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>
368 <sect2 id="new-qualified-operators">
369 <title>New qualified operator syntax</title>
371 <para>A new syntax for referencing qualified operators is
372 planned to be introduced by Haskell', and is enabled in GHC
374 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
375 option. In the new syntax, the prefix form of a qualified
377 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
378 (in Haskell 98 this would
379 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
380 and the infix form is
381 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
382 (in Haskell 98 this would
383 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
386 add x y = Prelude.(+) x y
387 subtract y = (`Prelude.(-)` y)
389 The new form of qualified operators is intended to regularise
390 the syntax by eliminating odd cases
391 like <literal>Prelude..</literal>. For example,
392 when <literal>NewQualifiedOperators</literal> is on, it is possible to
393 write the enerated sequence <literal>[Monday..]</literal>
394 without spaces, whereas in Haskell 98 this would be a
395 reference to the operator ‘<literal>.</literal>‘
396 from module <literal>Monday</literal>.</para>
398 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
399 98 syntax for qualified operators is not accepted, so this
400 option may cause existing Haskell 98 code to break.</para>
405 <!-- ====================== HIERARCHICAL MODULES ======================= -->
408 <sect2 id="hierarchical-modules">
409 <title>Hierarchical Modules</title>
411 <para>GHC supports a small extension to the syntax of module
412 names: a module name is allowed to contain a dot
413 <literal>‘.’</literal>. This is also known as the
414 “hierarchical module namespace” extension, because
415 it extends the normally flat Haskell module namespace into a
416 more flexible hierarchy of modules.</para>
418 <para>This extension has very little impact on the language
419 itself; modules names are <emphasis>always</emphasis> fully
420 qualified, so you can just think of the fully qualified module
421 name as <quote>the module name</quote>. In particular, this
422 means that the full module name must be given after the
423 <literal>module</literal> keyword at the beginning of the
424 module; for example, the module <literal>A.B.C</literal> must
427 <programlisting>module A.B.C</programlisting>
430 <para>It is a common strategy to use the <literal>as</literal>
431 keyword to save some typing when using qualified names with
432 hierarchical modules. For example:</para>
435 import qualified Control.Monad.ST.Strict as ST
438 <para>For details on how GHC searches for source and interface
439 files in the presence of hierarchical modules, see <xref
440 linkend="search-path"/>.</para>
442 <para>GHC comes with a large collection of libraries arranged
443 hierarchically; see the accompanying <ulink
444 url="../libraries/index.html">library
445 documentation</ulink>. More libraries to install are available
447 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
450 <!-- ====================== PATTERN GUARDS ======================= -->
452 <sect2 id="pattern-guards">
453 <title>Pattern guards</title>
456 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
457 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
461 Suppose we have an abstract data type of finite maps, with a
465 lookup :: FiniteMap -> Int -> Maybe Int
468 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
469 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
473 clunky env var1 var2 | ok1 && ok2 = val1 + val2
474 | otherwise = var1 + var2
485 The auxiliary functions are
489 maybeToBool :: Maybe a -> Bool
490 maybeToBool (Just x) = True
491 maybeToBool Nothing = False
493 expectJust :: Maybe a -> a
494 expectJust (Just x) = x
495 expectJust Nothing = error "Unexpected Nothing"
499 What is <function>clunky</function> doing? The guard <literal>ok1 &&
500 ok2</literal> checks that both lookups succeed, using
501 <function>maybeToBool</function> to convert the <function>Maybe</function>
502 types to booleans. The (lazily evaluated) <function>expectJust</function>
503 calls extract the values from the results of the lookups, and binds the
504 returned values to <varname>val1</varname> and <varname>val2</varname>
505 respectively. If either lookup fails, then clunky takes the
506 <literal>otherwise</literal> case and returns the sum of its arguments.
510 This is certainly legal Haskell, but it is a tremendously verbose and
511 un-obvious way to achieve the desired effect. Arguably, a more direct way
512 to write clunky would be to use case expressions:
516 clunky env var1 var2 = case lookup env var1 of
518 Just val1 -> case lookup env var2 of
520 Just val2 -> val1 + val2
526 This is a bit shorter, but hardly better. Of course, we can rewrite any set
527 of pattern-matching, guarded equations as case expressions; that is
528 precisely what the compiler does when compiling equations! The reason that
529 Haskell provides guarded equations is because they allow us to write down
530 the cases we want to consider, one at a time, independently of each other.
531 This structure is hidden in the case version. Two of the right-hand sides
532 are really the same (<function>fail</function>), and the whole expression
533 tends to become more and more indented.
537 Here is how I would write clunky:
542 | Just val1 <- lookup env var1
543 , Just val2 <- lookup env var2
545 ...other equations for clunky...
549 The semantics should be clear enough. The qualifiers are matched in order.
550 For a <literal><-</literal> qualifier, which I call a pattern guard, the
551 right hand side is evaluated and matched against the pattern on the left.
552 If the match fails then the whole guard fails and the next equation is
553 tried. If it succeeds, then the appropriate binding takes place, and the
554 next qualifier is matched, in the augmented environment. Unlike list
555 comprehensions, however, the type of the expression to the right of the
556 <literal><-</literal> is the same as the type of the pattern to its
557 left. The bindings introduced by pattern guards scope over all the
558 remaining guard qualifiers, and over the right hand side of the equation.
562 Just as with list comprehensions, boolean expressions can be freely mixed
563 with among the pattern guards. For example:
574 Haskell's current guards therefore emerge as a special case, in which the
575 qualifier list has just one element, a boolean expression.
579 <!-- ===================== View patterns =================== -->
581 <sect2 id="view-patterns">
586 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
587 More information and examples of view patterns can be found on the
588 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
593 View patterns are somewhat like pattern guards that can be nested inside
594 of other patterns. They are a convenient way of pattern-matching
595 against values of abstract types. For example, in a programming language
596 implementation, we might represent the syntax of the types of the
605 view :: Type -> TypeView
607 -- additional operations for constructing Typ's ...
610 The representation of Typ is held abstract, permitting implementations
611 to use a fancy representation (e.g., hash-consing to manage sharing).
613 Without view patterns, using this signature a little inconvenient:
615 size :: Typ -> Integer
616 size t = case view t of
618 Arrow t1 t2 -> size t1 + size t2
621 It is necessary to iterate the case, rather than using an equational
622 function definition. And the situation is even worse when the matching
623 against <literal>t</literal> is buried deep inside another pattern.
627 View patterns permit calling the view function inside the pattern and
628 matching against the result:
630 size (view -> Unit) = 1
631 size (view -> Arrow t1 t2) = size t1 + size t2
634 That is, we add a new form of pattern, written
635 <replaceable>expression</replaceable> <literal>-></literal>
636 <replaceable>pattern</replaceable> that means "apply the expression to
637 whatever we're trying to match against, and then match the result of
638 that application against the pattern". The expression can be any Haskell
639 expression of function type, and view patterns can be used wherever
644 The semantics of a pattern <literal>(</literal>
645 <replaceable>exp</replaceable> <literal>-></literal>
646 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
652 <para>The variables bound by the view pattern are the variables bound by
653 <replaceable>pat</replaceable>.
657 Any variables in <replaceable>exp</replaceable> are bound occurrences,
658 but variables bound "to the left" in a pattern are in scope. This
659 feature permits, for example, one argument to a function to be used in
660 the view of another argument. For example, the function
661 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
662 written using view patterns as follows:
665 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
666 ...other equations for clunky...
671 More precisely, the scoping rules are:
675 In a single pattern, variables bound by patterns to the left of a view
676 pattern expression are in scope. For example:
678 example :: Maybe ((String -> Integer,Integer), String) -> Bool
679 example Just ((f,_), f -> 4) = True
682 Additionally, in function definitions, variables bound by matching earlier curried
683 arguments may be used in view pattern expressions in later arguments:
685 example :: (String -> Integer) -> String -> Bool
686 example f (f -> 4) = True
688 That is, the scoping is the same as it would be if the curried arguments
689 were collected into a tuple.
695 In mutually recursive bindings, such as <literal>let</literal>,
696 <literal>where</literal>, or the top level, view patterns in one
697 declaration may not mention variables bound by other declarations. That
698 is, each declaration must be self-contained. For example, the following
699 program is not allowed:
706 restriction in the future; the only cost is that type checking patterns
707 would get a little more complicated.)
717 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
718 <replaceable>T1</replaceable> <literal>-></literal>
719 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
720 a <replaceable>T2</replaceable>, then the whole view pattern matches a
721 <replaceable>T1</replaceable>.
724 <listitem><para> Matching: To the equations in Section 3.17.3 of the
725 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
726 Report</ulink>, add the following:
728 case v of { (e -> p) -> e1 ; _ -> e2 }
730 case (e v) of { p -> e1 ; _ -> e2 }
732 That is, to match a variable <replaceable>v</replaceable> against a pattern
733 <literal>(</literal> <replaceable>exp</replaceable>
734 <literal>-></literal> <replaceable>pat</replaceable>
735 <literal>)</literal>, evaluate <literal>(</literal>
736 <replaceable>exp</replaceable> <replaceable> v</replaceable>
737 <literal>)</literal> and match the result against
738 <replaceable>pat</replaceable>.
741 <listitem><para> Efficiency: When the same view function is applied in
742 multiple branches of a function definition or a case expression (e.g.,
743 in <literal>size</literal> above), GHC makes an attempt to collect these
744 applications into a single nested case expression, so that the view
745 function is only applied once. Pattern compilation in GHC follows the
746 matrix algorithm described in Chapter 4 of <ulink
747 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
748 Implementation of Functional Programming Languages</ulink>. When the
749 top rows of the first column of a matrix are all view patterns with the
750 "same" expression, these patterns are transformed into a single nested
751 case. This includes, for example, adjacent view patterns that line up
754 f ((view -> A, p1), p2) = e1
755 f ((view -> B, p3), p4) = e2
759 <para> The current notion of when two view pattern expressions are "the
760 same" is very restricted: it is not even full syntactic equality.
761 However, it does include variables, literals, applications, and tuples;
762 e.g., two instances of <literal>view ("hi", "there")</literal> will be
763 collected. However, the current implementation does not compare up to
764 alpha-equivalence, so two instances of <literal>(x, view x ->
765 y)</literal> will not be coalesced.
775 <!-- ===================== Recursive do-notation =================== -->
777 <sect2 id="mdo-notation">
778 <title>The recursive do-notation
781 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
782 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
783 by Levent Erkok, John Launchbury,
784 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
785 This paper is essential reading for anyone making non-trivial use of mdo-notation,
786 and we do not repeat it here.
789 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
790 that is, the variables bound in a do-expression are visible only in the textually following
791 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
792 group. It turns out that several applications can benefit from recursive bindings in
793 the do-notation, and this extension provides the necessary syntactic support.
796 Here is a simple (yet contrived) example:
799 import Control.Monad.Fix
801 justOnes = mdo xs <- Just (1:xs)
805 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
809 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
812 class Monad m => MonadFix m where
813 mfix :: (a -> m a) -> m a
816 The function <literal>mfix</literal>
817 dictates how the required recursion operation should be performed. For example,
818 <literal>justOnes</literal> desugars as follows:
820 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
822 For full details of the way in which mdo is typechecked and desugared, see
823 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
824 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
827 If recursive bindings are required for a monad,
828 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
829 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
830 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
831 for Haskell's internal state monad (strict and lazy, respectively).
834 Here are some important points in using the recursive-do notation:
837 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
838 than <literal>do</literal>).
842 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
843 <literal>-fglasgow-exts</literal>.
847 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
848 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
849 be distinct (Section 3.3 of the paper).
853 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
854 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
855 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
856 and improve termination (Section 3.2 of the paper).
862 Historical note: The old implementation of the mdo-notation (and most
863 of the existing documents) used the name
864 <literal>MonadRec</literal> for the class and the corresponding library.
865 This name is not supported by GHC.
871 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
873 <sect2 id="parallel-list-comprehensions">
874 <title>Parallel List Comprehensions</title>
875 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
877 <indexterm><primary>parallel list comprehensions</primary>
880 <para>Parallel list comprehensions are a natural extension to list
881 comprehensions. List comprehensions can be thought of as a nice
882 syntax for writing maps and filters. Parallel comprehensions
883 extend this to include the zipWith family.</para>
885 <para>A parallel list comprehension has multiple independent
886 branches of qualifier lists, each separated by a `|' symbol. For
887 example, the following zips together two lists:</para>
890 [ (x, y) | x <- xs | y <- ys ]
893 <para>The behavior of parallel list comprehensions follows that of
894 zip, in that the resulting list will have the same length as the
895 shortest branch.</para>
897 <para>We can define parallel list comprehensions by translation to
898 regular comprehensions. Here's the basic idea:</para>
900 <para>Given a parallel comprehension of the form: </para>
903 [ e | p1 <- e11, p2 <- e12, ...
904 | q1 <- e21, q2 <- e22, ...
909 <para>This will be translated to: </para>
912 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
913 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
918 <para>where `zipN' is the appropriate zip for the given number of
923 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
925 <sect2 id="generalised-list-comprehensions">
926 <title>Generalised (SQL-Like) List Comprehensions</title>
927 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
929 <indexterm><primary>extended list comprehensions</primary>
931 <indexterm><primary>group</primary></indexterm>
932 <indexterm><primary>sql</primary></indexterm>
935 <para>Generalised list comprehensions are a further enhancement to the
936 list comprehension syntatic sugar to allow operations such as sorting
937 and grouping which are familiar from SQL. They are fully described in the
938 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
939 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
940 except that the syntax we use differs slightly from the paper.</para>
941 <para>Here is an example:
943 employees = [ ("Simon", "MS", 80)
944 , ("Erik", "MS", 100)
946 , ("Gordon", "Ed", 45)
947 , ("Paul", "Yale", 60)]
949 output = [ (the dept, sum salary)
950 | (name, dept, salary) <- employees
952 , then sortWith by (sum salary)
955 In this example, the list <literal>output</literal> would take on
959 [("Yale", 60), ("Ed", 85), ("MS", 180)]
962 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
963 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
964 function that is exported by <literal>GHC.Exts</literal>.)</para>
966 <para>There are five new forms of comprehension qualifier,
967 all introduced by the (existing) keyword <literal>then</literal>:
975 This statement requires that <literal>f</literal> have the type <literal>
976 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
977 motivating example, as this form is used to apply <literal>take 5</literal>.
988 This form is similar to the previous one, but allows you to create a function
989 which will be passed as the first argument to f. As a consequence f must have
990 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
991 from the type, this function lets f "project out" some information
992 from the elements of the list it is transforming.</para>
994 <para>An example is shown in the opening example, where <literal>sortWith</literal>
995 is supplied with a function that lets it find out the <literal>sum salary</literal>
996 for any item in the list comprehension it transforms.</para>
1004 then group by e using f
1007 <para>This is the most general of the grouping-type statements. In this form,
1008 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1009 As with the <literal>then f by e</literal> case above, the first argument
1010 is a function supplied to f by the compiler which lets it compute e on every
1011 element of the list being transformed. However, unlike the non-grouping case,
1012 f additionally partitions the list into a number of sublists: this means that
1013 at every point after this statement, binders occurring before it in the comprehension
1014 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1015 this, let's look at an example:</para>
1018 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1019 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1020 groupRuns f = groupBy (\x y -> f x == f y)
1022 output = [ (the x, y)
1023 | x <- ([1..3] ++ [1..2])
1025 , then group by x using groupRuns ]
1028 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1031 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1034 <para>Note that we have used the <literal>the</literal> function to change the type
1035 of x from a list to its original numeric type. The variable y, in contrast, is left
1036 unchanged from the list form introduced by the grouping.</para>
1046 <para>This form of grouping is essentially the same as the one described above. However,
1047 since no function to use for the grouping has been supplied it will fall back on the
1048 <literal>groupWith</literal> function defined in
1049 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1050 is the form of the group statement that we made use of in the opening example.</para>
1061 <para>With this form of the group statement, f is required to simply have the type
1062 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1063 comprehension so far directly. An example of this form is as follows:</para>
1069 , then group using inits]
1072 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1075 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1083 <!-- ===================== REBINDABLE SYNTAX =================== -->
1085 <sect2 id="rebindable-syntax">
1086 <title>Rebindable syntax and the implicit Prelude import</title>
1088 <para><indexterm><primary>-XNoImplicitPrelude
1089 option</primary></indexterm> GHC normally imports
1090 <filename>Prelude.hi</filename> files for you. If you'd
1091 rather it didn't, then give it a
1092 <option>-XNoImplicitPrelude</option> option. The idea is
1093 that you can then import a Prelude of your own. (But don't
1094 call it <literal>Prelude</literal>; the Haskell module
1095 namespace is flat, and you must not conflict with any
1096 Prelude module.)</para>
1098 <para>Suppose you are importing a Prelude of your own
1099 in order to define your own numeric class
1100 hierarchy. It completely defeats that purpose if the
1101 literal "1" means "<literal>Prelude.fromInteger
1102 1</literal>", which is what the Haskell Report specifies.
1103 So the <option>-XNoImplicitPrelude</option>
1104 flag <emphasis>also</emphasis> causes
1105 the following pieces of built-in syntax to refer to
1106 <emphasis>whatever is in scope</emphasis>, not the Prelude
1110 <para>An integer literal <literal>368</literal> means
1111 "<literal>fromInteger (368::Integer)</literal>", rather than
1112 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1115 <listitem><para>Fractional literals are handed in just the same way,
1116 except that the translation is
1117 <literal>fromRational (3.68::Rational)</literal>.
1120 <listitem><para>The equality test in an overloaded numeric pattern
1121 uses whatever <literal>(==)</literal> is in scope.
1124 <listitem><para>The subtraction operation, and the
1125 greater-than-or-equal test, in <literal>n+k</literal> patterns
1126 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1130 <para>Negation (e.g. "<literal>- (f x)</literal>")
1131 means "<literal>negate (f x)</literal>", both in numeric
1132 patterns, and expressions.
1136 <para>"Do" notation is translated using whatever
1137 functions <literal>(>>=)</literal>,
1138 <literal>(>>)</literal>, and <literal>fail</literal>,
1139 are in scope (not the Prelude
1140 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1141 comprehensions, are unaffected. </para></listitem>
1145 notation (see <xref linkend="arrow-notation"/>)
1146 uses whatever <literal>arr</literal>,
1147 <literal>(>>>)</literal>, <literal>first</literal>,
1148 <literal>app</literal>, <literal>(|||)</literal> and
1149 <literal>loop</literal> functions are in scope. But unlike the
1150 other constructs, the types of these functions must match the
1151 Prelude types very closely. Details are in flux; if you want
1155 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1156 even if that is a little unexpected. For example, the
1157 static semantics of the literal <literal>368</literal>
1158 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1159 <literal>fromInteger</literal> to have any of the types:
1161 fromInteger :: Integer -> Integer
1162 fromInteger :: forall a. Foo a => Integer -> a
1163 fromInteger :: Num a => a -> Integer
1164 fromInteger :: Integer -> Bool -> Bool
1168 <para>Be warned: this is an experimental facility, with
1169 fewer checks than usual. Use <literal>-dcore-lint</literal>
1170 to typecheck the desugared program. If Core Lint is happy
1171 you should be all right.</para>
1175 <sect2 id="postfix-operators">
1176 <title>Postfix operators</title>
1179 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="type-families">
3698 <title>Type families</title>
3701 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3702 facilitate type-level
3703 programming. Type families are a generalisation of <firstterm>associated
3704 data types</firstterm>
3705 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3706 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3707 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3708 Symposium on Principles of Programming Languages (POPL'05)”, pages
3709 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3710 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3711 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3713 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3714 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3715 themselves are described in the paper “<ulink
3716 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3717 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3719 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3720 13th ACM SIGPLAN International Conference on Functional
3721 Programming”, ACM Press, pages 51-62, 2008. Type families
3722 essentially provide type-indexed data types and named functions on types,
3723 which are useful for generic programming and highly parameterised library
3724 interfaces as well as interfaces with enhanced static information, much like
3725 dependent types. They might also be regarded as an alternative to functional
3726 dependencies, but provide a more functional style of type-level programming
3727 than the relational style of functional dependencies.
3730 Indexed type families, or type families for short, are type constructors that
3731 represent sets of types. Set members are denoted by supplying the type family
3732 constructor with type parameters, which are called <firstterm>type
3733 indices</firstterm>. The
3734 difference between vanilla parametrised type constructors and family
3735 constructors is much like between parametrically polymorphic functions and
3736 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3737 behave the same at all type instances, whereas class methods can change their
3738 behaviour in dependence on the class type parameters. Similarly, vanilla type
3739 constructors imply the same data representation for all type instances, but
3740 family constructors can have varying representation types for varying type
3744 Indexed type families come in two flavours: <firstterm>data
3745 families</firstterm> and <firstterm>type synonym
3746 families</firstterm>. They are the indexed family variants of algebraic
3747 data types and type synonyms, respectively. The instances of data families
3748 can be data types and newtypes.
3751 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3752 Additional information on the use of type families in GHC is available on
3753 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3754 Haskell wiki page on type families</ulink>.
3757 <sect2 id="data-families">
3758 <title>Data families</title>
3761 Data families appear in two flavours: (1) they can be defined on the
3763 or (2) they can appear inside type classes (in which case they are known as
3764 associated types). The former is the more general variant, as it lacks the
3765 requirement for the type-indexes to coincide with the class
3766 parameters. However, the latter can lead to more clearly structured code and
3767 compiler warnings if some type instances were - possibly accidentally -
3768 omitted. In the following, we always discuss the general toplevel form first
3769 and then cover the additional constraints placed on associated types.
3772 <sect3 id="data-family-declarations">
3773 <title>Data family declarations</title>
3776 Indexed data families are introduced by a signature, such as
3778 data family GMap k :: * -> *
3780 The special <literal>family</literal> distinguishes family from standard
3781 data declarations. The result kind annotation is optional and, as
3782 usual, defaults to <literal>*</literal> if omitted. An example is
3786 Named arguments can also be given explicit kind signatures if needed.
3788 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3789 declarations] named arguments are entirely optional, so that we can
3790 declare <literal>Array</literal> alternatively with
3792 data family Array :: * -> *
3796 <sect4 id="assoc-data-family-decl">
3797 <title>Associated data family declarations</title>
3799 When a data family is declared as part of a type class, we drop
3800 the <literal>family</literal> special. The <literal>GMap</literal>
3801 declaration takes the following form
3803 class GMapKey k where
3804 data GMap k :: * -> *
3807 In contrast to toplevel declarations, named arguments must be used for
3808 all type parameters that are to be used as type-indexes. Moreover,
3809 the argument names must be class parameters. Each class parameter may
3810 only be used at most once per associated type, but some may be omitted
3811 and they may be in an order other than in the class head. Hence, the
3812 following contrived example is admissible:
3821 <sect3 id="data-instance-declarations">
3822 <title>Data instance declarations</title>
3825 Instance declarations of data and newtype families are very similar to
3826 standard data and newtype declarations. The only two differences are
3827 that the keyword <literal>data</literal> or <literal>newtype</literal>
3828 is followed by <literal>instance</literal> and that some or all of the
3829 type arguments can be non-variable types, but may not contain forall
3830 types or type synonym families. However, data families are generally
3831 allowed in type parameters, and type synonyms are allowed as long as
3832 they are fully applied and expand to a type that is itself admissible -
3833 exactly as this is required for occurrences of type synonyms in class
3834 instance parameters. For example, the <literal>Either</literal>
3835 instance for <literal>GMap</literal> is
3837 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3839 In this example, the declaration has only one variant. In general, it
3843 Data and newtype instance declarations are only legit when an
3844 appropriate family declaration is in scope - just like class instances
3845 require the class declaration to be visible. Moreover, each instance
3846 declaration has to conform to the kind determined by its family
3847 declaration. This implies that the number of parameters of an instance
3848 declaration matches the arity determined by the kind of the family.
3849 Although, all data families are declared with
3850 the <literal>data</literal> keyword, instances can be
3851 either <literal>data</literal> or <literal>newtype</literal>s, or a mix
3855 Even if type families are defined as toplevel declarations, functions
3856 that perform different computations for different family instances still
3857 need to be defined as methods of type classes. In particular, the
3858 following is not possible:
3861 data instance T Int = A
3862 data instance T Char = B
3863 nonsence :: T a -> Int
3864 nonsence A = 1 -- WRONG: These two equations together...
3865 nonsence B = 2 -- ...will produce a type error.
3867 Given the functionality provided by GADTs (Generalised Algebraic Data
3868 Types), it might seem as if a definition, such as the above, should be
3869 feasible. However, type families are - in contrast to GADTs - are
3870 <emphasis>open;</emphasis> i.e., new instances can always be added,
3872 modules. Supporting pattern matching across different data instances
3873 would require a form of extensible case construct.
3876 <sect4 id="assoc-data-inst">
3877 <title>Associated data instances</title>
3879 When an associated data family instance is declared within a type
3880 class instance, we drop the <literal>instance</literal> keyword in the
3881 family instance. So, the <literal>Either</literal> instance
3882 for <literal>GMap</literal> becomes:
3884 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
3885 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3888 The most important point about associated family instances is that the
3889 type indexes corresponding to class parameters must be identical to
3890 the type given in the instance head; here this is the first argument
3891 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
3892 which coincides with the only class parameter. Any parameters to the
3893 family constructor that do not correspond to class parameters, need to
3894 be variables in every instance; here this is the
3895 variable <literal>v</literal>.
3898 Instances for an associated family can only appear as part of
3899 instances declarations of the class in which the family was declared -
3900 just as with the equations of the methods of a class. Also in
3901 correspondence to how methods are handled, declarations of associated
3902 types can be omitted in class instances. If an associated family
3903 instance is omitted, the corresponding instance type is not inhabited;
3904 i.e., only diverging expressions, such
3905 as <literal>undefined</literal>, can assume the type.
3909 <sect4 id="scoping-class-params">
3910 <title>Scoping of class parameters</title>
3912 In the case of multi-parameter type classes, the visibility of class
3913 parameters in the right-hand side of associated family instances
3914 depends <emphasis>solely</emphasis> on the parameters of the data
3915 family. As an example, consider the simple class declaration
3920 Only one of the two class parameters is a parameter to the data
3921 family. Hence, the following instance declaration is invalid:
3923 instance C [c] d where
3924 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
3926 Here, the right-hand side of the data instance mentions the type
3927 variable <literal>d</literal> that does not occur in its left-hand
3928 side. We cannot admit such data instances as they would compromise
3933 <sect4 id="family-class-inst">
3934 <title>Type class instances of family instances</title>
3936 Type class instances of instances of data families can be defined as
3937 usual, and in particular data instance declarations can
3938 have <literal>deriving</literal> clauses. For example, we can write
3940 data GMap () v = GMapUnit (Maybe v)
3943 which implicitly defines an instance of the form
3945 instance Show v => Show (GMap () v) where ...
3949 Note that class instances are always for
3950 particular <emphasis>instances</emphasis> of a data family and never
3951 for an entire family as a whole. This is for essentially the same
3952 reasons that we cannot define a toplevel function that performs
3953 pattern matching on the data constructors
3954 of <emphasis>different</emphasis> instances of a single type family.
3955 It would require a form of extensible case construct.
3959 <sect4 id="data-family-overlap">
3960 <title>Overlap of data instances</title>
3962 The instance declarations of a data family used in a single program
3963 may not overlap at all, independent of whether they are associated or
3964 not. In contrast to type class instances, this is not only a matter
3965 of consistency, but one of type safety.
3971 <sect3 id="data-family-import-export">
3972 <title>Import and export</title>
3975 The association of data constructors with type families is more dynamic
3976 than that is the case with standard data and newtype declarations. In
3977 the standard case, the notation <literal>T(..)</literal> in an import or
3978 export list denotes the type constructor and all the data constructors
3979 introduced in its declaration. However, a family declaration never
3980 introduces any data constructors; instead, data constructors are
3981 introduced by family instances. As a result, which data constructors
3982 are associated with a type family depends on the currently visible
3983 instance declarations for that family. Consequently, an import or
3984 export item of the form <literal>T(..)</literal> denotes the family
3985 constructor and all currently visible data constructors - in the case of
3986 an export item, these may be either imported or defined in the current
3987 module. The treatment of import and export items that explicitly list
3988 data constructors, such as <literal>GMap(GMapEither)</literal>, is
3992 <sect4 id="data-family-impexp-assoc">
3993 <title>Associated families</title>
3995 As expected, an import or export item of the
3996 form <literal>C(..)</literal> denotes all of the class' methods and
3997 associated types. However, when associated types are explicitly
3998 listed as subitems of a class, we need some new syntax, as uppercase
3999 identifiers as subitems are usually data constructors, not type
4000 constructors. To clarify that we denote types here, each associated
4001 type name needs to be prefixed by the keyword <literal>type</literal>.
4002 So for example, when explicitly listing the components of
4003 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4004 GMap, empty, lookup, insert)</literal>.
4008 <sect4 id="data-family-impexp-examples">
4009 <title>Examples</title>
4011 Assuming our running <literal>GMapKey</literal> class example, let us
4012 look at some export lists and their meaning:
4015 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4016 just the class name.</para>
4019 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4020 Exports the class, the associated type <literal>GMap</literal>
4022 functions <literal>empty</literal>, <literal>lookup</literal>,
4023 and <literal>insert</literal>. None of the data constructors is
4027 <para><literal>module GMap (GMapKey(..), GMap(..))
4028 where...</literal>: As before, but also exports all the data
4029 constructors <literal>GMapInt</literal>,
4030 <literal>GMapChar</literal>,
4031 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4032 and <literal>GMapUnit</literal>.</para>
4035 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4036 GMap(..)) where...</literal>: As before.</para>
4039 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4040 where...</literal>: As before.</para>
4045 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4046 both the class <literal>GMapKey</literal> as well as its associated
4047 type <literal>GMap</literal>. However, you cannot
4048 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4049 sub-component specifications cannot be nested. To
4050 specify <literal>GMap</literal>'s data constructors, you have to list
4055 <sect4 id="data-family-impexp-instances">
4056 <title>Instances</title>
4058 Family instances are implicitly exported, just like class instances.
4059 However, this applies only to the heads of instances, not to the data
4060 constructors an instance defines.
4068 <sect2 id="synonym-families">
4069 <title>Synonym families</title>
4072 Type families appear in two flavours: (1) they can be defined on the
4073 toplevel or (2) they can appear inside type classes (in which case they
4074 are known as associated type synonyms). The former is the more general
4075 variant, as it lacks the requirement for the type-indexes to coincide with
4076 the class parameters. However, the latter can lead to more clearly
4077 structured code and compiler warnings if some type instances were -
4078 possibly accidentally - omitted. In the following, we always discuss the
4079 general toplevel form first and then cover the additional constraints
4080 placed on associated types.
4083 <sect3 id="type-family-declarations">
4084 <title>Type family declarations</title>
4087 Indexed type families are introduced by a signature, such as
4089 type family Elem c :: *
4091 The special <literal>family</literal> distinguishes family from standard
4092 type declarations. The result kind annotation is optional and, as
4093 usual, defaults to <literal>*</literal> if omitted. An example is
4097 Parameters can also be given explicit kind signatures if needed. We
4098 call the number of parameters in a type family declaration, the family's
4099 arity, and all applications of a type family must be fully saturated
4100 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4101 and it implies that the kind of a type family is not sufficient to
4102 determine a family's arity, and hence in general, also insufficient to
4103 determine whether a type family application is well formed. As an
4104 example, consider the following declaration:
4106 type family F a b :: * -> * -- F's arity is 2,
4107 -- although it's overall kind is * -> * -> * -> *
4109 Given this declaration the following are examples of well-formed and
4112 F Char [Int] -- OK! Kind: * -> *
4113 F Char [Int] Bool -- OK! Kind: *
4114 F IO Bool -- WRONG: kind mismatch in the first argument
4115 F Bool -- WRONG: unsaturated application
4119 <sect4 id="assoc-type-family-decl">
4120 <title>Associated type family declarations</title>
4122 When a type family is declared as part of a type class, we drop
4123 the <literal>family</literal> special. The <literal>Elem</literal>
4124 declaration takes the following form
4126 class Collects ce where
4130 The argument names of the type family must be class parameters. Each
4131 class parameter may only be used at most once per associated type, but
4132 some may be omitted and they may be in an order other than in the
4133 class head. Hence, the following contrived example is admissible:
4138 These rules are exactly as for associated data families.
4143 <sect3 id="type-instance-declarations">
4144 <title>Type instance declarations</title>
4146 Instance declarations of type families are very similar to standard type
4147 synonym declarations. The only two differences are that the
4148 keyword <literal>type</literal> is followed
4149 by <literal>instance</literal> and that some or all of the type
4150 arguments can be non-variable types, but may not contain forall types or
4151 type synonym families. However, data families are generally allowed, and
4152 type synonyms are allowed as long as they are fully applied and expand
4153 to a type that is admissible - these are the exact same requirements as
4154 for data instances. For example, the <literal>[e]</literal> instance
4155 for <literal>Elem</literal> is
4157 type instance Elem [e] = e
4161 Type family instance declarations are only legitimate when an
4162 appropriate family declaration is in scope - just like class instances
4163 require the class declaration to be visible. Moreover, each instance
4164 declaration has to conform to the kind determined by its family
4165 declaration, and the number of type parameters in an instance
4166 declaration must match the number of type parameters in the family
4167 declaration. Finally, the right-hand side of a type instance must be a
4168 monotype (i.e., it may not include foralls) and after the expansion of
4169 all saturated vanilla type synonyms, no synonyms, except family synonyms
4170 may remain. Here are some examples of admissible and illegal type
4173 type family F a :: *
4174 type instance F [Int] = Int -- OK!
4175 type instance F String = Char -- OK!
4176 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4177 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4178 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4180 type family G a b :: * -> *
4181 type instance G Int = (,) -- WRONG: must be two type parameters
4182 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4186 <sect4 id="assoc-type-instance">
4187 <title>Associated type instance declarations</title>
4189 When an associated family instance is declared within a type class
4190 instance, we drop the <literal>instance</literal> keyword in the family
4191 instance. So, the <literal>[e]</literal> instance
4192 for <literal>Elem</literal> becomes:
4194 instance (Eq (Elem [e])) => Collects ([e]) where
4198 The most important point about associated family instances is that the
4199 type indexes corresponding to class parameters must be identical to the
4200 type given in the instance head; here this is <literal>[e]</literal>,
4201 which coincides with the only class parameter.
4204 Instances for an associated family can only appear as part of instances
4205 declarations of the class in which the family was declared - just as
4206 with the equations of the methods of a class. Also in correspondence to
4207 how methods are handled, declarations of associated types can be omitted
4208 in class instances. If an associated family instance is omitted, the
4209 corresponding instance type is not inhabited; i.e., only diverging
4210 expressions, such as <literal>undefined</literal>, can assume the type.
4214 <sect4 id="type-family-overlap">
4215 <title>Overlap of type synonym instances</title>
4217 The instance declarations of a type family used in a single program
4218 may only overlap if the right-hand sides of the overlapping instances
4219 coincide for the overlapping types. More formally, two instance
4220 declarations overlap if there is a substitution that makes the
4221 left-hand sides of the instances syntactically the same. Whenever
4222 that is the case, the right-hand sides of the instances must also be
4223 syntactically equal under the same substitution. This condition is
4224 independent of whether the type family is associated or not, and it is
4225 not only a matter of consistency, but one of type safety.
4228 Here are two example to illustrate the condition under which overlap
4231 type instance F (a, Int) = [a]
4232 type instance F (Int, b) = [b] -- overlap permitted
4234 type instance G (a, Int) = [a]
4235 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4240 <sect4 id="type-family-decidability">
4241 <title>Decidability of type synonym instances</title>
4243 In order to guarantee that type inference in the presence of type
4244 families decidable, we need to place a number of additional
4245 restrictions on the formation of type instance declarations (c.f.,
4246 Definition 5 (Relaxed Conditions) of “<ulink
4247 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4248 Checking with Open Type Functions</ulink>”). Instance
4249 declarations have the general form
4251 type instance F t1 .. tn = t
4253 where we require that for every type family application <literal>(G s1
4254 .. sm)</literal> in <literal>t</literal>,
4257 <para><literal>s1 .. sm</literal> do not contain any type family
4258 constructors,</para>
4261 <para>the total number of symbols (data type constructors and type
4262 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4263 in <literal>t1 .. tn</literal>, and</para>
4266 <para>for every type
4267 variable <literal>a</literal>, <literal>a</literal> occurs
4268 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4269 .. tn</literal>.</para>
4272 These restrictions are easily verified and ensure termination of type
4273 inference. However, they are not sufficient to guarantee completeness
4274 of type inference in the presence of, so called, ''loopy equalities'',
4275 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4276 a type variable is underneath a family application and data
4277 constructor application - see the above mentioned paper for details.
4280 If the option <option>-XUndecidableInstances</option> is passed to the
4281 compiler, the above restrictions are not enforced and it is on the
4282 programmer to ensure termination of the normalisation of type families
4283 during type inference.
4288 <sect3 id-="equality-constraints">
4289 <title>Equality constraints</title>
4291 Type context can include equality constraints of the form <literal>t1 ~
4292 t2</literal>, which denote that the types <literal>t1</literal>
4293 and <literal>t2</literal> need to be the same. In the presence of type
4294 families, whether two types are equal cannot generally be decided
4295 locally. Hence, the contexts of function signatures may include
4296 equality constraints, as in the following example:
4298 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4300 where we require that the element type of <literal>c1</literal>
4301 and <literal>c2</literal> are the same. In general, the
4302 types <literal>t1</literal> and <literal>t2</literal> of an equality
4303 constraint may be arbitrary monotypes; i.e., they may not contain any
4304 quantifiers, independent of whether higher-rank types are otherwise
4308 Equality constraints can also appear in class and instance contexts.
4309 The former enable a simple translation of programs using functional
4310 dependencies into programs using family synonyms instead. The general
4311 idea is to rewrite a class declaration of the form
4313 class C a b | a -> b
4317 class (F a ~ b) => C a b where
4320 That is, we represent every functional dependency (FD) <literal>a1 .. an
4321 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4322 superclass context equality <literal>F a1 .. an ~ b</literal>,
4323 essentially giving a name to the functional dependency. In class
4324 instances, we define the type instances of FD families in accordance
4325 with the class head. Method signatures are not affected by that
4329 NB: Equalities in superclass contexts are not fully implemented in
4338 <sect1 id="other-type-extensions">
4339 <title>Other type system extensions</title>
4341 <sect2 id="type-restrictions">
4342 <title>Type signatures</title>
4344 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4346 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4347 that the type-class constraints in a type signature must have the
4348 form <emphasis>(class type-variable)</emphasis> or
4349 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4350 With <option>-XFlexibleContexts</option>
4351 these type signatures are perfectly OK
4354 g :: Ord (T a ()) => ...
4358 GHC imposes the following restrictions on the constraints in a type signature.
4362 forall tv1..tvn (c1, ...,cn) => type
4365 (Here, we write the "foralls" explicitly, although the Haskell source
4366 language omits them; in Haskell 98, all the free type variables of an
4367 explicit source-language type signature are universally quantified,
4368 except for the class type variables in a class declaration. However,
4369 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4378 <emphasis>Each universally quantified type variable
4379 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4381 A type variable <literal>a</literal> is "reachable" if it appears
4382 in the same constraint as either a type variable free in
4383 <literal>type</literal>, or another reachable type variable.
4384 A value with a type that does not obey
4385 this reachability restriction cannot be used without introducing
4386 ambiguity; that is why the type is rejected.
4387 Here, for example, is an illegal type:
4391 forall a. Eq a => Int
4395 When a value with this type was used, the constraint <literal>Eq tv</literal>
4396 would be introduced where <literal>tv</literal> is a fresh type variable, and
4397 (in the dictionary-translation implementation) the value would be
4398 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4399 can never know which instance of <literal>Eq</literal> to use because we never
4400 get any more information about <literal>tv</literal>.
4404 that the reachability condition is weaker than saying that <literal>a</literal> is
4405 functionally dependent on a type variable free in
4406 <literal>type</literal> (see <xref
4407 linkend="functional-dependencies"/>). The reason for this is there
4408 might be a "hidden" dependency, in a superclass perhaps. So
4409 "reachable" is a conservative approximation to "functionally dependent".
4410 For example, consider:
4412 class C a b | a -> b where ...
4413 class C a b => D a b where ...
4414 f :: forall a b. D a b => a -> a
4416 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4417 but that is not immediately apparent from <literal>f</literal>'s type.
4423 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4424 universally quantified type variables <literal>tvi</literal></emphasis>.
4426 For example, this type is OK because <literal>C a b</literal> mentions the
4427 universally quantified type variable <literal>b</literal>:
4431 forall a. C a b => burble
4435 The next type is illegal because the constraint <literal>Eq b</literal> does not
4436 mention <literal>a</literal>:
4440 forall a. Eq b => burble
4444 The reason for this restriction is milder than the other one. The
4445 excluded types are never useful or necessary (because the offending
4446 context doesn't need to be witnessed at this point; it can be floated
4447 out). Furthermore, floating them out increases sharing. Lastly,
4448 excluding them is a conservative choice; it leaves a patch of
4449 territory free in case we need it later.
4463 <sect2 id="implicit-parameters">
4464 <title>Implicit parameters</title>
4466 <para> Implicit parameters are implemented as described in
4467 "Implicit parameters: dynamic scoping with static types",
4468 J Lewis, MB Shields, E Meijer, J Launchbury,
4469 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4473 <para>(Most of the following, still rather incomplete, documentation is
4474 due to Jeff Lewis.)</para>
4476 <para>Implicit parameter support is enabled with the option
4477 <option>-XImplicitParams</option>.</para>
4480 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4481 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4482 context. In Haskell, all variables are statically bound. Dynamic
4483 binding of variables is a notion that goes back to Lisp, but was later
4484 discarded in more modern incarnations, such as Scheme. Dynamic binding
4485 can be very confusing in an untyped language, and unfortunately, typed
4486 languages, in particular Hindley-Milner typed languages like Haskell,
4487 only support static scoping of variables.
4490 However, by a simple extension to the type class system of Haskell, we
4491 can support dynamic binding. Basically, we express the use of a
4492 dynamically bound variable as a constraint on the type. These
4493 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4494 function uses a dynamically-bound variable <literal>?x</literal>
4495 of type <literal>t'</literal>". For
4496 example, the following expresses the type of a sort function,
4497 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4499 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4501 The dynamic binding constraints are just a new form of predicate in the type class system.
4504 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4505 where <literal>x</literal> is
4506 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4507 Use of this construct also introduces a new
4508 dynamic-binding constraint in the type of the expression.
4509 For example, the following definition
4510 shows how we can define an implicitly parameterized sort function in
4511 terms of an explicitly parameterized <literal>sortBy</literal> function:
4513 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4515 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4521 <title>Implicit-parameter type constraints</title>
4523 Dynamic binding constraints behave just like other type class
4524 constraints in that they are automatically propagated. Thus, when a
4525 function is used, its implicit parameters are inherited by the
4526 function that called it. For example, our <literal>sort</literal> function might be used
4527 to pick out the least value in a list:
4529 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4530 least xs = head (sort xs)
4532 Without lifting a finger, the <literal>?cmp</literal> parameter is
4533 propagated to become a parameter of <literal>least</literal> as well. With explicit
4534 parameters, the default is that parameters must always be explicit
4535 propagated. With implicit parameters, the default is to always
4539 An implicit-parameter type constraint differs from other type class constraints in the
4540 following way: All uses of a particular implicit parameter must have
4541 the same type. This means that the type of <literal>(?x, ?x)</literal>
4542 is <literal>(?x::a) => (a,a)</literal>, and not
4543 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4547 <para> You can't have an implicit parameter in the context of a class or instance
4548 declaration. For example, both these declarations are illegal:
4550 class (?x::Int) => C a where ...
4551 instance (?x::a) => Foo [a] where ...
4553 Reason: exactly which implicit parameter you pick up depends on exactly where
4554 you invoke a function. But the ``invocation'' of instance declarations is done
4555 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4556 Easiest thing is to outlaw the offending types.</para>
4558 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4560 f :: (?x :: [a]) => Int -> Int
4563 g :: (Read a, Show a) => String -> String
4566 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4567 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4568 quite unambiguous, and fixes the type <literal>a</literal>.
4573 <title>Implicit-parameter bindings</title>
4576 An implicit parameter is <emphasis>bound</emphasis> using the standard
4577 <literal>let</literal> or <literal>where</literal> binding forms.
4578 For example, we define the <literal>min</literal> function by binding
4579 <literal>cmp</literal>.
4582 min = let ?cmp = (<=) in least
4586 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4587 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4588 (including in a list comprehension, or do-notation, or pattern guards),
4589 or a <literal>where</literal> clause.
4590 Note the following points:
4593 An implicit-parameter binding group must be a
4594 collection of simple bindings to implicit-style variables (no
4595 function-style bindings, and no type signatures); these bindings are
4596 neither polymorphic or recursive.
4599 You may not mix implicit-parameter bindings with ordinary bindings in a
4600 single <literal>let</literal>
4601 expression; use two nested <literal>let</literal>s instead.
4602 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4606 You may put multiple implicit-parameter bindings in a
4607 single binding group; but they are <emphasis>not</emphasis> treated
4608 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4609 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4610 parameter. The bindings are not nested, and may be re-ordered without changing
4611 the meaning of the program.
4612 For example, consider:
4614 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4616 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4617 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4619 f :: (?x::Int) => Int -> Int
4627 <sect3><title>Implicit parameters and polymorphic recursion</title>
4630 Consider these two definitions:
4633 len1 xs = let ?acc = 0 in len_acc1 xs
4636 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4641 len2 xs = let ?acc = 0 in len_acc2 xs
4643 len_acc2 :: (?acc :: Int) => [a] -> Int
4645 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4647 The only difference between the two groups is that in the second group
4648 <literal>len_acc</literal> is given a type signature.
4649 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4650 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4651 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4652 has a type signature, the recursive call is made to the
4653 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4654 as an implicit parameter. So we get the following results in GHCi:
4661 Adding a type signature dramatically changes the result! This is a rather
4662 counter-intuitive phenomenon, worth watching out for.
4666 <sect3><title>Implicit parameters and monomorphism</title>
4668 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4669 Haskell Report) to implicit parameters. For example, consider:
4677 Since the binding for <literal>y</literal> falls under the Monomorphism
4678 Restriction it is not generalised, so the type of <literal>y</literal> is
4679 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4680 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4681 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4682 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4683 <literal>y</literal> in the body of the <literal>let</literal> will see the
4684 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4685 <literal>14</literal>.
4690 <!-- ======================= COMMENTED OUT ========================
4692 We intend to remove linear implicit parameters, so I'm at least removing
4693 them from the 6.6 user manual
4695 <sect2 id="linear-implicit-parameters">
4696 <title>Linear implicit parameters</title>
4698 Linear implicit parameters are an idea developed by Koen Claessen,
4699 Mark Shields, and Simon PJ. They address the long-standing
4700 problem that monads seem over-kill for certain sorts of problem, notably:
4703 <listitem> <para> distributing a supply of unique names </para> </listitem>
4704 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4705 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4709 Linear implicit parameters are just like ordinary implicit parameters,
4710 except that they are "linear"; that is, they cannot be copied, and
4711 must be explicitly "split" instead. Linear implicit parameters are
4712 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4713 (The '/' in the '%' suggests the split!)
4718 import GHC.Exts( Splittable )
4720 data NameSupply = ...
4722 splitNS :: NameSupply -> (NameSupply, NameSupply)
4723 newName :: NameSupply -> Name
4725 instance Splittable NameSupply where
4729 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4730 f env (Lam x e) = Lam x' (f env e)
4733 env' = extend env x x'
4734 ...more equations for f...
4736 Notice that the implicit parameter %ns is consumed
4738 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4739 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4743 So the translation done by the type checker makes
4744 the parameter explicit:
4746 f :: NameSupply -> Env -> Expr -> Expr
4747 f ns env (Lam x e) = Lam x' (f ns1 env e)
4749 (ns1,ns2) = splitNS ns
4751 env = extend env x x'
4753 Notice the call to 'split' introduced by the type checker.
4754 How did it know to use 'splitNS'? Because what it really did
4755 was to introduce a call to the overloaded function 'split',
4756 defined by the class <literal>Splittable</literal>:
4758 class Splittable a where
4761 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4762 split for name supplies. But we can simply write
4768 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4770 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4771 <literal>GHC.Exts</literal>.
4776 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4777 are entirely distinct implicit parameters: you
4778 can use them together and they won't interfere with each other. </para>
4781 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4783 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4784 in the context of a class or instance declaration. </para></listitem>
4788 <sect3><title>Warnings</title>
4791 The monomorphism restriction is even more important than usual.
4792 Consider the example above:
4794 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4795 f env (Lam x e) = Lam x' (f env e)
4798 env' = extend env x x'
4800 If we replaced the two occurrences of x' by (newName %ns), which is
4801 usually a harmless thing to do, we get:
4803 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4804 f env (Lam x e) = Lam (newName %ns) (f env e)
4806 env' = extend env x (newName %ns)
4808 But now the name supply is consumed in <emphasis>three</emphasis> places
4809 (the two calls to newName,and the recursive call to f), so
4810 the result is utterly different. Urk! We don't even have
4814 Well, this is an experimental change. With implicit
4815 parameters we have already lost beta reduction anyway, and
4816 (as John Launchbury puts it) we can't sensibly reason about
4817 Haskell programs without knowing their typing.
4822 <sect3><title>Recursive functions</title>
4823 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4826 foo :: %x::T => Int -> [Int]
4828 foo n = %x : foo (n-1)
4830 where T is some type in class Splittable.</para>
4832 Do you get a list of all the same T's or all different T's
4833 (assuming that split gives two distinct T's back)?
4835 If you supply the type signature, taking advantage of polymorphic
4836 recursion, you get what you'd probably expect. Here's the
4837 translated term, where the implicit param is made explicit:
4840 foo x n = let (x1,x2) = split x
4841 in x1 : foo x2 (n-1)
4843 But if you don't supply a type signature, GHC uses the Hindley
4844 Milner trick of using a single monomorphic instance of the function
4845 for the recursive calls. That is what makes Hindley Milner type inference
4846 work. So the translation becomes
4850 foom n = x : foom (n-1)
4854 Result: 'x' is not split, and you get a list of identical T's. So the
4855 semantics of the program depends on whether or not foo has a type signature.
4858 You may say that this is a good reason to dislike linear implicit parameters
4859 and you'd be right. That is why they are an experimental feature.
4865 ================ END OF Linear Implicit Parameters commented out -->
4867 <sect2 id="kinding">
4868 <title>Explicitly-kinded quantification</title>
4871 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4872 to give the kind explicitly as (machine-checked) documentation,
4873 just as it is nice to give a type signature for a function. On some occasions,
4874 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4875 John Hughes had to define the data type:
4877 data Set cxt a = Set [a]
4878 | Unused (cxt a -> ())
4880 The only use for the <literal>Unused</literal> constructor was to force the correct
4881 kind for the type variable <literal>cxt</literal>.
4884 GHC now instead allows you to specify the kind of a type variable directly, wherever
4885 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4888 This flag enables kind signatures in the following places:
4890 <listitem><para><literal>data</literal> declarations:
4892 data Set (cxt :: * -> *) a = Set [a]
4893 </screen></para></listitem>
4894 <listitem><para><literal>type</literal> declarations:
4896 type T (f :: * -> *) = f Int
4897 </screen></para></listitem>
4898 <listitem><para><literal>class</literal> declarations:
4900 class (Eq a) => C (f :: * -> *) a where ...
4901 </screen></para></listitem>
4902 <listitem><para><literal>forall</literal>'s in type signatures:
4904 f :: forall (cxt :: * -> *). Set cxt Int
4905 </screen></para></listitem>
4910 The parentheses are required. Some of the spaces are required too, to
4911 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4912 will get a parse error, because "<literal>::*->*</literal>" is a
4913 single lexeme in Haskell.
4917 As part of the same extension, you can put kind annotations in types
4920 f :: (Int :: *) -> Int
4921 g :: forall a. a -> (a :: *)
4925 atype ::= '(' ctype '::' kind ')
4927 The parentheses are required.
4932 <sect2 id="universal-quantification">
4933 <title>Arbitrary-rank polymorphism
4937 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4938 allows us to say exactly what this means. For example:
4946 g :: forall b. (b -> b)
4948 The two are treated identically.
4952 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4953 explicit universal quantification in
4955 For example, all the following types are legal:
4957 f1 :: forall a b. a -> b -> a
4958 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4960 f2 :: (forall a. a->a) -> Int -> Int
4961 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4963 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4965 f4 :: Int -> (forall a. a -> a)
4967 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4968 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4969 The <literal>forall</literal> makes explicit the universal quantification that
4970 is implicitly added by Haskell.
4973 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4974 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4975 shows, the polymorphic type on the left of the function arrow can be overloaded.
4978 The function <literal>f3</literal> has a rank-3 type;
4979 it has rank-2 types on the left of a function arrow.
4982 GHC has three flags to control higher-rank types:
4985 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4988 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4991 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4992 That is, you can nest <literal>forall</literal>s
4993 arbitrarily deep in function arrows.
4994 In particular, a forall-type (also called a "type scheme"),
4995 including an operational type class context, is legal:
4997 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4998 of a function arrow </para> </listitem>
4999 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5000 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5001 field type signatures.</para> </listitem>
5002 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5003 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5007 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5008 a type variable any more!
5017 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5018 the types of the constructor arguments. Here are several examples:
5024 data T a = T1 (forall b. b -> b -> b) a
5026 data MonadT m = MkMonad { return :: forall a. a -> m a,
5027 bind :: forall a b. m a -> (a -> m b) -> m b
5030 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5036 The constructors have rank-2 types:
5042 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5043 MkMonad :: forall m. (forall a. a -> m a)
5044 -> (forall a b. m a -> (a -> m b) -> m b)
5046 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5052 Notice that you don't need to use a <literal>forall</literal> if there's an
5053 explicit context. For example in the first argument of the
5054 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5055 prefixed to the argument type. The implicit <literal>forall</literal>
5056 quantifies all type variables that are not already in scope, and are
5057 mentioned in the type quantified over.
5061 As for type signatures, implicit quantification happens for non-overloaded
5062 types too. So if you write this:
5065 data T a = MkT (Either a b) (b -> b)
5068 it's just as if you had written this:
5071 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5074 That is, since the type variable <literal>b</literal> isn't in scope, it's
5075 implicitly universally quantified. (Arguably, it would be better
5076 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5077 where that is what is wanted. Feedback welcomed.)
5081 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5082 the constructor to suitable values, just as usual. For example,
5093 a3 = MkSwizzle reverse
5096 a4 = let r x = Just x
5103 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5104 mkTs f x y = [T1 f x, T1 f y]
5110 The type of the argument can, as usual, be more general than the type
5111 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5112 does not need the <literal>Ord</literal> constraint.)
5116 When you use pattern matching, the bound variables may now have
5117 polymorphic types. For example:
5123 f :: T a -> a -> (a, Char)
5124 f (T1 w k) x = (w k x, w 'c' 'd')
5126 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5127 g (MkSwizzle s) xs f = s (map f (s xs))
5129 h :: MonadT m -> [m a] -> m [a]
5130 h m [] = return m []
5131 h m (x:xs) = bind m x $ \y ->
5132 bind m (h m xs) $ \ys ->
5139 In the function <function>h</function> we use the record selectors <literal>return</literal>
5140 and <literal>bind</literal> to extract the polymorphic bind and return functions
5141 from the <literal>MonadT</literal> data structure, rather than using pattern
5147 <title>Type inference</title>
5150 In general, type inference for arbitrary-rank types is undecidable.
5151 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5152 to get a decidable algorithm by requiring some help from the programmer.
5153 We do not yet have a formal specification of "some help" but the rule is this:
5156 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5157 provides an explicit polymorphic type for x, or GHC's type inference will assume
5158 that x's type has no foralls in it</emphasis>.
5161 What does it mean to "provide" an explicit type for x? You can do that by
5162 giving a type signature for x directly, using a pattern type signature
5163 (<xref linkend="scoped-type-variables"/>), thus:
5165 \ f :: (forall a. a->a) -> (f True, f 'c')
5167 Alternatively, you can give a type signature to the enclosing
5168 context, which GHC can "push down" to find the type for the variable:
5170 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5172 Here the type signature on the expression can be pushed inwards
5173 to give a type signature for f. Similarly, and more commonly,
5174 one can give a type signature for the function itself:
5176 h :: (forall a. a->a) -> (Bool,Char)
5177 h f = (f True, f 'c')
5179 You don't need to give a type signature if the lambda bound variable
5180 is a constructor argument. Here is an example we saw earlier:
5182 f :: T a -> a -> (a, Char)
5183 f (T1 w k) x = (w k x, w 'c' 'd')
5185 Here we do not need to give a type signature to <literal>w</literal>, because
5186 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5193 <sect3 id="implicit-quant">
5194 <title>Implicit quantification</title>
5197 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5198 user-written types, if and only if there is no explicit <literal>forall</literal>,
5199 GHC finds all the type variables mentioned in the type that are not already
5200 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5204 f :: forall a. a -> a
5211 h :: forall b. a -> b -> b
5217 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5220 f :: (a -> a) -> Int
5222 f :: forall a. (a -> a) -> Int
5224 f :: (forall a. a -> a) -> Int
5227 g :: (Ord a => a -> a) -> Int
5228 -- MEANS the illegal type
5229 g :: forall a. (Ord a => a -> a) -> Int
5231 g :: (forall a. Ord a => a -> a) -> Int
5233 The latter produces an illegal type, which you might think is silly,
5234 but at least the rule is simple. If you want the latter type, you
5235 can write your for-alls explicitly. Indeed, doing so is strongly advised
5242 <sect2 id="impredicative-polymorphism">
5243 <title>Impredicative polymorphism
5245 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5246 enabled with <option>-XImpredicativeTypes</option>.
5248 that you can call a polymorphic function at a polymorphic type, and
5249 parameterise data structures over polymorphic types. For example:
5251 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5252 f (Just g) = Just (g [3], g "hello")
5255 Notice here that the <literal>Maybe</literal> type is parameterised by the
5256 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5259 <para>The technical details of this extension are described in the paper
5260 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5261 type inference for higher-rank types and impredicativity</ulink>,
5262 which appeared at ICFP 2006.
5266 <sect2 id="scoped-type-variables">
5267 <title>Lexically scoped type variables
5271 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5272 which some type signatures are simply impossible to write. For example:
5274 f :: forall a. [a] -> [a]
5280 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
5281 the entire definition of <literal>f</literal>.
5282 In particular, it is in scope at the type signature for <varname>ys</varname>.
5283 In Haskell 98 it is not possible to declare
5284 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5285 it becomes possible to do so.
5287 <para>Lexically-scoped type variables are enabled by
5288 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5290 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5291 variables work, compared to earlier releases. Read this section
5295 <title>Overview</title>
5297 <para>The design follows the following principles
5299 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5300 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5301 design.)</para></listitem>
5302 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5303 type variables. This means that every programmer-written type signature
5304 (including one that contains free scoped type variables) denotes a
5305 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5306 checker, and no inference is involved.</para></listitem>
5307 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5308 changing the program.</para></listitem>
5312 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5314 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5315 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5316 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5317 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5321 In Haskell, a programmer-written type signature is implicitly quantified over
5322 its free type variables (<ulink
5323 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5325 of the Haskell Report).
5326 Lexically scoped type variables affect this implicit quantification rules
5327 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5328 quantified. For example, if type variable <literal>a</literal> is in scope,
5331 (e :: a -> a) means (e :: a -> a)
5332 (e :: b -> b) means (e :: forall b. b->b)
5333 (e :: a -> b) means (e :: forall b. a->b)
5341 <sect3 id="decl-type-sigs">
5342 <title>Declaration type signatures</title>
5343 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5344 quantification (using <literal>forall</literal>) brings into scope the
5345 explicitly-quantified
5346 type variables, in the definition of the named function. For example:
5348 f :: forall a. [a] -> [a]
5349 f (x:xs) = xs ++ [ x :: a ]
5351 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5352 the definition of "<literal>f</literal>".
5354 <para>This only happens if:
5356 <listitem><para> The quantification in <literal>f</literal>'s type
5357 signature is explicit. For example:
5360 g (x:xs) = xs ++ [ x :: a ]
5362 This program will be rejected, because "<literal>a</literal>" does not scope
5363 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5364 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5365 quantification rules.
5367 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5368 not a pattern binding.
5371 f1 :: forall a. [a] -> [a]
5372 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5374 f2 :: forall a. [a] -> [a]
5375 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5377 f3 :: forall a. [a] -> [a]
5378 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5380 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5381 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5382 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5383 the type signature brings <literal>a</literal> into scope.
5389 <sect3 id="exp-type-sigs">
5390 <title>Expression type signatures</title>
5392 <para>An expression type signature that has <emphasis>explicit</emphasis>
5393 quantification (using <literal>forall</literal>) brings into scope the
5394 explicitly-quantified
5395 type variables, in the annotated expression. For example:
5397 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5399 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5400 type variable <literal>s</literal> into scope, in the annotated expression
5401 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5406 <sect3 id="pattern-type-sigs">
5407 <title>Pattern type signatures</title>
5409 A type signature may occur in any pattern; this is a <emphasis>pattern type
5410 signature</emphasis>.
5413 -- f and g assume that 'a' is already in scope
5414 f = \(x::Int, y::a) -> x
5416 h ((x,y) :: (Int,Bool)) = (y,x)
5418 In the case where all the type variables in the pattern type signature are
5419 already in scope (i.e. bound by the enclosing context), matters are simple: the
5420 signature simply constrains the type of the pattern in the obvious way.
5423 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5424 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5425 that are already in scope. For example:
5427 f :: forall a. [a] -> (Int, [a])
5430 (ys::[a], n) = (reverse xs, length xs) -- OK
5431 zs::[a] = xs ++ ys -- OK
5433 Just (v::b) = ... -- Not OK; b is not in scope
5435 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5436 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5440 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5441 type signature may mention a type variable that is not in scope; in this case,
5442 <emphasis>the signature brings that type variable into scope</emphasis>.
5443 This is particularly important for existential data constructors. For example:
5445 data T = forall a. MkT [a]
5448 k (MkT [t::a]) = MkT t3
5452 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5453 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5454 because it is bound by the pattern match. GHC's rule is that in this situation
5455 (and only then), a pattern type signature can mention a type variable that is
5456 not already in scope; the effect is to bring it into scope, standing for the
5457 existentially-bound type variable.
5460 When a pattern type signature binds a type variable in this way, GHC insists that the
5461 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5462 This means that any user-written type signature always stands for a completely known type.
5465 If all this seems a little odd, we think so too. But we must have
5466 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5467 could not name existentially-bound type variables in subsequent type signatures.
5470 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5471 signature is allowed to mention a lexical variable that is not already in
5473 For example, both <literal>f</literal> and <literal>g</literal> would be
5474 illegal if <literal>a</literal> was not already in scope.
5480 <!-- ==================== Commented out part about result type signatures
5482 <sect3 id="result-type-sigs">
5483 <title>Result type signatures</title>
5486 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5489 {- f assumes that 'a' is already in scope -}
5490 f x y :: [a] = [x,y,x]
5492 g = \ x :: [Int] -> [3,4]
5494 h :: forall a. [a] -> a
5498 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5499 the result of the function. Similarly, the body of the lambda in the RHS of
5500 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5501 alternative in <literal>h</literal> is <literal>a</literal>.
5503 <para> A result type signature never brings new type variables into scope.</para>
5505 There are a couple of syntactic wrinkles. First, notice that all three
5506 examples would parse quite differently with parentheses:
5508 {- f assumes that 'a' is already in scope -}
5509 f x (y :: [a]) = [x,y,x]
5511 g = \ (x :: [Int]) -> [3,4]
5513 h :: forall a. [a] -> a
5517 Now the signature is on the <emphasis>pattern</emphasis>; and
5518 <literal>h</literal> would certainly be ill-typed (since the pattern
5519 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5521 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5522 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5523 token or a parenthesised type of some sort). To see why,
5524 consider how one would parse this:
5533 <sect3 id="cls-inst-scoped-tyvars">
5534 <title>Class and instance declarations</title>
5537 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5538 scope over the methods defined in the <literal>where</literal> part. For example:
5556 <sect2 id="typing-binds">
5557 <title>Generalised typing of mutually recursive bindings</title>
5560 The Haskell Report specifies that a group of bindings (at top level, or in a
5561 <literal>let</literal> or <literal>where</literal>) should be sorted into
5562 strongly-connected components, and then type-checked in dependency order
5563 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5564 Report, Section 4.5.1</ulink>).
5565 As each group is type-checked, any binders of the group that
5567 an explicit type signature are put in the type environment with the specified
5569 and all others are monomorphic until the group is generalised
5570 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5573 <para>Following a suggestion of Mark Jones, in his paper
5574 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5576 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5578 <emphasis>the dependency analysis ignores references to variables that have an explicit
5579 type signature</emphasis>.
5580 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5581 typecheck. For example, consider:
5583 f :: Eq a => a -> Bool
5584 f x = (x == x) || g True || g "Yes"
5586 g y = (y <= y) || f True
5588 This is rejected by Haskell 98, but under Jones's scheme the definition for
5589 <literal>g</literal> is typechecked first, separately from that for
5590 <literal>f</literal>,
5591 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5592 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5593 type is generalised, to get
5595 g :: Ord a => a -> Bool
5597 Now, the definition for <literal>f</literal> is typechecked, with this type for
5598 <literal>g</literal> in the type environment.
5602 The same refined dependency analysis also allows the type signatures of
5603 mutually-recursive functions to have different contexts, something that is illegal in
5604 Haskell 98 (Section 4.5.2, last sentence). With
5605 <option>-XRelaxedPolyRec</option>
5606 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5607 type signatures; in practice this means that only variables bound by the same
5608 pattern binding must have the same context. For example, this is fine:
5610 f :: Eq a => a -> Bool
5611 f x = (x == x) || g True
5613 g :: Ord a => a -> Bool
5614 g y = (y <= y) || f True
5620 <!-- ==================== End of type system extensions ================= -->
5622 <!-- ====================== TEMPLATE HASKELL ======================= -->
5624 <sect1 id="template-haskell">
5625 <title>Template Haskell</title>
5627 <para>Template Haskell allows you to do compile-time meta-programming in
5630 the main technical innovations is discussed in "<ulink
5631 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5632 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5635 There is a Wiki page about
5636 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5637 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5641 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5642 Haskell library reference material</ulink>
5643 (look for module <literal>Language.Haskell.TH</literal>).
5644 Many changes to the original design are described in
5645 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5646 Notes on Template Haskell version 2</ulink>.
5647 Not all of these changes are in GHC, however.
5650 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5651 as a worked example to help get you started.
5655 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5656 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5661 <title>Syntax</title>
5663 <para> Template Haskell has the following new syntactic
5664 constructions. You need to use the flag
5665 <option>-XTemplateHaskell</option>
5666 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5667 </indexterm>to switch these syntactic extensions on
5668 (<option>-XTemplateHaskell</option> is no longer implied by
5669 <option>-fglasgow-exts</option>).</para>
5673 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5674 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5675 There must be no space between the "$" and the identifier or parenthesis. This use
5676 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5677 of "." as an infix operator. If you want the infix operator, put spaces around it.
5679 <para> A splice can occur in place of
5681 <listitem><para> an expression; the spliced expression must
5682 have type <literal>Q Exp</literal></para></listitem>
5683 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5686 Inside a splice you can can only call functions defined in imported modules,
5687 not functions defined elsewhere in the same module.</listitem>
5691 A expression quotation is written in Oxford brackets, thus:
5693 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5694 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5695 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5696 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5697 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5698 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5699 </itemizedlist></para></listitem>
5702 A quasi-quotation can appear in either a pattern context or an
5703 expression context and is also written in Oxford brackets:
5705 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5706 where the "..." is an arbitrary string; a full description of the
5707 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5708 </itemizedlist></para></listitem>
5711 A name can be quoted with either one or two prefix single quotes:
5713 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5714 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5715 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5717 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5718 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5721 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5722 may also be given as an argument to the <literal>reify</literal> function.
5728 (Compared to the original paper, there are many differences of detail.
5729 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5730 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5731 Type splices are not implemented, and neither are pattern splices or quotations.
5735 <sect2> <title> Using Template Haskell </title>
5739 The data types and monadic constructor functions for Template Haskell are in the library
5740 <literal>Language.Haskell.THSyntax</literal>.
5744 You can only run a function at compile time if it is imported from another module. That is,
5745 you can't define a function in a module, and call it from within a splice in the same module.
5746 (It would make sense to do so, but it's hard to implement.)
5750 You can only run a function at compile time if it is imported
5751 from another module <emphasis>that is not part of a mutually-recursive group of modules
5752 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5753 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5754 splice is to be run.</para>
5756 For example, when compiling module A,
5757 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5758 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5762 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5765 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5766 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5767 compiles and runs a program, and then looks at the result. So it's important that
5768 the program it compiles produces results whose representations are identical to
5769 those of the compiler itself.
5773 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5774 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5779 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5780 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5781 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5788 -- Import our template "pr"
5789 import Printf ( pr )
5791 -- The splice operator $ takes the Haskell source code
5792 -- generated at compile time by "pr" and splices it into
5793 -- the argument of "putStrLn".
5794 main = putStrLn ( $(pr "Hello") )
5800 -- Skeletal printf from the paper.
5801 -- It needs to be in a separate module to the one where
5802 -- you intend to use it.
5804 -- Import some Template Haskell syntax
5805 import Language.Haskell.TH
5807 -- Describe a format string
5808 data Format = D | S | L String
5810 -- Parse a format string. This is left largely to you
5811 -- as we are here interested in building our first ever
5812 -- Template Haskell program and not in building printf.
5813 parse :: String -> [Format]
5816 -- Generate Haskell source code from a parsed representation
5817 -- of the format string. This code will be spliced into
5818 -- the module which calls "pr", at compile time.
5819 gen :: [Format] -> Q Exp
5820 gen [D] = [| \n -> show n |]
5821 gen [S] = [| \s -> s |]
5822 gen [L s] = stringE s
5824 -- Here we generate the Haskell code for the splice
5825 -- from an input format string.
5826 pr :: String -> Q Exp
5827 pr s = gen (parse s)
5830 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5833 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5836 <para>Run "main.exe" and here is your output:</para>
5846 <title>Using Template Haskell with Profiling</title>
5847 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5849 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5850 interpreter to run the splice expressions. The bytecode interpreter
5851 runs the compiled expression on top of the same runtime on which GHC
5852 itself is running; this means that the compiled code referred to by
5853 the interpreted expression must be compatible with this runtime, and
5854 in particular this means that object code that is compiled for
5855 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5856 expression, because profiled object code is only compatible with the
5857 profiling version of the runtime.</para>
5859 <para>This causes difficulties if you have a multi-module program
5860 containing Template Haskell code and you need to compile it for
5861 profiling, because GHC cannot load the profiled object code and use it
5862 when executing the splices. Fortunately GHC provides a workaround.
5863 The basic idea is to compile the program twice:</para>
5867 <para>Compile the program or library first the normal way, without
5868 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5871 <para>Then compile it again with <option>-prof</option>, and
5872 additionally use <option>-osuf
5873 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5874 to name the object files differently (you can choose any suffix
5875 that isn't the normal object suffix here). GHC will automatically
5876 load the object files built in the first step when executing splice
5877 expressions. If you omit the <option>-osuf</option> flag when
5878 building with <option>-prof</option> and Template Haskell is used,
5879 GHC will emit an error message. </para>
5884 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5885 <para>Quasi-quotation allows patterns and expressions to be written using
5886 programmer-defined concrete syntax; the motivation behind the extension and
5887 several examples are documented in
5888 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5889 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5890 2007). The example below shows how to write a quasiquoter for a simple
5891 expression language.</para>
5894 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5895 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5896 functions for quoting expressions and patterns, respectively. The first argument
5897 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5898 context of the quasi-quotation statement determines which of the two parsers is
5899 called: if the quasi-quotation occurs in an expression context, the expression
5900 parser is called, and if it occurs in a pattern context, the pattern parser is
5904 Note that in the example we make use of an antiquoted
5905 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5906 (this syntax for anti-quotation was defined by the parser's
5907 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5908 integer value argument of the constructor <literal>IntExpr</literal> when
5909 pattern matching. Please see the referenced paper for further details regarding
5910 anti-quotation as well as the description of a technique that uses SYB to
5911 leverage a single parser of type <literal>String -> a</literal> to generate both
5912 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5913 pattern parser that returns a value of type <literal>Q Pat</literal>.
5916 <para>In general, a quasi-quote has the form
5917 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5918 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5919 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5920 can be arbitrary, and may contain newlines.
5923 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5924 the example, <literal>expr</literal> cannot be defined
5925 in <literal>Main.hs</literal> where it is used, but must be imported.
5936 main = do { print $ eval [$expr|1 + 2|]
5938 { [$expr|'int:n|] -> print n
5947 import qualified Language.Haskell.TH as TH
5948 import Language.Haskell.TH.Quasi
5950 data Expr = IntExpr Integer
5951 | AntiIntExpr String
5952 | BinopExpr BinOp Expr Expr
5954 deriving(Show, Typeable, Data)
5960 deriving(Show, Typeable, Data)
5962 eval :: Expr -> Integer
5963 eval (IntExpr n) = n
5964 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5971 expr = QuasiQuoter parseExprExp parseExprPat
5973 -- Parse an Expr, returning its representation as
5974 -- either a Q Exp or a Q Pat. See the referenced paper
5975 -- for how to use SYB to do this by writing a single
5976 -- parser of type String -> Expr instead of two
5977 -- separate parsers.
5979 parseExprExp :: String -> Q Exp
5982 parseExprPat :: String -> Q Pat
5986 <para>Now run the compiler:
5989 $ ghc --make -XQuasiQuotes Main.hs -o main
5992 <para>Run "main" and here is your output:</para>
6004 <!-- ===================== Arrow notation =================== -->
6006 <sect1 id="arrow-notation">
6007 <title>Arrow notation
6010 <para>Arrows are a generalization of monads introduced by John Hughes.
6011 For more details, see
6016 “Generalising Monads to Arrows”,
6017 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6018 pp67–111, May 2000.
6019 The paper that introduced arrows: a friendly introduction, motivated with
6020 programming examples.
6026 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6027 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6028 Introduced the notation described here.
6034 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6035 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6042 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6043 John Hughes, in <citetitle>5th International Summer School on
6044 Advanced Functional Programming</citetitle>,
6045 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6047 This paper includes another introduction to the notation,
6048 with practical examples.
6054 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6055 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6056 A terse enumeration of the formal rules used
6057 (extracted from comments in the source code).
6063 The arrows web page at
6064 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6069 With the <option>-XArrows</option> flag, GHC supports the arrow
6070 notation described in the second of these papers,
6071 translating it using combinators from the
6072 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6074 What follows is a brief introduction to the notation;
6075 it won't make much sense unless you've read Hughes's paper.
6078 <para>The extension adds a new kind of expression for defining arrows:
6080 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6081 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6083 where <literal>proc</literal> is a new keyword.
6084 The variables of the pattern are bound in the body of the
6085 <literal>proc</literal>-expression,
6086 which is a new sort of thing called a <firstterm>command</firstterm>.
6087 The syntax of commands is as follows:
6089 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6090 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6091 | <replaceable>cmd</replaceable><superscript>0</superscript>
6093 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6094 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6095 infix operators as for expressions, and
6097 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6098 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6099 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6100 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6101 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6102 | <replaceable>fcmd</replaceable>
6104 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6105 | ( <replaceable>cmd</replaceable> )
6106 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6108 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6109 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6110 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6111 | <replaceable>cmd</replaceable>
6113 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6114 except that the bodies are commands instead of expressions.
6118 Commands produce values, but (like monadic computations)
6119 may yield more than one value,
6120 or none, and may do other things as well.
6121 For the most part, familiarity with monadic notation is a good guide to
6123 However the values of expressions, even monadic ones,
6124 are determined by the values of the variables they contain;
6125 this is not necessarily the case for commands.
6129 A simple example of the new notation is the expression
6131 proc x -> f -< x+1
6133 We call this a <firstterm>procedure</firstterm> or
6134 <firstterm>arrow abstraction</firstterm>.
6135 As with a lambda expression, the variable <literal>x</literal>
6136 is a new variable bound within the <literal>proc</literal>-expression.
6137 It refers to the input to the arrow.
6138 In the above example, <literal>-<</literal> is not an identifier but an
6139 new reserved symbol used for building commands from an expression of arrow
6140 type and an expression to be fed as input to that arrow.
6141 (The weird look will make more sense later.)
6142 It may be read as analogue of application for arrows.
6143 The above example is equivalent to the Haskell expression
6145 arr (\ x -> x+1) >>> f
6147 That would make no sense if the expression to the left of
6148 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6149 More generally, the expression to the left of <literal>-<</literal>
6150 may not involve any <firstterm>local variable</firstterm>,
6151 i.e. a variable bound in the current arrow abstraction.
6152 For such a situation there is a variant <literal>-<<</literal>, as in
6154 proc x -> f x -<< x+1
6156 which is equivalent to
6158 arr (\ x -> (f x, x+1)) >>> app
6160 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6162 Such an arrow is equivalent to a monad, so if you're using this form
6163 you may find a monadic formulation more convenient.
6167 <title>do-notation for commands</title>
6170 Another form of command is a form of <literal>do</literal>-notation.
6171 For example, you can write
6180 You can read this much like ordinary <literal>do</literal>-notation,
6181 but with commands in place of monadic expressions.
6182 The first line sends the value of <literal>x+1</literal> as an input to
6183 the arrow <literal>f</literal>, and matches its output against
6184 <literal>y</literal>.
6185 In the next line, the output is discarded.
6186 The arrow <function>returnA</function> is defined in the
6187 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6188 module as <literal>arr id</literal>.
6189 The above example is treated as an abbreviation for
6191 arr (\ x -> (x, x)) >>>
6192 first (arr (\ x -> x+1) >>> f) >>>
6193 arr (\ (y, x) -> (y, (x, y))) >>>
6194 first (arr (\ y -> 2*y) >>> g) >>>
6196 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6197 first (arr (\ (x, z) -> x*z) >>> h) >>>
6198 arr (\ (t, z) -> t+z) >>>
6201 Note that variables not used later in the composition are projected out.
6202 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6204 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6205 module, this reduces to
6207 arr (\ x -> (x+1, x)) >>>
6209 arr (\ (y, x) -> (2*y, (x, y))) >>>
6211 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6213 arr (\ (t, z) -> t+z)
6215 which is what you might have written by hand.
6216 With arrow notation, GHC keeps track of all those tuples of variables for you.
6220 Note that although the above translation suggests that
6221 <literal>let</literal>-bound variables like <literal>z</literal> must be
6222 monomorphic, the actual translation produces Core,
6223 so polymorphic variables are allowed.
6227 It's also possible to have mutually recursive bindings,
6228 using the new <literal>rec</literal> keyword, as in the following example:
6230 counter :: ArrowCircuit a => a Bool Int
6231 counter = proc reset -> do
6232 rec output <- returnA -< if reset then 0 else next
6233 next <- delay 0 -< output+1
6234 returnA -< output
6236 The translation of such forms uses the <function>loop</function> combinator,
6237 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6243 <title>Conditional commands</title>
6246 In the previous example, we used a conditional expression to construct the
6248 Sometimes we want to conditionally execute different commands, as in
6255 which is translated to
6257 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6258 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6260 Since the translation uses <function>|||</function>,
6261 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6265 There are also <literal>case</literal> commands, like
6271 y <- h -< (x1, x2)
6275 The syntax is the same as for <literal>case</literal> expressions,
6276 except that the bodies of the alternatives are commands rather than expressions.
6277 The translation is similar to that of <literal>if</literal> commands.
6283 <title>Defining your own control structures</title>
6286 As we're seen, arrow notation provides constructs,
6287 modelled on those for expressions,
6288 for sequencing, value recursion and conditionals.
6289 But suitable combinators,
6290 which you can define in ordinary Haskell,
6291 may also be used to build new commands out of existing ones.
6292 The basic idea is that a command defines an arrow from environments to values.
6293 These environments assign values to the free local variables of the command.
6294 Thus combinators that produce arrows from arrows
6295 may also be used to build commands from commands.
6296 For example, the <literal>ArrowChoice</literal> class includes a combinator
6298 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6300 so we can use it to build commands:
6302 expr' = proc x -> do
6305 symbol Plus -< ()
6306 y <- term -< ()
6309 symbol Minus -< ()
6310 y <- term -< ()
6313 (The <literal>do</literal> on the first line is needed to prevent the first
6314 <literal><+> ...</literal> from being interpreted as part of the
6315 expression on the previous line.)
6316 This is equivalent to
6318 expr' = (proc x -> returnA -< x)
6319 <+> (proc x -> do
6320 symbol Plus -< ()
6321 y <- term -< ()
6323 <+> (proc x -> do
6324 symbol Minus -< ()
6325 y <- term -< ()
6328 It is essential that this operator be polymorphic in <literal>e</literal>
6329 (representing the environment input to the command
6330 and thence to its subcommands)
6331 and satisfy the corresponding naturality property
6333 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6335 at least for strict <literal>k</literal>.
6336 (This should be automatic if you're not using <function>seq</function>.)
6337 This ensures that environments seen by the subcommands are environments
6338 of the whole command,
6339 and also allows the translation to safely trim these environments.
6340 The operator must also not use any variable defined within the current
6345 We could define our own operator
6347 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6348 untilA body cond = proc x ->
6349 b <- cond -< x
6350 if b then returnA -< ()
6353 untilA body cond -< x
6355 and use it in the same way.
6356 Of course this infix syntax only makes sense for binary operators;
6357 there is also a more general syntax involving special brackets:
6361 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6368 <title>Primitive constructs</title>
6371 Some operators will need to pass additional inputs to their subcommands.
6372 For example, in an arrow type supporting exceptions,
6373 the operator that attaches an exception handler will wish to pass the
6374 exception that occurred to the handler.
6375 Such an operator might have a type
6377 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6379 where <literal>Ex</literal> is the type of exceptions handled.
6380 You could then use this with arrow notation by writing a command
6382 body `handleA` \ ex -> handler
6384 so that if an exception is raised in the command <literal>body</literal>,
6385 the variable <literal>ex</literal> is bound to the value of the exception
6386 and the command <literal>handler</literal>,
6387 which typically refers to <literal>ex</literal>, is entered.
6388 Though the syntax here looks like a functional lambda,
6389 we are talking about commands, and something different is going on.
6390 The input to the arrow represented by a command consists of values for
6391 the free local variables in the command, plus a stack of anonymous values.
6392 In all the prior examples, this stack was empty.
6393 In the second argument to <function>handleA</function>,
6394 this stack consists of one value, the value of the exception.
6395 The command form of lambda merely gives this value a name.
6400 the values on the stack are paired to the right of the environment.
6401 So operators like <function>handleA</function> that pass
6402 extra inputs to their subcommands can be designed for use with the notation
6403 by pairing the values with the environment in this way.
6404 More precisely, the type of each argument of the operator (and its result)
6405 should have the form
6407 a (...(e,t1), ... tn) t
6409 where <replaceable>e</replaceable> is a polymorphic variable
6410 (representing the environment)
6411 and <replaceable>ti</replaceable> are the types of the values on the stack,
6412 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6413 The polymorphic variable <replaceable>e</replaceable> must not occur in
6414 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6415 <replaceable>t</replaceable>.
6416 However the arrows involved need not be the same.
6417 Here are some more examples of suitable operators:
6419 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6420 runReader :: ... => a e c -> a' (e,State) c
6421 runState :: ... => a e c -> a' (e,State) (c,State)
6423 We can supply the extra input required by commands built with the last two
6424 by applying them to ordinary expressions, as in
6428 (|runReader (do { ... })|) s
6430 which adds <literal>s</literal> to the stack of inputs to the command
6431 built using <function>runReader</function>.
6435 The command versions of lambda abstraction and application are analogous to
6436 the expression versions.
6437 In particular, the beta and eta rules describe equivalences of commands.
6438 These three features (operators, lambda abstraction and application)
6439 are the core of the notation; everything else can be built using them,
6440 though the results would be somewhat clumsy.
6441 For example, we could simulate <literal>do</literal>-notation by defining
6443 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6444 u `bind` f = returnA &&& u >>> f
6446 bind_ :: Arrow a => a e b -> a e c -> a e c
6447 u `bind_` f = u `bind` (arr fst >>> f)
6449 We could simulate <literal>if</literal> by defining
6451 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6452 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6459 <title>Differences with the paper</title>
6464 <para>Instead of a single form of arrow application (arrow tail) with two
6465 translations, the implementation provides two forms
6466 <quote><literal>-<</literal></quote> (first-order)
6467 and <quote><literal>-<<</literal></quote> (higher-order).
6472 <para>User-defined operators are flagged with banana brackets instead of
6473 a new <literal>form</literal> keyword.
6482 <title>Portability</title>
6485 Although only GHC implements arrow notation directly,
6486 there is also a preprocessor
6488 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6489 that translates arrow notation into Haskell 98
6490 for use with other Haskell systems.
6491 You would still want to check arrow programs with GHC;
6492 tracing type errors in the preprocessor output is not easy.
6493 Modules intended for both GHC and the preprocessor must observe some
6494 additional restrictions:
6499 The module must import
6500 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6506 The preprocessor cannot cope with other Haskell extensions.
6507 These would have to go in separate modules.
6513 Because the preprocessor targets Haskell (rather than Core),
6514 <literal>let</literal>-bound variables are monomorphic.
6525 <!-- ==================== BANG PATTERNS ================= -->
6527 <sect1 id="bang-patterns">
6528 <title>Bang patterns
6529 <indexterm><primary>Bang patterns</primary></indexterm>
6531 <para>GHC supports an extension of pattern matching called <emphasis>bang
6532 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
6534 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6535 prime feature description</ulink> contains more discussion and examples
6536 than the material below.
6539 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6542 <sect2 id="bang-patterns-informal">
6543 <title>Informal description of bang patterns
6546 The main idea is to add a single new production to the syntax of patterns:
6550 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6551 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6556 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6557 whereas without the bang it would be lazy.
6558 Bang patterns can be nested of course:
6562 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6563 <literal>y</literal>.
6564 A bang only really has an effect if it precedes a variable or wild-card pattern:
6569 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
6570 forces evaluation anyway does nothing.
6572 Bang patterns work in <literal>case</literal> expressions too, of course:
6574 g5 x = let y = f x in body
6575 g6 x = case f x of { y -> body }
6576 g7 x = case f x of { !y -> body }
6578 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6579 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6580 result, and then evaluates <literal>body</literal>.
6582 Bang patterns work in <literal>let</literal> and <literal>where</literal>
6583 definitions too. For example:
6587 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
6588 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
6589 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
6590 in a function argument <literal>![x,y]</literal> means the
6591 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
6592 is part of the syntax of <literal>let</literal> bindings.
6597 <sect2 id="bang-patterns-sem">
6598 <title>Syntax and semantics
6602 We add a single new production to the syntax of patterns:
6606 There is one problem with syntactic ambiguity. Consider:
6610 Is this a definition of the infix function "<literal>(!)</literal>",
6611 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6612 ambiguity in favour of the latter. If you want to define
6613 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6618 The semantics of Haskell pattern matching is described in <ulink
6619 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6620 Section 3.17.2</ulink> of the Haskell Report. To this description add
6621 one extra item 10, saying:
6622 <itemizedlist><listitem><para>Matching
6623 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6624 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6625 <listitem><para>otherwise, <literal>pat</literal> is matched against
6626 <literal>v</literal></para></listitem>
6628 </para></listitem></itemizedlist>
6629 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6630 Section 3.17.3</ulink>, add a new case (t):
6632 case v of { !pat -> e; _ -> e' }
6633 = v `seq` case v of { pat -> e; _ -> e' }
6636 That leaves let expressions, whose translation is given in
6637 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6639 of the Haskell Report.
6640 In the translation box, first apply
6641 the following transformation: for each pattern <literal>pi</literal> that is of
6642 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6643 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6644 have a bang at the top, apply the rules in the existing box.
6646 <para>The effect of the let rule is to force complete matching of the pattern
6647 <literal>qi</literal> before evaluation of the body is begun. The bang is
6648 retained in the translated form in case <literal>qi</literal> is a variable,
6656 The let-binding can be recursive. However, it is much more common for
6657 the let-binding to be non-recursive, in which case the following law holds:
6658 <literal>(let !p = rhs in body)</literal>
6660 <literal>(case rhs of !p -> body)</literal>
6663 A pattern with a bang at the outermost level is not allowed at the top level of
6669 <!-- ==================== ASSERTIONS ================= -->
6671 <sect1 id="assertions">
6673 <indexterm><primary>Assertions</primary></indexterm>
6677 If you want to make use of assertions in your standard Haskell code, you
6678 could define a function like the following:
6684 assert :: Bool -> a -> a
6685 assert False x = error "assertion failed!"
6692 which works, but gives you back a less than useful error message --
6693 an assertion failed, but which and where?
6697 One way out is to define an extended <function>assert</function> function which also
6698 takes a descriptive string to include in the error message and
6699 perhaps combine this with the use of a pre-processor which inserts
6700 the source location where <function>assert</function> was used.
6704 Ghc offers a helping hand here, doing all of this for you. For every
6705 use of <function>assert</function> in the user's source:
6711 kelvinToC :: Double -> Double
6712 kelvinToC k = assert (k >= 0.0) (k+273.15)
6718 Ghc will rewrite this to also include the source location where the
6725 assert pred val ==> assertError "Main.hs|15" pred val
6731 The rewrite is only performed by the compiler when it spots
6732 applications of <function>Control.Exception.assert</function>, so you
6733 can still define and use your own versions of
6734 <function>assert</function>, should you so wish. If not, import
6735 <literal>Control.Exception</literal> to make use
6736 <function>assert</function> in your code.
6740 GHC ignores assertions when optimisation is turned on with the
6741 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6742 <literal>assert pred e</literal> will be rewritten to
6743 <literal>e</literal>. You can also disable assertions using the
6744 <option>-fignore-asserts</option>
6745 option<indexterm><primary><option>-fignore-asserts</option></primary>
6746 </indexterm>.</para>
6749 Assertion failures can be caught, see the documentation for the
6750 <literal>Control.Exception</literal> library for the details.
6756 <!-- =============================== PRAGMAS =========================== -->
6758 <sect1 id="pragmas">
6759 <title>Pragmas</title>
6761 <indexterm><primary>pragma</primary></indexterm>
6763 <para>GHC supports several pragmas, or instructions to the
6764 compiler placed in the source code. Pragmas don't normally affect
6765 the meaning of the program, but they might affect the efficiency
6766 of the generated code.</para>
6768 <para>Pragmas all take the form
6770 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6772 where <replaceable>word</replaceable> indicates the type of
6773 pragma, and is followed optionally by information specific to that
6774 type of pragma. Case is ignored in
6775 <replaceable>word</replaceable>. The various values for
6776 <replaceable>word</replaceable> that GHC understands are described
6777 in the following sections; any pragma encountered with an
6778 unrecognised <replaceable>word</replaceable> is (silently)
6779 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6780 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6782 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6783 pragma must precede the <literal>module</literal> keyword in the file.
6784 There can be as many file-header pragmas as you please, and they can be
6785 preceded or followed by comments.</para>
6787 <sect2 id="language-pragma">
6788 <title>LANGUAGE pragma</title>
6790 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6791 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6793 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6795 It is the intention that all Haskell compilers support the
6796 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6797 all extensions are supported by all compilers, of
6798 course. The <literal>LANGUAGE</literal> pragma should be used instead
6799 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6801 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6803 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6805 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6807 <para>Every language extension can also be turned into a command-line flag
6808 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6809 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6812 <para>A list of all supported language extensions can be obtained by invoking
6813 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6815 <para>Any extension from the <literal>Extension</literal> type defined in
6817 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6818 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6822 <sect2 id="options-pragma">
6823 <title>OPTIONS_GHC pragma</title>
6824 <indexterm><primary>OPTIONS_GHC</primary>
6826 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6829 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6830 additional options that are given to the compiler when compiling
6831 this source file. See <xref linkend="source-file-options"/> for
6834 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6835 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6838 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6840 <sect2 id="include-pragma">
6841 <title>INCLUDE pragma</title>
6843 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6844 of C header files that should be <literal>#include</literal>'d into
6845 the C source code generated by the compiler for the current module (if
6846 compiling via C). For example:</para>
6849 {-# INCLUDE "foo.h" #-}
6850 {-# INCLUDE <stdio.h> #-}</programlisting>
6852 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6854 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6855 to the <option>-#include</option> option (<xref
6856 linkend="options-C-compiler" />), because the
6857 <literal>INCLUDE</literal> pragma is understood by other
6858 compilers. Yet another alternative is to add the include file to each
6859 <literal>foreign import</literal> declaration in your code, but we
6860 don't recommend using this approach with GHC.</para>
6863 <sect2 id="warning-deprecated-pragma">
6864 <title>WARNING and DEPRECATED pragmas</title>
6865 <indexterm><primary>WARNING</primary></indexterm>
6866 <indexterm><primary>DEPRECATED</primary></indexterm>
6868 <para>The WARNING pragma allows you to attach an arbitrary warning
6869 to a particular function, class, or type.
6870 A DEPRECATED pragma lets you specify that
6871 a particular function, class, or type is deprecated.
6872 There are two ways of using these pragmas.
6876 <para>You can work on an entire module thus:</para>
6878 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6883 module Wibble {-# WARNING "This is an unstable interface." #-} where
6886 <para>When you compile any module that import
6887 <literal>Wibble</literal>, GHC will print the specified
6892 <para>You can attach a warning to a function, class, type, or data constructor, with the
6893 following top-level declarations:</para>
6895 {-# DEPRECATED f, C, T "Don't use these" #-}
6896 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6898 <para>When you compile any module that imports and uses any
6899 of the specified entities, GHC will print the specified
6901 <para> You can only attach to entities declared at top level in the module
6902 being compiled, and you can only use unqualified names in the list of
6903 entities. A capitalised name, such as <literal>T</literal>
6904 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6905 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6906 both are in scope. If both are in scope, there is currently no way to
6907 specify one without the other (c.f. fixities
6908 <xref linkend="infix-tycons"/>).</para>
6911 Warnings and deprecations are not reported for
6912 (a) uses within the defining module, and
6913 (b) uses in an export list.
6914 The latter reduces spurious complaints within a library
6915 in which one module gathers together and re-exports
6916 the exports of several others.
6918 <para>You can suppress the warnings with the flag
6919 <option>-fno-warn-warnings-deprecations</option>.</para>
6922 <sect2 id="inline-noinline-pragma">
6923 <title>INLINE and NOINLINE pragmas</title>
6925 <para>These pragmas control the inlining of function
6928 <sect3 id="inline-pragma">
6929 <title>INLINE pragma</title>
6930 <indexterm><primary>INLINE</primary></indexterm>
6932 <para>GHC (with <option>-O</option>, as always) tries to
6933 inline (or “unfold”) functions/values that are
6934 “small enough,” thus avoiding the call overhead
6935 and possibly exposing other more-wonderful optimisations.
6936 Normally, if GHC decides a function is “too
6937 expensive” to inline, it will not do so, nor will it
6938 export that unfolding for other modules to use.</para>
6940 <para>The sledgehammer you can bring to bear is the
6941 <literal>INLINE</literal><indexterm><primary>INLINE
6942 pragma</primary></indexterm> pragma, used thusly:</para>
6945 key_function :: Int -> String -> (Bool, Double)
6946 {-# INLINE key_function #-}
6949 <para>The major effect of an <literal>INLINE</literal> pragma
6950 is to declare a function's “cost” to be very low.
6951 The normal unfolding machinery will then be very keen to
6952 inline it. However, an <literal>INLINE</literal> pragma for a
6953 function "<literal>f</literal>" has a number of other effects:
6956 No functions are inlined into <literal>f</literal>. Otherwise
6957 GHC might inline a big function into <literal>f</literal>'s right hand side,
6958 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6961 The float-in, float-out, and common-sub-expression transformations are not
6962 applied to the body of <literal>f</literal>.
6965 An INLINE function is not worker/wrappered by strictness analysis.
6966 It's going to be inlined wholesale instead.
6969 All of these effects are aimed at ensuring that what gets inlined is
6970 exactly what you asked for, no more and no less.
6972 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6973 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6974 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6975 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6976 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6977 when there is no choice even an INLINE function can be selected, in which case
6978 the INLINE pragma is ignored.
6979 For example, for a self-recursive function, the loop breaker can only be the function
6980 itself, so an INLINE pragma is always ignored.</para>
6982 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6983 function can be put anywhere its type signature could be
6986 <para><literal>INLINE</literal> pragmas are a particularly
6988 <literal>then</literal>/<literal>return</literal> (or
6989 <literal>bind</literal>/<literal>unit</literal>) functions in
6990 a monad. For example, in GHC's own
6991 <literal>UniqueSupply</literal> monad code, we have:</para>
6994 {-# INLINE thenUs #-}
6995 {-# INLINE returnUs #-}
6998 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6999 linkend="noinline-pragma"/>).</para>
7001 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7002 so if you want your code to be HBC-compatible you'll have to surround
7003 the pragma with C pre-processor directives
7004 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7008 <sect3 id="noinline-pragma">
7009 <title>NOINLINE pragma</title>
7011 <indexterm><primary>NOINLINE</primary></indexterm>
7012 <indexterm><primary>NOTINLINE</primary></indexterm>
7014 <para>The <literal>NOINLINE</literal> pragma does exactly what
7015 you'd expect: it stops the named function from being inlined
7016 by the compiler. You shouldn't ever need to do this, unless
7017 you're very cautious about code size.</para>
7019 <para><literal>NOTINLINE</literal> is a synonym for
7020 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7021 specified by Haskell 98 as the standard way to disable
7022 inlining, so it should be used if you want your code to be
7026 <sect3 id="phase-control">
7027 <title>Phase control</title>
7029 <para> Sometimes you want to control exactly when in GHC's
7030 pipeline the INLINE pragma is switched on. Inlining happens
7031 only during runs of the <emphasis>simplifier</emphasis>. Each
7032 run of the simplifier has a different <emphasis>phase
7033 number</emphasis>; the phase number decreases towards zero.
7034 If you use <option>-dverbose-core2core</option> you'll see the
7035 sequence of phase numbers for successive runs of the
7036 simplifier. In an INLINE pragma you can optionally specify a
7040 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7041 <literal>f</literal>
7042 until phase <literal>k</literal>, but from phase
7043 <literal>k</literal> onwards be very keen to inline it.
7046 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7047 <literal>f</literal>
7048 until phase <literal>k</literal>, but from phase
7049 <literal>k</literal> onwards do not inline it.
7052 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7053 <literal>f</literal>
7054 until phase <literal>k</literal>, but from phase
7055 <literal>k</literal> onwards be willing to inline it (as if
7056 there was no pragma).
7059 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7060 <literal>f</literal>
7061 until phase <literal>k</literal>, but from phase
7062 <literal>k</literal> onwards do not inline it.
7065 The same information is summarised here:
7067 -- Before phase 2 Phase 2 and later
7068 {-# INLINE [2] f #-} -- No Yes
7069 {-# INLINE [~2] f #-} -- Yes No
7070 {-# NOINLINE [2] f #-} -- No Maybe
7071 {-# NOINLINE [~2] f #-} -- Maybe No
7073 {-# INLINE f #-} -- Yes Yes
7074 {-# NOINLINE f #-} -- No No
7076 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7077 function body is small, or it is applied to interesting-looking arguments etc).
7078 Another way to understand the semantics is this:
7080 <listitem><para>For both INLINE and NOINLINE, the phase number says
7081 when inlining is allowed at all.</para></listitem>
7082 <listitem><para>The INLINE pragma has the additional effect of making the
7083 function body look small, so that when inlining is allowed it is very likely to
7088 <para>The same phase-numbering control is available for RULES
7089 (<xref linkend="rewrite-rules"/>).</para>
7093 <sect2 id="line-pragma">
7094 <title>LINE pragma</title>
7096 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7097 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7098 <para>This pragma is similar to C's <literal>#line</literal>
7099 pragma, and is mainly for use in automatically generated Haskell
7100 code. It lets you specify the line number and filename of the
7101 original code; for example</para>
7103 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7105 <para>if you'd generated the current file from something called
7106 <filename>Foo.vhs</filename> and this line corresponds to line
7107 42 in the original. GHC will adjust its error messages to refer
7108 to the line/file named in the <literal>LINE</literal>
7113 <title>RULES pragma</title>
7115 <para>The RULES pragma lets you specify rewrite rules. It is
7116 described in <xref linkend="rewrite-rules"/>.</para>
7119 <sect2 id="specialize-pragma">
7120 <title>SPECIALIZE pragma</title>
7122 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7123 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7124 <indexterm><primary>overloading, death to</primary></indexterm>
7126 <para>(UK spelling also accepted.) For key overloaded
7127 functions, you can create extra versions (NB: more code space)
7128 specialised to particular types. Thus, if you have an
7129 overloaded function:</para>
7132 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7135 <para>If it is heavily used on lists with
7136 <literal>Widget</literal> keys, you could specialise it as
7140 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7143 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7144 be put anywhere its type signature could be put.</para>
7146 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7147 (a) a specialised version of the function and (b) a rewrite rule
7148 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7149 un-specialised function into a call to the specialised one.</para>
7151 <para>The type in a SPECIALIZE pragma can be any type that is less
7152 polymorphic than the type of the original function. In concrete terms,
7153 if the original function is <literal>f</literal> then the pragma
7155 {-# SPECIALIZE f :: <type> #-}
7157 is valid if and only if the definition
7159 f_spec :: <type>
7162 is valid. Here are some examples (where we only give the type signature
7163 for the original function, not its code):
7165 f :: Eq a => a -> b -> b
7166 {-# SPECIALISE f :: Int -> b -> b #-}
7168 g :: (Eq a, Ix b) => a -> b -> b
7169 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7171 h :: Eq a => a -> a -> a
7172 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7174 The last of these examples will generate a
7175 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7176 well. If you use this kind of specialisation, let us know how well it works.
7179 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7180 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7181 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7182 The <literal>INLINE</literal> pragma affects the specialised version of the
7183 function (only), and applies even if the function is recursive. The motivating
7186 -- A GADT for arrays with type-indexed representation
7188 ArrInt :: !Int -> ByteArray# -> Arr Int
7189 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7191 (!:) :: Arr e -> Int -> e
7192 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7193 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7194 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7195 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7197 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7198 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7199 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7200 the specialised function will be inlined. It has two calls to
7201 <literal>(!:)</literal>,
7202 both at type <literal>Int</literal>. Both these calls fire the first
7203 specialisation, whose body is also inlined. The result is a type-based
7204 unrolling of the indexing function.</para>
7205 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7206 on an ordinarily-recursive function.</para>
7208 <para>Note: In earlier versions of GHC, it was possible to provide your own
7209 specialised function for a given type:
7212 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7215 This feature has been removed, as it is now subsumed by the
7216 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7220 <sect2 id="specialize-instance-pragma">
7221 <title>SPECIALIZE instance pragma
7225 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7226 <indexterm><primary>overloading, death to</primary></indexterm>
7227 Same idea, except for instance declarations. For example:
7230 instance (Eq a) => Eq (Foo a) where {
7231 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7235 The pragma must occur inside the <literal>where</literal> part
7236 of the instance declaration.
7239 Compatible with HBC, by the way, except perhaps in the placement
7245 <sect2 id="unpack-pragma">
7246 <title>UNPACK pragma</title>
7248 <indexterm><primary>UNPACK</primary></indexterm>
7250 <para>The <literal>UNPACK</literal> indicates to the compiler
7251 that it should unpack the contents of a constructor field into
7252 the constructor itself, removing a level of indirection. For
7256 data T = T {-# UNPACK #-} !Float
7257 {-# UNPACK #-} !Float
7260 <para>will create a constructor <literal>T</literal> containing
7261 two unboxed floats. This may not always be an optimisation: if
7262 the <function>T</function> constructor is scrutinised and the
7263 floats passed to a non-strict function for example, they will
7264 have to be reboxed (this is done automatically by the
7267 <para>Unpacking constructor fields should only be used in
7268 conjunction with <option>-O</option>, in order to expose
7269 unfoldings to the compiler so the reboxing can be removed as
7270 often as possible. For example:</para>
7274 f (T f1 f2) = f1 + f2
7277 <para>The compiler will avoid reboxing <function>f1</function>
7278 and <function>f2</function> by inlining <function>+</function>
7279 on floats, but only when <option>-O</option> is on.</para>
7281 <para>Any single-constructor data is eligible for unpacking; for
7285 data T = T {-# UNPACK #-} !(Int,Int)
7288 <para>will store the two <literal>Int</literal>s directly in the
7289 <function>T</function> constructor, by flattening the pair.
7290 Multi-level unpacking is also supported:
7293 data T = T {-# UNPACK #-} !S
7294 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7297 will store two unboxed <literal>Int#</literal>s
7298 directly in the <function>T</function> constructor. The
7299 unpacker can see through newtypes, too.</para>
7301 <para>If a field cannot be unpacked, you will not get a warning,
7302 so it might be an idea to check the generated code with
7303 <option>-ddump-simpl</option>.</para>
7305 <para>See also the <option>-funbox-strict-fields</option> flag,
7306 which essentially has the effect of adding
7307 <literal>{-# UNPACK #-}</literal> to every strict
7308 constructor field.</para>
7311 <sect2 id="source-pragma">
7312 <title>SOURCE pragma</title>
7314 <indexterm><primary>SOURCE</primary></indexterm>
7315 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7316 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7322 <!-- ======================= REWRITE RULES ======================== -->
7324 <sect1 id="rewrite-rules">
7325 <title>Rewrite rules
7327 <indexterm><primary>RULES pragma</primary></indexterm>
7328 <indexterm><primary>pragma, RULES</primary></indexterm>
7329 <indexterm><primary>rewrite rules</primary></indexterm></title>
7332 The programmer can specify rewrite rules as part of the source program
7338 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7343 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7344 If you need more information, then <option>-ddump-rule-firings</option> shows you
7345 each individual rule firing in detail.
7349 <title>Syntax</title>
7352 From a syntactic point of view:
7358 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7359 may be generated by the layout rule).
7365 The layout rule applies in a pragma.
7366 Currently no new indentation level
7367 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7368 you must lay out the starting in the same column as the enclosing definitions.
7371 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7372 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7375 Furthermore, the closing <literal>#-}</literal>
7376 should start in a column to the right of the opening <literal>{-#</literal>.
7382 Each rule has a name, enclosed in double quotes. The name itself has
7383 no significance at all. It is only used when reporting how many times the rule fired.
7389 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7390 immediately after the name of the rule. Thus:
7393 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7396 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7397 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7406 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7407 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7408 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7409 by spaces, just like in a type <literal>forall</literal>.
7415 A pattern variable may optionally have a type signature.
7416 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7417 For example, here is the <literal>foldr/build</literal> rule:
7420 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7421 foldr k z (build g) = g k z
7424 Since <function>g</function> has a polymorphic type, it must have a type signature.
7431 The left hand side of a rule must consist of a top-level variable applied
7432 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7435 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7436 "wrong2" forall f. f True = True
7439 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7446 A rule does not need to be in the same module as (any of) the
7447 variables it mentions, though of course they need to be in scope.
7453 All rules are implicitly exported from the module, and are therefore
7454 in force in any module that imports the module that defined the rule, directly
7455 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7456 in force when compiling A.) The situation is very similar to that for instance
7464 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7465 any other flag settings. Furthermore, inside a RULE, the language extension
7466 <option>-XScopedTypeVariables</option> is automatically enabled; see
7467 <xref linkend="scoped-type-variables"/>.
7473 Like other pragmas, RULE pragmas are always checked for scope errors, and
7474 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7475 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7476 if the <option>-fenable-rewrite-rules</option> flag is
7477 on (see <xref linkend="rule-semantics"/>).
7486 <sect2 id="rule-semantics">
7487 <title>Semantics</title>
7490 From a semantic point of view:
7495 Rules are enabled (that is, used during optimisation)
7496 by the <option>-fenable-rewrite-rules</option> flag.
7497 This flag is implied by <option>-O</option>, and may be switched
7498 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7499 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7500 may not do what you expect, though, because without <option>-O</option> GHC
7501 ignores all optimisation information in interface files;
7502 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7503 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7504 has no effect on parsing or typechecking.
7510 Rules are regarded as left-to-right rewrite rules.
7511 When GHC finds an expression that is a substitution instance of the LHS
7512 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7513 By "a substitution instance" we mean that the LHS can be made equal to the
7514 expression by substituting for the pattern variables.
7521 GHC makes absolutely no attempt to verify that the LHS and RHS
7522 of a rule have the same meaning. That is undecidable in general, and
7523 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7530 GHC makes no attempt to make sure that the rules are confluent or
7531 terminating. For example:
7534 "loop" forall x y. f x y = f y x
7537 This rule will cause the compiler to go into an infinite loop.
7544 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7550 GHC currently uses a very simple, syntactic, matching algorithm
7551 for matching a rule LHS with an expression. It seeks a substitution
7552 which makes the LHS and expression syntactically equal modulo alpha
7553 conversion. The pattern (rule), but not the expression, is eta-expanded if
7554 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7555 But not beta conversion (that's called higher-order matching).
7559 Matching is carried out on GHC's intermediate language, which includes
7560 type abstractions and applications. So a rule only matches if the
7561 types match too. See <xref linkend="rule-spec"/> below.
7567 GHC keeps trying to apply the rules as it optimises the program.
7568 For example, consider:
7577 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7578 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7579 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7580 not be substituted, and the rule would not fire.
7587 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7588 results. Consider this (artificial) example
7591 {-# RULES "f" f True = False #-}
7597 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7602 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7604 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7605 would have been a better chance that <literal>f</literal>'s RULE might fire.
7608 The way to get predictable behaviour is to use a NOINLINE
7609 pragma on <literal>f</literal>, to ensure
7610 that it is not inlined until its RULEs have had a chance to fire.
7620 <title>List fusion</title>
7623 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7624 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7625 intermediate list should be eliminated entirely.
7629 The following are good producers:
7641 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7647 Explicit lists (e.g. <literal>[True, False]</literal>)
7653 The cons constructor (e.g <literal>3:4:[]</literal>)
7659 <function>++</function>
7665 <function>map</function>
7671 <function>take</function>, <function>filter</function>
7677 <function>iterate</function>, <function>repeat</function>
7683 <function>zip</function>, <function>zipWith</function>
7692 The following are good consumers:
7704 <function>array</function> (on its second argument)
7710 <function>++</function> (on its first argument)
7716 <function>foldr</function>
7722 <function>map</function>
7728 <function>take</function>, <function>filter</function>
7734 <function>concat</function>
7740 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7746 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7747 will fuse with one but not the other)
7753 <function>partition</function>
7759 <function>head</function>
7765 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7771 <function>sequence_</function>
7777 <function>msum</function>
7783 <function>sortBy</function>
7792 So, for example, the following should generate no intermediate lists:
7795 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7801 This list could readily be extended; if there are Prelude functions that you use
7802 a lot which are not included, please tell us.
7806 If you want to write your own good consumers or producers, look at the
7807 Prelude definitions of the above functions to see how to do so.
7812 <sect2 id="rule-spec">
7813 <title>Specialisation
7817 Rewrite rules can be used to get the same effect as a feature
7818 present in earlier versions of GHC.
7819 For example, suppose that:
7822 genericLookup :: Ord a => Table a b -> a -> b
7823 intLookup :: Table Int b -> Int -> b
7826 where <function>intLookup</function> is an implementation of
7827 <function>genericLookup</function> that works very fast for
7828 keys of type <literal>Int</literal>. You might wish
7829 to tell GHC to use <function>intLookup</function> instead of
7830 <function>genericLookup</function> whenever the latter was called with
7831 type <literal>Table Int b -> Int -> b</literal>.
7832 It used to be possible to write
7835 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7838 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7841 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7844 This slightly odd-looking rule instructs GHC to replace
7845 <function>genericLookup</function> by <function>intLookup</function>
7846 <emphasis>whenever the types match</emphasis>.
7847 What is more, this rule does not need to be in the same
7848 file as <function>genericLookup</function>, unlike the
7849 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7850 have an original definition available to specialise).
7853 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7854 <function>intLookup</function> really behaves as a specialised version
7855 of <function>genericLookup</function>!!!</para>
7857 <para>An example in which using <literal>RULES</literal> for
7858 specialisation will Win Big:
7861 toDouble :: Real a => a -> Double
7862 toDouble = fromRational . toRational
7864 {-# RULES "toDouble/Int" toDouble = i2d #-}
7865 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7868 The <function>i2d</function> function is virtually one machine
7869 instruction; the default conversion—via an intermediate
7870 <literal>Rational</literal>—is obscenely expensive by
7877 <title>Controlling what's going on</title>
7885 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7891 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7892 If you add <option>-dppr-debug</option> you get a more detailed listing.
7898 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7901 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7902 {-# INLINE build #-}
7906 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7907 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7908 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7909 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7916 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7917 see how to write rules that will do fusion and yet give an efficient
7918 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7928 <sect2 id="core-pragma">
7929 <title>CORE pragma</title>
7931 <indexterm><primary>CORE pragma</primary></indexterm>
7932 <indexterm><primary>pragma, CORE</primary></indexterm>
7933 <indexterm><primary>core, annotation</primary></indexterm>
7936 The external core format supports <quote>Note</quote> annotations;
7937 the <literal>CORE</literal> pragma gives a way to specify what these
7938 should be in your Haskell source code. Syntactically, core
7939 annotations are attached to expressions and take a Haskell string
7940 literal as an argument. The following function definition shows an
7944 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7947 Semantically, this is equivalent to:
7955 However, when external core is generated (via
7956 <option>-fext-core</option>), there will be Notes attached to the
7957 expressions <function>show</function> and <varname>x</varname>.
7958 The core function declaration for <function>f</function> is:
7962 f :: %forall a . GHCziShow.ZCTShow a ->
7963 a -> GHCziBase.ZMZN GHCziBase.Char =
7964 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7966 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7968 (tpl1::GHCziBase.Int ->
7970 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7972 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7973 (tpl3::GHCziBase.ZMZN a ->
7974 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7982 Here, we can see that the function <function>show</function> (which
7983 has been expanded out to a case expression over the Show dictionary)
7984 has a <literal>%note</literal> attached to it, as does the
7985 expression <varname>eta</varname> (which used to be called
7986 <varname>x</varname>).
7993 <sect1 id="special-ids">
7994 <title>Special built-in functions</title>
7995 <para>GHC has a few built-in functions with special behaviour. These
7996 are now described in the module <ulink
7997 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7998 in the library documentation.</para>
8002 <sect1 id="generic-classes">
8003 <title>Generic classes</title>
8006 The ideas behind this extension are described in detail in "Derivable type classes",
8007 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8008 An example will give the idea:
8016 fromBin :: [Int] -> (a, [Int])
8018 toBin {| Unit |} Unit = []
8019 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8020 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8021 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8023 fromBin {| Unit |} bs = (Unit, bs)
8024 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8025 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8026 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8027 (y,bs'') = fromBin bs'
8030 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8031 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8032 which are defined thus in the library module <literal>Generics</literal>:
8036 data a :+: b = Inl a | Inr b
8037 data a :*: b = a :*: b
8040 Now you can make a data type into an instance of Bin like this:
8042 instance (Bin a, Bin b) => Bin (a,b)
8043 instance Bin a => Bin [a]
8045 That is, just leave off the "where" clause. Of course, you can put in the
8046 where clause and over-ride whichever methods you please.
8050 <title> Using generics </title>
8051 <para>To use generics you need to</para>
8054 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8055 <option>-XGenerics</option> (to generate extra per-data-type code),
8056 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8060 <para>Import the module <literal>Generics</literal> from the
8061 <literal>lang</literal> package. This import brings into
8062 scope the data types <literal>Unit</literal>,
8063 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8064 don't need this import if you don't mention these types
8065 explicitly; for example, if you are simply giving instance
8066 declarations.)</para>
8071 <sect2> <title> Changes wrt the paper </title>
8073 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8074 can be written infix (indeed, you can now use
8075 any operator starting in a colon as an infix type constructor). Also note that
8076 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8077 Finally, note that the syntax of the type patterns in the class declaration
8078 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8079 alone would ambiguous when they appear on right hand sides (an extension we
8080 anticipate wanting).
8084 <sect2> <title>Terminology and restrictions</title>
8086 Terminology. A "generic default method" in a class declaration
8087 is one that is defined using type patterns as above.
8088 A "polymorphic default method" is a default method defined as in Haskell 98.
8089 A "generic class declaration" is a class declaration with at least one
8090 generic default method.
8098 Alas, we do not yet implement the stuff about constructor names and
8105 A generic class can have only one parameter; you can't have a generic
8106 multi-parameter class.
8112 A default method must be defined entirely using type patterns, or entirely
8113 without. So this is illegal:
8116 op :: a -> (a, Bool)
8117 op {| Unit |} Unit = (Unit, True)
8120 However it is perfectly OK for some methods of a generic class to have
8121 generic default methods and others to have polymorphic default methods.
8127 The type variable(s) in the type pattern for a generic method declaration
8128 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:
8132 op {| p :*: q |} (x :*: y) = op (x :: p)
8140 The type patterns in a generic default method must take one of the forms:
8146 where "a" and "b" are type variables. Furthermore, all the type patterns for
8147 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8148 must use the same type variables. So this is illegal:
8152 op {| a :+: b |} (Inl x) = True
8153 op {| p :+: q |} (Inr y) = False
8155 The type patterns must be identical, even in equations for different methods of the class.
8156 So this too is illegal:
8160 op1 {| a :*: b |} (x :*: y) = True
8163 op2 {| p :*: q |} (x :*: y) = False
8165 (The reason for this restriction is that we gather all the equations for a particular type constructor
8166 into a single generic instance declaration.)
8172 A generic method declaration must give a case for each of the three type constructors.
8178 The type for a generic method can be built only from:
8180 <listitem> <para> Function arrows </para> </listitem>
8181 <listitem> <para> Type variables </para> </listitem>
8182 <listitem> <para> Tuples </para> </listitem>
8183 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8185 Here are some example type signatures for generic methods:
8188 op2 :: Bool -> (a,Bool)
8189 op3 :: [Int] -> a -> a
8192 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8196 This restriction is an implementation restriction: we just haven't got around to
8197 implementing the necessary bidirectional maps over arbitrary type constructors.
8198 It would be relatively easy to add specific type constructors, such as Maybe and list,
8199 to the ones that are allowed.</para>
8204 In an instance declaration for a generic class, the idea is that the compiler
8205 will fill in the methods for you, based on the generic templates. However it can only
8210 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8215 No constructor of the instance type has unboxed fields.
8219 (Of course, these things can only arise if you are already using GHC extensions.)
8220 However, you can still give an instance declarations for types which break these rules,
8221 provided you give explicit code to override any generic default methods.
8229 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8230 what the compiler does with generic declarations.
8235 <sect2> <title> Another example </title>
8237 Just to finish with, here's another example I rather like:
8241 nCons {| Unit |} _ = 1
8242 nCons {| a :*: b |} _ = 1
8243 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8246 tag {| Unit |} _ = 1
8247 tag {| a :*: b |} _ = 1
8248 tag {| a :+: b |} (Inl x) = tag x
8249 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8255 <sect1 id="monomorphism">
8256 <title>Control over monomorphism</title>
8258 <para>GHC supports two flags that control the way in which generalisation is
8259 carried out at let and where bindings.
8263 <title>Switching off the dreaded Monomorphism Restriction</title>
8264 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8266 <para>Haskell's monomorphism restriction (see
8267 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8269 of the Haskell Report)
8270 can be completely switched off by
8271 <option>-XNoMonomorphismRestriction</option>.
8276 <title>Monomorphic pattern bindings</title>
8277 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8278 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8280 <para> As an experimental change, we are exploring the possibility of
8281 making pattern bindings monomorphic; that is, not generalised at all.
8282 A pattern binding is a binding whose LHS has no function arguments,
8283 and is not a simple variable. For example:
8285 f x = x -- Not a pattern binding
8286 f = \x -> x -- Not a pattern binding
8287 f :: Int -> Int = \x -> x -- Not a pattern binding
8289 (g,h) = e -- A pattern binding
8290 (f) = e -- A pattern binding
8291 [x] = e -- A pattern binding
8293 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8294 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8303 ;;; Local Variables: ***
8305 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8306 ;;; ispell-local-dictionary: "british" ***
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