5421 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5428 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
5429 John Hughes, in <citetitle>5th International Summer School on
5430 Advanced Functional Programming</citetitle>,
5431 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
5433 This paper includes another introduction to the notation,
5434 with practical examples.
5440 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
5441 Ross Paterson and Simon Peyton Jones, September 16, 2004.
5442 A terse enumeration of the formal rules used
5443 (extracted from comments in the source code).
5449 The arrows web page at
5450 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5455 With the <option>-XArrows</option> flag, GHC supports the arrow
5456 notation described in the second of these papers,
5457 translating it using combinators from the
5458 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5460 What follows is a brief introduction to the notation;
5461 it won't make much sense unless you've read Hughes's paper.
5464 <para>The extension adds a new kind of expression for defining arrows:
5466 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5467 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5469 where <literal>proc</literal> is a new keyword.
5470 The variables of the pattern are bound in the body of the
5471 <literal>proc</literal>-expression,
5472 which is a new sort of thing called a <firstterm>command</firstterm>.
5473 The syntax of commands is as follows:
5475 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5476 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5477 | <replaceable>cmd</replaceable><superscript>0</superscript>
5479 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5480 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5481 infix operators as for expressions, and
5483 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5484 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5485 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5486 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5487 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5488 | <replaceable>fcmd</replaceable>
5490 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5491 | ( <replaceable>cmd</replaceable> )
5492 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5494 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5495 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5496 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5497 | <replaceable>cmd</replaceable>
5499 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5500 except that the bodies are commands instead of expressions.
5504 Commands produce values, but (like monadic computations)
5505 may yield more than one value,
5506 or none, and may do other things as well.
5507 For the most part, familiarity with monadic notation is a good guide to
5509 However the values of expressions, even monadic ones,
5510 are determined by the values of the variables they contain;
5511 this is not necessarily the case for commands.
5515 A simple example of the new notation is the expression
5517 proc x -> f -< x+1
5519 We call this a <firstterm>procedure</firstterm> or
5520 <firstterm>arrow abstraction</firstterm>.
5521 As with a lambda expression, the variable <literal>x</literal>
5522 is a new variable bound within the <literal>proc</literal>-expression.
5523 It refers to the input to the arrow.
5524 In the above example, <literal>-<</literal> is not an identifier but an
5525 new reserved symbol used for building commands from an expression of arrow
5526 type and an expression to be fed as input to that arrow.
5527 (The weird look will make more sense later.)
5528 It may be read as analogue of application for arrows.
5529 The above example is equivalent to the Haskell expression
5531 arr (\ x -> x+1) >>> f
5533 That would make no sense if the expression to the left of
5534 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5535 More generally, the expression to the left of <literal>-<</literal>
5536 may not involve any <firstterm>local variable</firstterm>,
5537 i.e. a variable bound in the current arrow abstraction.
5538 For such a situation there is a variant <literal>-<<</literal>, as in
5540 proc x -> f x -<< x+1
5542 which is equivalent to
5544 arr (\ x -> (f x, x+1)) >>> app
5546 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5548 Such an arrow is equivalent to a monad, so if you're using this form
5549 you may find a monadic formulation more convenient.
5553 <title>do-notation for commands</title>
5556 Another form of command is a form of <literal>do</literal>-notation.
5557 For example, you can write
5566 You can read this much like ordinary <literal>do</literal>-notation,
5567 but with commands in place of monadic expressions.
5568 The first line sends the value of <literal>x+1</literal> as an input to
5569 the arrow <literal>f</literal>, and matches its output against
5570 <literal>y</literal>.
5571 In the next line, the output is discarded.
5572 The arrow <function>returnA</function> is defined in the
5573 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5574 module as <literal>arr id</literal>.
5575 The above example is treated as an abbreviation for
5577 arr (\ x -> (x, x)) >>>
5578 first (arr (\ x -> x+1) >>> f) >>>
5579 arr (\ (y, x) -> (y, (x, y))) >>>
5580 first (arr (\ y -> 2*y) >>> g) >>>
5582 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5583 first (arr (\ (x, z) -> x*z) >>> h) >>>
5584 arr (\ (t, z) -> t+z) >>>
5587 Note that variables not used later in the composition are projected out.
5588 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5590 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5591 module, this reduces to
5593 arr (\ x -> (x+1, x)) >>>
5595 arr (\ (y, x) -> (2*y, (x, y))) >>>
5597 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5599 arr (\ (t, z) -> t+z)
5601 which is what you might have written by hand.
5602 With arrow notation, GHC keeps track of all those tuples of variables for you.
5606 Note that although the above translation suggests that
5607 <literal>let</literal>-bound variables like <literal>z</literal> must be
5608 monomorphic, the actual translation produces Core,
5609 so polymorphic variables are allowed.
5613 It's also possible to have mutually recursive bindings,
5614 using the new <literal>rec</literal> keyword, as in the following example:
5616 counter :: ArrowCircuit a => a Bool Int
5617 counter = proc reset -> do
5618 rec output <- returnA -< if reset then 0 else next
5619 next <- delay 0 -< output+1
5620 returnA -< output
5622 The translation of such forms uses the <function>loop</function> combinator,
5623 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5629 <title>Conditional commands</title>
5632 In the previous example, we used a conditional expression to construct the
5634 Sometimes we want to conditionally execute different commands, as in
5641 which is translated to
5643 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5644 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5646 Since the translation uses <function>|||</function>,
5647 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5651 There are also <literal>case</literal> commands, like
5657 y <- h -< (x1, x2)
5661 The syntax is the same as for <literal>case</literal> expressions,
5662 except that the bodies of the alternatives are commands rather than expressions.
5663 The translation is similar to that of <literal>if</literal> commands.
5669 <title>Defining your own control structures</title>
5672 As we're seen, arrow notation provides constructs,
5673 modelled on those for expressions,
5674 for sequencing, value recursion and conditionals.
5675 But suitable combinators,
5676 which you can define in ordinary Haskell,
5677 may also be used to build new commands out of existing ones.
5678 The basic idea is that a command defines an arrow from environments to values.
5679 These environments assign values to the free local variables of the command.
5680 Thus combinators that produce arrows from arrows
5681 may also be used to build commands from commands.
5682 For example, the <literal>ArrowChoice</literal> class includes a combinator
5684 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5686 so we can use it to build commands:
5688 expr' = proc x -> do
5691 symbol Plus -< ()
5692 y <- term -< ()
5695 symbol Minus -< ()
5696 y <- term -< ()
5699 (The <literal>do</literal> on the first line is needed to prevent the first
5700 <literal><+> ...</literal> from being interpreted as part of the
5701 expression on the previous line.)
5702 This is equivalent to
5704 expr' = (proc x -> returnA -< x)
5705 <+> (proc x -> do
5706 symbol Plus -< ()
5707 y <- term -< ()
5709 <+> (proc x -> do
5710 symbol Minus -< ()
5711 y <- term -< ()
5714 It is essential that this operator be polymorphic in <literal>e</literal>
5715 (representing the environment input to the command
5716 and thence to its subcommands)
5717 and satisfy the corresponding naturality property
5719 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5721 at least for strict <literal>k</literal>.
5722 (This should be automatic if you're not using <function>seq</function>.)
5723 This ensures that environments seen by the subcommands are environments
5724 of the whole command,
5725 and also allows the translation to safely trim these environments.
5726 The operator must also not use any variable defined within the current
5731 We could define our own operator
5733 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5734 untilA body cond = proc x ->
5735 b <- cond -< x
5736 if b then returnA -< ()
5739 untilA body cond -< x
5741 and use it in the same way.
5742 Of course this infix syntax only makes sense for binary operators;
5743 there is also a more general syntax involving special brackets:
5747 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5754 <title>Primitive constructs</title>
5757 Some operators will need to pass additional inputs to their subcommands.
5758 For example, in an arrow type supporting exceptions,
5759 the operator that attaches an exception handler will wish to pass the
5760 exception that occurred to the handler.
5761 Such an operator might have a type
5763 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5765 where <literal>Ex</literal> is the type of exceptions handled.
5766 You could then use this with arrow notation by writing a command
5768 body `handleA` \ ex -> handler
5770 so that if an exception is raised in the command <literal>body</literal>,
5771 the variable <literal>ex</literal> is bound to the value of the exception
5772 and the command <literal>handler</literal>,
5773 which typically refers to <literal>ex</literal>, is entered.
5774 Though the syntax here looks like a functional lambda,
5775 we are talking about commands, and something different is going on.
5776 The input to the arrow represented by a command consists of values for
5777 the free local variables in the command, plus a stack of anonymous values.
5778 In all the prior examples, this stack was empty.
5779 In the second argument to <function>handleA</function>,
5780 this stack consists of one value, the value of the exception.
5781 The command form of lambda merely gives this value a name.
5786 the values on the stack are paired to the right of the environment.
5787 So operators like <function>handleA</function> that pass
5788 extra inputs to their subcommands can be designed for use with the notation
5789 by pairing the values with the environment in this way.
5790 More precisely, the type of each argument of the operator (and its result)
5791 should have the form
5793 a (...(e,t1), ... tn) t
5795 where <replaceable>e</replaceable> is a polymorphic variable
5796 (representing the environment)
5797 and <replaceable>ti</replaceable> are the types of the values on the stack,
5798 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5799 The polymorphic variable <replaceable>e</replaceable> must not occur in
5800 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5801 <replaceable>t</replaceable>.
5802 However the arrows involved need not be the same.
5803 Here are some more examples of suitable operators:
5805 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5806 runReader :: ... => a e c -> a' (e,State) c
5807 runState :: ... => a e c -> a' (e,State) (c,State)
5809 We can supply the extra input required by commands built with the last two
5810 by applying them to ordinary expressions, as in
5814 (|runReader (do { ... })|) s
5816 which adds <literal>s</literal> to the stack of inputs to the command
5817 built using <function>runReader</function>.
5821 The command versions of lambda abstraction and application are analogous to
5822 the expression versions.
5823 In particular, the beta and eta rules describe equivalences of commands.
5824 These three features (operators, lambda abstraction and application)
5825 are the core of the notation; everything else can be built using them,
5826 though the results would be somewhat clumsy.
5827 For example, we could simulate <literal>do</literal>-notation by defining
5829 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5830 u `bind` f = returnA &&& u >>> f
5832 bind_ :: Arrow a => a e b -> a e c -> a e c
5833 u `bind_` f = u `bind` (arr fst >>> f)
5835 We could simulate <literal>if</literal> by defining
5837 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5838 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5845 <title>Differences with the paper</title>
5850 <para>Instead of a single form of arrow application (arrow tail) with two
5851 translations, the implementation provides two forms
5852 <quote><literal>-<</literal></quote> (first-order)
5853 and <quote><literal>-<<</literal></quote> (higher-order).
5858 <para>User-defined operators are flagged with banana brackets instead of
5859 a new <literal>form</literal> keyword.
5868 <title>Portability</title>
5871 Although only GHC implements arrow notation directly,
5872 there is also a preprocessor
5874 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5875 that translates arrow notation into Haskell 98
5876 for use with other Haskell systems.
5877 You would still want to check arrow programs with GHC;
5878 tracing type errors in the preprocessor output is not easy.
5879 Modules intended for both GHC and the preprocessor must observe some
5880 additional restrictions:
5885 The module must import
5886 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5892 The preprocessor cannot cope with other Haskell extensions.
5893 These would have to go in separate modules.
5899 Because the preprocessor targets Haskell (rather than Core),
5900 <literal>let</literal>-bound variables are monomorphic.
5911 <!-- ==================== BANG PATTERNS ================= -->
5913 <sect1 id="bang-patterns">
5914 <title>Bang patterns
5915 <indexterm><primary>Bang patterns</primary></indexterm>
5917 <para>GHC supports an extension of pattern matching called <emphasis>bang
5918 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5920 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5921 prime feature description</ulink> contains more discussion and examples
5922 than the material below.
5925 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5928 <sect2 id="bang-patterns-informal">
5929 <title>Informal description of bang patterns
5932 The main idea is to add a single new production to the syntax of patterns:
5936 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5937 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5942 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5943 whereas without the bang it would be lazy.
5944 Bang patterns can be nested of course:
5948 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5949 <literal>y</literal>.
5950 A bang only really has an effect if it precedes a variable or wild-card pattern:
5955 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5956 forces evaluation anyway does nothing.
5958 Bang patterns work in <literal>case</literal> expressions too, of course:
5960 g5 x = let y = f x in body
5961 g6 x = case f x of { y -> body }
5962 g7 x = case f x of { !y -> body }
5964 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5965 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5966 result, and then evaluates <literal>body</literal>.
5968 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5969 definitions too. For example:
5973 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5974 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5975 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5976 in a function argument <literal>![x,y]</literal> means the
5977 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5978 is part of the syntax of <literal>let</literal> bindings.
5983 <sect2 id="bang-patterns-sem">
5984 <title>Syntax and semantics
5988 We add a single new production to the syntax of patterns:
5992 There is one problem with syntactic ambiguity. Consider:
5996 Is this a definition of the infix function "<literal>(!)</literal>",
5997 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5998 ambiguity in favour of the latter. If you want to define
5999 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6004 The semantics of Haskell pattern matching is described in <ulink
6005 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6006 Section 3.17.2</ulink> of the Haskell Report. To this description add
6007 one extra item 10, saying:
6008 <itemizedlist><listitem><para>Matching
6009 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6010 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6011 <listitem><para>otherwise, <literal>pat</literal> is matched against
6012 <literal>v</literal></para></listitem>
6014 </para></listitem></itemizedlist>
6015 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6016 Section 3.17.3</ulink>, add a new case (t):
6018 case v of { !pat -> e; _ -> e' }
6019 = v `seq` case v of { pat -> e; _ -> e' }
6022 That leaves let expressions, whose translation is given in
6023 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6025 of the Haskell Report.
6026 In the translation box, first apply
6027 the following transformation: for each pattern <literal>pi</literal> that is of
6028 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6029 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6030 have a bang at the top, apply the rules in the existing box.
6032 <para>The effect of the let rule is to force complete matching of the pattern
6033 <literal>qi</literal> before evaluation of the body is begun. The bang is
6034 retained in the translated form in case <literal>qi</literal> is a variable,
6042 The let-binding can be recursive. However, it is much more common for
6043 the let-binding to be non-recursive, in which case the following law holds:
6044 <literal>(let !p = rhs in body)</literal>
6046 <literal>(case rhs of !p -> body)</literal>
6049 A pattern with a bang at the outermost level is not allowed at the top level of
6055 <!-- ==================== ASSERTIONS ================= -->
6057 <sect1 id="assertions">
6059 <indexterm><primary>Assertions</primary></indexterm>
6063 If you want to make use of assertions in your standard Haskell code, you
6064 could define a function like the following:
6070 assert :: Bool -> a -> a
6071 assert False x = error "assertion failed!"
6078 which works, but gives you back a less than useful error message --
6079 an assertion failed, but which and where?
6083 One way out is to define an extended <function>assert</function> function which also
6084 takes a descriptive string to include in the error message and
6085 perhaps combine this with the use of a pre-processor which inserts
6086 the source location where <function>assert</function> was used.
6090 Ghc offers a helping hand here, doing all of this for you. For every
6091 use of <function>assert</function> in the user's source:
6097 kelvinToC :: Double -> Double
6098 kelvinToC k = assert (k >= 0.0) (k+273.15)
6104 Ghc will rewrite this to also include the source location where the
6111 assert pred val ==> assertError "Main.hs|15" pred val
6117 The rewrite is only performed by the compiler when it spots
6118 applications of <function>Control.Exception.assert</function>, so you
6119 can still define and use your own versions of
6120 <function>assert</function>, should you so wish. If not, import
6121 <literal>Control.Exception</literal> to make use
6122 <function>assert</function> in your code.
6126 GHC ignores assertions when optimisation is turned on with the
6127 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6128 <literal>assert pred e</literal> will be rewritten to
6129 <literal>e</literal>. You can also disable assertions using the
6130 <option>-fignore-asserts</option>
6131 option<indexterm><primary><option>-fignore-asserts</option></primary>
6132 </indexterm>.</para>
6135 Assertion failures can be caught, see the documentation for the
6136 <literal>Control.Exception</literal> library for the details.
6142 <!-- =============================== PRAGMAS =========================== -->
6144 <sect1 id="pragmas">
6145 <title>Pragmas</title>
6147 <indexterm><primary>pragma</primary></indexterm>
6149 <para>GHC supports several pragmas, or instructions to the
6150 compiler placed in the source code. Pragmas don't normally affect
6151 the meaning of the program, but they might affect the efficiency
6152 of the generated code.</para>
6154 <para>Pragmas all take the form
6156 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6158 where <replaceable>word</replaceable> indicates the type of
6159 pragma, and is followed optionally by information specific to that
6160 type of pragma. Case is ignored in
6161 <replaceable>word</replaceable>. The various values for
6162 <replaceable>word</replaceable> that GHC understands are described
6163 in the following sections; any pragma encountered with an
6164 unrecognised <replaceable>word</replaceable> is (silently)
6165 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6166 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6168 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6169 pragma must precede the <literal>module</literal> keyword in the file.
6170 There can be as many file-header pragmas as you please, and they can be
6171 preceded or followed by comments.</para>
6173 <sect2 id="language-pragma">
6174 <title>LANGUAGE pragma</title>
6176 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6177 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6179 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6181 It is the intention that all Haskell compilers support the
6182 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6183 all extensions are supported by all compilers, of
6184 course. The <literal>LANGUAGE</literal> pragma should be used instead
6185 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6187 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6189 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6191 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6193 <para>Every language extension can also be turned into a command-line flag
6194 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6195 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6198 <para>A list of all supported language extensions can be obtained by invoking
6199 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6201 <para>Any extension from the <literal>Extension</literal> type defined in
6203 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6204 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6208 <sect2 id="options-pragma">
6209 <title>OPTIONS_GHC pragma</title>
6210 <indexterm><primary>OPTIONS_GHC</primary>
6212 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6215 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6216 additional options that are given to the compiler when compiling
6217 this source file. See <xref linkend="source-file-options"/> for
6220 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6221 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6224 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6226 <sect2 id="include-pragma">
6227 <title>INCLUDE pragma</title>
6229 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6230 of C header files that should be <literal>#include</literal>'d into
6231 the C source code generated by the compiler for the current module (if
6232 compiling via C). For example:</para>
6235 {-# INCLUDE "foo.h" #-}
6236 {-# INCLUDE <stdio.h> #-}</programlisting>
6238 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6240 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6241 to the <option>-#include</option> option (<xref
6242 linkend="options-C-compiler" />), because the
6243 <literal>INCLUDE</literal> pragma is understood by other
6244 compilers. Yet another alternative is to add the include file to each
6245 <literal>foreign import</literal> declaration in your code, but we
6246 don't recommend using this approach with GHC.</para>
6249 <sect2 id="warning-deprecated-pragma">
6250 <title>WARNING and DEPRECATED pragmas</title>
6251 <indexterm><primary>WARNING</primary></indexterm>
6252 <indexterm><primary>DEPRECATED</primary></indexterm>
6254 <para>The WARNING pragma allows you to attach an arbitrary warning
6255 to a particular function, class, or type.
6256 A DEPRECATED pragma lets you specify that
6257 a particular function, class, or type is deprecated.
6258 There are two ways of using these pragmas.
6262 <para>You can work on an entire module thus:</para>
6264 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6269 module Wibble {-# WARNING "This is an unstable interface." #-} where
6272 <para>When you compile any module that import
6273 <literal>Wibble</literal>, GHC will print the specified
6278 <para>You can attach a warning to a function, class, type, or data constructor, with the
6279 following top-level declarations:</para>
6281 {-# DEPRECATED f, C, T "Don't use these" #-}
6282 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6284 <para>When you compile any module that imports and uses any
6285 of the specified entities, GHC will print the specified
6287 <para> You can only attach to entities declared at top level in the module
6288 being compiled, and you can only use unqualified names in the list of
6289 entities. A capitalised name, such as <literal>T</literal>
6290 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6291 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6292 both are in scope. If both are in scope, there is currently no way to
6293 specify one without the other (c.f. fixities
6294 <xref linkend="infix-tycons"/>).</para>
6297 Warnings and deprecations are not reported for
6298 (a) uses within the defining module, and
6299 (b) uses in an export list.
6300 The latter reduces spurious complaints within a library
6301 in which one module gathers together and re-exports
6302 the exports of several others.
6304 <para>You can suppress the warnings with the flag
6305 <option>-fno-warn-warnings-deprecations</option>.</para>
6308 <sect2 id="inline-noinline-pragma">
6309 <title>INLINE and NOINLINE pragmas</title>
6311 <para>These pragmas control the inlining of function
6314 <sect3 id="inline-pragma">
6315 <title>INLINE pragma</title>
6316 <indexterm><primary>INLINE</primary></indexterm>
6318 <para>GHC (with <option>-O</option>, as always) tries to
6319 inline (or “unfold”) functions/values that are
6320 “small enough,” thus avoiding the call overhead
6321 and possibly exposing other more-wonderful optimisations.
6322 Normally, if GHC decides a function is “too
6323 expensive” to inline, it will not do so, nor will it
6324 export that unfolding for other modules to use.</para>
6326 <para>The sledgehammer you can bring to bear is the
6327 <literal>INLINE</literal><indexterm><primary>INLINE
6328 pragma</primary></indexterm> pragma, used thusly:</para>
6331 key_function :: Int -> String -> (Bool, Double)
6332 {-# INLINE key_function #-}
6335 <para>The major effect of an <literal>INLINE</literal> pragma
6336 is to declare a function's “cost” to be very low.
6337 The normal unfolding machinery will then be very keen to
6338 inline it. However, an <literal>INLINE</literal> pragma for a
6339 function "<literal>f</literal>" has a number of other effects:
6342 No functions are inlined into <literal>f</literal>. Otherwise
6343 GHC might inline a big function into <literal>f</literal>'s right hand side,
6344 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6347 The float-in, float-out, and common-sub-expression transformations are not
6348 applied to the body of <literal>f</literal>.
6351 An INLINE function is not worker/wrappered by strictness analysis.
6352 It's going to be inlined wholesale instead.
6355 All of these effects are aimed at ensuring that what gets inlined is
6356 exactly what you asked for, no more and no less.
6358 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6359 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6360 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6361 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6362 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6363 when there is no choice even an INLINE function can be selected, in which case
6364 the INLINE pragma is ignored.
6365 For example, for a self-recursive function, the loop breaker can only be the function
6366 itself, so an INLINE pragma is always ignored.</para>
6368 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6369 function can be put anywhere its type signature could be
6372 <para><literal>INLINE</literal> pragmas are a particularly
6374 <literal>then</literal>/<literal>return</literal> (or
6375 <literal>bind</literal>/<literal>unit</literal>) functions in
6376 a monad. For example, in GHC's own
6377 <literal>UniqueSupply</literal> monad code, we have:</para>
6380 {-# INLINE thenUs #-}
6381 {-# INLINE returnUs #-}
6384 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6385 linkend="noinline-pragma"/>).</para>
6387 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6388 so if you want your code to be HBC-compatible you'll have to surround
6389 the pragma with C pre-processor directives
6390 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6394 <sect3 id="noinline-pragma">
6395 <title>NOINLINE pragma</title>
6397 <indexterm><primary>NOINLINE</primary></indexterm>
6398 <indexterm><primary>NOTINLINE</primary></indexterm>
6400 <para>The <literal>NOINLINE</literal> pragma does exactly what
6401 you'd expect: it stops the named function from being inlined
6402 by the compiler. You shouldn't ever need to do this, unless
6403 you're very cautious about code size.</para>
6405 <para><literal>NOTINLINE</literal> is a synonym for
6406 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6407 specified by Haskell 98 as the standard way to disable
6408 inlining, so it should be used if you want your code to be
6412 <sect3 id="phase-control">
6413 <title>Phase control</title>
6415 <para> Sometimes you want to control exactly when in GHC's
6416 pipeline the INLINE pragma is switched on. Inlining happens
6417 only during runs of the <emphasis>simplifier</emphasis>. Each
6418 run of the simplifier has a different <emphasis>phase
6419 number</emphasis>; the phase number decreases towards zero.
6420 If you use <option>-dverbose-core2core</option> you'll see the
6421 sequence of phase numbers for successive runs of the
6422 simplifier. In an INLINE pragma you can optionally specify a
6426 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6427 <literal>f</literal>
6428 until phase <literal>k</literal>, but from phase
6429 <literal>k</literal> onwards be very keen to inline it.
6432 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6433 <literal>f</literal>
6434 until phase <literal>k</literal>, but from phase
6435 <literal>k</literal> onwards do not inline it.
6438 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6439 <literal>f</literal>
6440 until phase <literal>k</literal>, but from phase
6441 <literal>k</literal> onwards be willing to inline it (as if
6442 there was no pragma).
6445 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6446 <literal>f</literal>
6447 until phase <literal>k</literal>, but from phase
6448 <literal>k</literal> onwards do not inline it.
6451 The same information is summarised here:
6453 -- Before phase 2 Phase 2 and later
6454 {-# INLINE [2] f #-} -- No Yes
6455 {-# INLINE [~2] f #-} -- Yes No
6456 {-# NOINLINE [2] f #-} -- No Maybe
6457 {-# NOINLINE [~2] f #-} -- Maybe No
6459 {-# INLINE f #-} -- Yes Yes
6460 {-# NOINLINE f #-} -- No No
6462 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6463 function body is small, or it is applied to interesting-looking arguments etc).
6464 Another way to understand the semantics is this:
6466 <listitem><para>For both INLINE and NOINLINE, the phase number says
6467 when inlining is allowed at all.</para></listitem>
6468 <listitem><para>The INLINE pragma has the additional effect of making the
6469 function body look small, so that when inlining is allowed it is very likely to
6474 <para>The same phase-numbering control is available for RULES
6475 (<xref linkend="rewrite-rules"/>).</para>
6479 <sect2 id="line-pragma">
6480 <title>LINE pragma</title>
6482 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6483 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6484 <para>This pragma is similar to C's <literal>#line</literal>
6485 pragma, and is mainly for use in automatically generated Haskell
6486 code. It lets you specify the line number and filename of the
6487 original code; for example</para>
6489 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6491 <para>if you'd generated the current file from something called
6492 <filename>Foo.vhs</filename> and this line corresponds to line
6493 42 in the original. GHC will adjust its error messages to refer
6494 to the line/file named in the <literal>LINE</literal>
6499 <title>RULES pragma</title>
6501 <para>The RULES pragma lets you specify rewrite rules. It is
6502 described in <xref linkend="rewrite-rules"/>.</para>
6505 <sect2 id="specialize-pragma">
6506 <title>SPECIALIZE pragma</title>
6508 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6509 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6510 <indexterm><primary>overloading, death to</primary></indexterm>
6512 <para>(UK spelling also accepted.) For key overloaded
6513 functions, you can create extra versions (NB: more code space)
6514 specialised to particular types. Thus, if you have an
6515 overloaded function:</para>
6518 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6521 <para>If it is heavily used on lists with
6522 <literal>Widget</literal> keys, you could specialise it as
6526 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6529 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6530 be put anywhere its type signature could be put.</para>
6532 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6533 (a) a specialised version of the function and (b) a rewrite rule
6534 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6535 un-specialised function into a call to the specialised one.</para>
6537 <para>The type in a SPECIALIZE pragma can be any type that is less
6538 polymorphic than the type of the original function. In concrete terms,
6539 if the original function is <literal>f</literal> then the pragma
6541 {-# SPECIALIZE f :: <type> #-}
6543 is valid if and only if the definition
6545 f_spec :: <type>
6548 is valid. Here are some examples (where we only give the type signature
6549 for the original function, not its code):
6551 f :: Eq a => a -> b -> b
6552 {-# SPECIALISE f :: Int -> b -> b #-}
6554 g :: (Eq a, Ix b) => a -> b -> b
6555 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6557 h :: Eq a => a -> a -> a
6558 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6560 The last of these examples will generate a
6561 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6562 well. If you use this kind of specialisation, let us know how well it works.
6565 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6566 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6567 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6568 The <literal>INLINE</literal> pragma affects the specialised version of the
6569 function (only), and applies even if the function is recursive. The motivating
6572 -- A GADT for arrays with type-indexed representation
6574 ArrInt :: !Int -> ByteArray# -> Arr Int
6575 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6577 (!:) :: Arr e -> Int -> e
6578 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6579 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6580 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6581 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6583 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6584 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6585 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6586 the specialised function will be inlined. It has two calls to
6587 <literal>(!:)</literal>,
6588 both at type <literal>Int</literal>. Both these calls fire the first
6589 specialisation, whose body is also inlined. The result is a type-based
6590 unrolling of the indexing function.</para>
6591 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6592 on an ordinarily-recursive function.</para>
6594 <para>Note: In earlier versions of GHC, it was possible to provide your own
6595 specialised function for a given type:
6598 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6601 This feature has been removed, as it is now subsumed by the
6602 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6606 <sect2 id="specialize-instance-pragma">
6607 <title>SPECIALIZE instance pragma
6611 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6612 <indexterm><primary>overloading, death to</primary></indexterm>
6613 Same idea, except for instance declarations. For example:
6616 instance (Eq a) => Eq (Foo a) where {
6617 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6621 The pragma must occur inside the <literal>where</literal> part
6622 of the instance declaration.
6625 Compatible with HBC, by the way, except perhaps in the placement
6631 <sect2 id="unpack-pragma">
6632 <title>UNPACK pragma</title>
6634 <indexterm><primary>UNPACK</primary></indexterm>
6636 <para>The <literal>UNPACK</literal> indicates to the compiler
6637 that it should unpack the contents of a constructor field into
6638 the constructor itself, removing a level of indirection. For
6642 data T = T {-# UNPACK #-} !Float
6643 {-# UNPACK #-} !Float
6646 <para>will create a constructor <literal>T</literal> containing
6647 two unboxed floats. This may not always be an optimisation: if
6648 the <function>T</function> constructor is scrutinised and the
6649 floats passed to a non-strict function for example, they will
6650 have to be reboxed (this is done automatically by the
6653 <para>Unpacking constructor fields should only be used in
6654 conjunction with <option>-O</option>, in order to expose
6655 unfoldings to the compiler so the reboxing can be removed as
6656 often as possible. For example:</para>
6660 f (T f1 f2) = f1 + f2
6663 <para>The compiler will avoid reboxing <function>f1</function>
6664 and <function>f2</function> by inlining <function>+</function>
6665 on floats, but only when <option>-O</option> is on.</para>
6667 <para>Any single-constructor data is eligible for unpacking; for
6671 data T = T {-# UNPACK #-} !(Int,Int)
6674 <para>will store the two <literal>Int</literal>s directly in the
6675 <function>T</function> constructor, by flattening the pair.
6676 Multi-level unpacking is also supported:
6679 data T = T {-# UNPACK #-} !S
6680 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6683 will store two unboxed <literal>Int#</literal>s
6684 directly in the <function>T</function> constructor. The
6685 unpacker can see through newtypes, too.</para>
6687 <para>If a field cannot be unpacked, you will not get a warning,
6688 so it might be an idea to check the generated code with
6689 <option>-ddump-simpl</option>.</para>
6691 <para>See also the <option>-funbox-strict-fields</option> flag,
6692 which essentially has the effect of adding
6693 <literal>{-# UNPACK #-}</literal> to every strict
6694 constructor field.</para>
6697 <sect2 id="source-pragma">
6698 <title>SOURCE pragma</title>
6700 <indexterm><primary>SOURCE</primary></indexterm>
6701 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6702 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6708 <!-- ======================= REWRITE RULES ======================== -->
6710 <sect1 id="rewrite-rules">
6711 <title>Rewrite rules
6713 <indexterm><primary>RULES pragma</primary></indexterm>
6714 <indexterm><primary>pragma, RULES</primary></indexterm>
6715 <indexterm><primary>rewrite rules</primary></indexterm></title>
6718 The programmer can specify rewrite rules as part of the source program
6724 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6729 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6730 If you need more information, then <option>-ddump-rule-firings</option> shows you
6731 each individual rule firing in detail.
6735 <title>Syntax</title>
6738 From a syntactic point of view:
6744 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6745 may be generated by the layout rule).
6751 The layout rule applies in a pragma.
6752 Currently no new indentation level
6753 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6754 you must lay out the starting in the same column as the enclosing definitions.
6757 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6758 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6761 Furthermore, the closing <literal>#-}</literal>
6762 should start in a column to the right of the opening <literal>{-#</literal>.
6768 Each rule has a name, enclosed in double quotes. The name itself has
6769 no significance at all. It is only used when reporting how many times the rule fired.
6775 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6776 immediately after the name of the rule. Thus:
6779 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6782 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6783 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6792 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6793 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6794 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6795 by spaces, just like in a type <literal>forall</literal>.
6801 A pattern variable may optionally have a type signature.
6802 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6803 For example, here is the <literal>foldr/build</literal> rule:
6806 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6807 foldr k z (build g) = g k z
6810 Since <function>g</function> has a polymorphic type, it must have a type signature.
6817 The left hand side of a rule must consist of a top-level variable applied
6818 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6821 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6822 "wrong2" forall f. f True = True
6825 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6832 A rule does not need to be in the same module as (any of) the
6833 variables it mentions, though of course they need to be in scope.
6839 All rules are implicitly exported from the module, and are therefore
6840 in force in any module that imports the module that defined the rule, directly
6841 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6842 in force when compiling A.) The situation is very similar to that for instance
6850 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
6851 any other flag settings. Furthermore, inside a RULE, the language extension
6852 <option>-XScopedTypeVariables</option> is automatically enabled; see
6853 <xref linkend="scoped-type-variables"/>.
6859 Like other pragmas, RULE pragmas are always checked for scope errors, and
6860 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
6861 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
6862 if the <option>-fenable-rewrite-rules</option> flag is
6863 on (see <xref linkend="rule-semantics"/>).
6872 <sect2 id="rule-semantics">
6873 <title>Semantics</title>
6876 From a semantic point of view:
6881 Rules are enabled (that is, used during optimisation)
6882 by the <option>-fenable-rewrite-rules</option> flag.
6883 This flag is implied by <option>-O</option>, and may be switched
6884 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
6885 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
6886 may not do what you expect, though, because without <option>-O</option> GHC
6887 ignores all optimisation information in interface files;
6888 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
6889 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
6890 has no effect on parsing or typechecking.
6896 Rules are regarded as left-to-right rewrite rules.
6897 When GHC finds an expression that is a substitution instance of the LHS
6898 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6899 By "a substitution instance" we mean that the LHS can be made equal to the
6900 expression by substituting for the pattern variables.
6907 GHC makes absolutely no attempt to verify that the LHS and RHS
6908 of a rule have the same meaning. That is undecidable in general, and
6909 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6916 GHC makes no attempt to make sure that the rules are confluent or
6917 terminating. For example:
6920 "loop" forall x y. f x y = f y x
6923 This rule will cause the compiler to go into an infinite loop.
6930 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6936 GHC currently uses a very simple, syntactic, matching algorithm
6937 for matching a rule LHS with an expression. It seeks a substitution
6938 which makes the LHS and expression syntactically equal modulo alpha
6939 conversion. The pattern (rule), but not the expression, is eta-expanded if
6940 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6941 But not beta conversion (that's called higher-order matching).
6945 Matching is carried out on GHC's intermediate language, which includes
6946 type abstractions and applications. So a rule only matches if the
6947 types match too. See <xref linkend="rule-spec"/> below.
6953 GHC keeps trying to apply the rules as it optimises the program.
6954 For example, consider:
6963 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6964 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6965 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6966 not be substituted, and the rule would not fire.
6973 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6974 results. Consider this (artificial) example
6977 {-# RULES "f" f True = False #-}
6983 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
6988 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
6990 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
6991 would have been a better chance that <literal>f</literal>'s RULE might fire.
6994 The way to get predictable behaviour is to use a NOINLINE
6995 pragma on <literal>f</literal>, to ensure
6996 that it is not inlined until its RULEs have had a chance to fire.
7006 <title>List fusion</title>
7009 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7010 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7011 intermediate list should be eliminated entirely.
7015 The following are good producers:
7027 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7033 Explicit lists (e.g. <literal>[True, False]</literal>)
7039 The cons constructor (e.g <literal>3:4:[]</literal>)
7045 <function>++</function>
7051 <function>map</function>
7057 <function>take</function>, <function>filter</function>
7063 <function>iterate</function>, <function>repeat</function>
7069 <function>zip</function>, <function>zipWith</function>
7078 The following are good consumers:
7090 <function>array</function> (on its second argument)
7096 <function>++</function> (on its first argument)
7102 <function>foldr</function>
7108 <function>map</function>
7114 <function>take</function>, <function>filter</function>
7120 <function>concat</function>
7126 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7132 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7133 will fuse with one but not the other)
7139 <function>partition</function>
7145 <function>head</function>
7151 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7157 <function>sequence_</function>
7163 <function>msum</function>
7169 <function>sortBy</function>
7178 So, for example, the following should generate no intermediate lists:
7181 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7187 This list could readily be extended; if there are Prelude functions that you use
7188 a lot which are not included, please tell us.
7192 If you want to write your own good consumers or producers, look at the
7193 Prelude definitions of the above functions to see how to do so.
7198 <sect2 id="rule-spec">
7199 <title>Specialisation
7203 Rewrite rules can be used to get the same effect as a feature
7204 present in earlier versions of GHC.
7205 For example, suppose that:
7208 genericLookup :: Ord a => Table a b -> a -> b
7209 intLookup :: Table Int b -> Int -> b
7212 where <function>intLookup</function> is an implementation of
7213 <function>genericLookup</function> that works very fast for
7214 keys of type <literal>Int</literal>. You might wish
7215 to tell GHC to use <function>intLookup</function> instead of
7216 <function>genericLookup</function> whenever the latter was called with
7217 type <literal>Table Int b -> Int -> b</literal>.
7218 It used to be possible to write
7221 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7224 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7227 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7230 This slightly odd-looking rule instructs GHC to replace
7231 <function>genericLookup</function> by <function>intLookup</function>
7232 <emphasis>whenever the types match</emphasis>.
7233 What is more, this rule does not need to be in the same
7234 file as <function>genericLookup</function>, unlike the
7235 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7236 have an original definition available to specialise).
7239 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7240 <function>intLookup</function> really behaves as a specialised version
7241 of <function>genericLookup</function>!!!</para>
7243 <para>An example in which using <literal>RULES</literal> for
7244 specialisation will Win Big:
7247 toDouble :: Real a => a -> Double
7248 toDouble = fromRational . toRational
7250 {-# RULES "toDouble/Int" toDouble = i2d #-}
7251 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7254 The <function>i2d</function> function is virtually one machine
7255 instruction; the default conversion—via an intermediate
7256 <literal>Rational</literal>—is obscenely expensive by
7263 <title>Controlling what's going on</title>
7271 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7277 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7278 If you add <option>-dppr-debug</option> you get a more detailed listing.
7284 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7287 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7288 {-# INLINE build #-}
7292 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7293 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7294 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7295 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7302 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7303 see how to write rules that will do fusion and yet give an efficient
7304 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7314 <sect2 id="core-pragma">
7315 <title>CORE pragma</title>
7317 <indexterm><primary>CORE pragma</primary></indexterm>
7318 <indexterm><primary>pragma, CORE</primary></indexterm>
7319 <indexterm><primary>core, annotation</primary></indexterm>
7322 The external core format supports <quote>Note</quote> annotations;
7323 the <literal>CORE</literal> pragma gives a way to specify what these
7324 should be in your Haskell source code. Syntactically, core
7325 annotations are attached to expressions and take a Haskell string
7326 literal as an argument. The following function definition shows an
7330 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7333 Semantically, this is equivalent to:
7341 However, when external core is generated (via
7342 <option>-fext-core</option>), there will be Notes attached to the
7343 expressions <function>show</function> and <varname>x</varname>.
7344 The core function declaration for <function>f</function> is:
7348 f :: %forall a . GHCziShow.ZCTShow a ->
7349 a -> GHCziBase.ZMZN GHCziBase.Char =
7350 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7352 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7354 (tpl1::GHCziBase.Int ->
7356 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7358 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7359 (tpl3::GHCziBase.ZMZN a ->
7360 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7368 Here, we can see that the function <function>show</function> (which
7369 has been expanded out to a case expression over the Show dictionary)
7370 has a <literal>%note</literal> attached to it, as does the
7371 expression <varname>eta</varname> (which used to be called
7372 <varname>x</varname>).
7379 <sect1 id="special-ids">
7380 <title>Special built-in functions</title>
7381 <para>GHC has a few built-in functions with special behaviour. These
7382 are now described in the module <ulink
7383 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7384 in the library documentation.</para>
7388 <sect1 id="generic-classes">
7389 <title>Generic classes</title>
7392 The ideas behind this extension are described in detail in "Derivable type classes",
7393 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7394 An example will give the idea:
7402 fromBin :: [Int] -> (a, [Int])
7404 toBin {| Unit |} Unit = []
7405 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7406 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7407 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7409 fromBin {| Unit |} bs = (Unit, bs)
7410 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7411 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7412 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7413 (y,bs'') = fromBin bs'
7416 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7417 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7418 which are defined thus in the library module <literal>Generics</literal>:
7422 data a :+: b = Inl a | Inr b
7423 data a :*: b = a :*: b
7426 Now you can make a data type into an instance of Bin like this:
7428 instance (Bin a, Bin b) => Bin (a,b)
7429 instance Bin a => Bin [a]
7431 That is, just leave off the "where" clause. Of course, you can put in the
7432 where clause and over-ride whichever methods you please.
7436 <title> Using generics </title>
7437 <para>To use generics you need to</para>
7440 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7441 <option>-XGenerics</option> (to generate extra per-data-type code),
7442 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7446 <para>Import the module <literal>Generics</literal> from the
7447 <literal>lang</literal> package. This import brings into
7448 scope the data types <literal>Unit</literal>,
7449 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7450 don't need this import if you don't mention these types
7451 explicitly; for example, if you are simply giving instance
7452 declarations.)</para>
7457 <sect2> <title> Changes wrt the paper </title>
7459 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7460 can be written infix (indeed, you can now use
7461 any operator starting in a colon as an infix type constructor). Also note that
7462 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7463 Finally, note that the syntax of the type patterns in the class declaration
7464 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7465 alone would ambiguous when they appear on right hand sides (an extension we
7466 anticipate wanting).
7470 <sect2> <title>Terminology and restrictions</title>
7472 Terminology. A "generic default method" in a class declaration
7473 is one that is defined using type patterns as above.
7474 A "polymorphic default method" is a default method defined as in Haskell 98.
7475 A "generic class declaration" is a class declaration with at least one
7476 generic default method.
7484 Alas, we do not yet implement the stuff about constructor names and
7491 A generic class can have only one parameter; you can't have a generic
7492 multi-parameter class.
7498 A default method must be defined entirely using type patterns, or entirely
7499 without. So this is illegal:
7502 op :: a -> (a, Bool)
7503 op {| Unit |} Unit = (Unit, True)
7506 However it is perfectly OK for some methods of a generic class to have
7507 generic default methods and others to have polymorphic default methods.
7513 The type variable(s) in the type pattern for a generic method declaration
7514 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:
7518 op {| p :*: q |} (x :*: y) = op (x :: p)
7526 The type patterns in a generic default method must take one of the forms:
7532 where "a" and "b" are type variables. Furthermore, all the type patterns for
7533 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7534 must use the same type variables. So this is illegal:
7538 op {| a :+: b |} (Inl x) = True
7539 op {| p :+: q |} (Inr y) = False
7541 The type patterns must be identical, even in equations for different methods of the class.
7542 So this too is illegal:
7546 op1 {| a :*: b |} (x :*: y) = True
7549 op2 {| p :*: q |} (x :*: y) = False
7551 (The reason for this restriction is that we gather all the equations for a particular type constructor
7552 into a single generic instance declaration.)
7558 A generic method declaration must give a case for each of the three type constructors.
7564 The type for a generic method can be built only from:
7566 <listitem> <para> Function arrows </para> </listitem>
7567 <listitem> <para> Type variables </para> </listitem>
7568 <listitem> <para> Tuples </para> </listitem>
7569 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7571 Here are some example type signatures for generic methods:
7574 op2 :: Bool -> (a,Bool)
7575 op3 :: [Int] -> a -> a
7578 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7582 This restriction is an implementation restriction: we just haven't got around to
7583 implementing the necessary bidirectional maps over arbitrary type constructors.
7584 It would be relatively easy to add specific type constructors, such as Maybe and list,
7585 to the ones that are allowed.</para>
7590 In an instance declaration for a generic class, the idea is that the compiler
7591 will fill in the methods for you, based on the generic templates. However it can only
7596 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7601 No constructor of the instance type has unboxed fields.
7605 (Of course, these things can only arise if you are already using GHC extensions.)
7606 However, you can still give an instance declarations for types which break these rules,
7607 provided you give explicit code to override any generic default methods.
7615 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7616 what the compiler does with generic declarations.
7621 <sect2> <title> Another example </title>
7623 Just to finish with, here's another example I rather like:
7627 nCons {| Unit |} _ = 1
7628 nCons {| a :*: b |} _ = 1
7629 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7632 tag {| Unit |} _ = 1
7633 tag {| a :*: b |} _ = 1
7634 tag {| a :+: b |} (Inl x) = tag x
7635 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7641 <sect1 id="monomorphism">
7642 <title>Control over monomorphism</title>
7644 <para>GHC supports two flags that control the way in which generalisation is
7645 carried out at let and where bindings.
7649 <title>Switching off the dreaded Monomorphism Restriction</title>
7650 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7652 <para>Haskell's monomorphism restriction (see
7653 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7655 of the Haskell Report)
7656 can be completely switched off by
7657 <option>-XNoMonomorphismRestriction</option>.
7662 <title>Monomorphic pattern bindings</title>
7663 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7664 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7666 <para> As an experimental change, we are exploring the possibility of
7667 making pattern bindings monomorphic; that is, not generalised at all.
7668 A pattern binding is a binding whose LHS has no function arguments,
7669 and is not a simple variable. For example:
7671 f x = x -- Not a pattern binding
7672 f = \x -> x -- Not a pattern binding
7673 f :: Int -> Int = \x -> x -- Not a pattern binding
7675 (g,h) = e -- A pattern binding
7676 (f) = e -- A pattern binding
7677 [x] = e -- A pattern binding
7679 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7680 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7689 ;;; Local Variables: ***
7691 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7692 ;;; ispell-local-dictionary: "british" ***
projects / ghc-hetmet.git / blob