1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>The flag <option>-fglasgow-exts</option>
56 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
57 is equivalent to enabling the following extensions:
58 <option>-XPrintExplicitForalls</option>,
59 <option>-XForeignFunctionInterface</option>,
60 <option>-XUnliftedFFITypes</option>,
61 <option>-XGADTs</option>,
62 <option>-XImplicitParams</option>,
63 <option>-XScopedTypeVariables</option>,
64 <option>-XUnboxedTuples</option>,
65 <option>-XTypeSynonymInstances</option>,
66 <option>-XStandaloneDeriving</option>,
67 <option>-XDeriveDataTypeable</option>,
68 <option>-XFlexibleContexts</option>,
69 <option>-XFlexibleInstances</option>,
70 <option>-XConstrainedClassMethods</option>,
71 <option>-XMultiParamTypeClasses</option>,
72 <option>-XFunctionalDependencies</option>,
73 <option>-XMagicHash</option>,
74 <option>-XPolymorphicComponents</option>,
75 <option>-XExistentialQuantification</option>,
76 <option>-XUnicodeSyntax</option>,
77 <option>-XPostfixOperators</option>,
78 <option>-XPatternGuards</option>,
79 <option>-XLiberalTypeSynonyms</option>,
80 <option>-XRankNTypes</option>,
81 <option>-XImpredicativeTypes</option>,
82 <option>-XTypeOperators</option>,
83 <option>-XRecursiveDo</option>,
84 <option>-XParallelListComp</option>,
85 <option>-XEmptyDataDecls</option>,
86 <option>-XKindSignatures</option>,
87 <option>-XGeneralizedNewtypeDeriving</option>,
88 <option>-XTypeFamilies</option>.
89 Enabling these options is the <emphasis>only</emphasis>
90 effect of <option>-fglasgow-exts</option>.
91 We are trying to move away from this portmanteau flag,
92 and towards enabling features individually.</para>
96 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
97 <sect1 id="primitives">
98 <title>Unboxed types and primitive operations</title>
100 <para>GHC is built on a raft of primitive data types and operations;
101 "primitive" in the sense that they cannot be defined in Haskell itself.
102 While you really can use this stuff to write fast code,
103 we generally find it a lot less painful, and more satisfying in the
104 long run, to use higher-level language features and libraries. With
105 any luck, the code you write will be optimised to the efficient
106 unboxed version in any case. And if it isn't, we'd like to know
109 <para>All these primitive data types and operations are exported by the
110 library <literal>GHC.Prim</literal>, for which there is
111 <ulink url="../libraries/base/GHC.Prim.html">detailed online documentation</ulink>.
112 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
115 If you want to mention any of the primitive data types or operations in your
116 program, you must first import <literal>GHC.Prim</literal> to bring them
117 into scope. Many of them have names ending in "#", and to mention such
118 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
121 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
122 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
123 we briefly summarise here. </para>
125 <sect2 id="glasgow-unboxed">
130 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
133 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
134 that values of that type are represented by a pointer to a heap
135 object. The representation of a Haskell <literal>Int</literal>, for
136 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
137 type, however, is represented by the value itself, no pointers or heap
138 allocation are involved.
142 Unboxed types correspond to the “raw machine” types you
143 would use in C: <literal>Int#</literal> (long int),
144 <literal>Double#</literal> (double), <literal>Addr#</literal>
145 (void *), etc. The <emphasis>primitive operations</emphasis>
146 (PrimOps) on these types are what you might expect; e.g.,
147 <literal>(+#)</literal> is addition on
148 <literal>Int#</literal>s, and is the machine-addition that we all
149 know and love—usually one instruction.
153 Primitive (unboxed) types cannot be defined in Haskell, and are
154 therefore built into the language and compiler. Primitive types are
155 always unlifted; that is, a value of a primitive type cannot be
156 bottom. We use the convention (but it is only a convention)
157 that primitive types, values, and
158 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
159 For some primitive types we have special syntax for literals, also
160 described in the <link linkend="magic-hash">same section</link>.
164 Primitive values are often represented by a simple bit-pattern, such
165 as <literal>Int#</literal>, <literal>Float#</literal>,
166 <literal>Double#</literal>. But this is not necessarily the case:
167 a primitive value might be represented by a pointer to a
168 heap-allocated object. Examples include
169 <literal>Array#</literal>, the type of primitive arrays. A
170 primitive array is heap-allocated because it is too big a value to fit
171 in a register, and would be too expensive to copy around; in a sense,
172 it is accidental that it is represented by a pointer. If a pointer
173 represents a primitive value, then it really does point to that value:
174 no unevaluated thunks, no indirections…nothing can be at the
175 other end of the pointer than the primitive value.
176 A numerically-intensive program using unboxed types can
177 go a <emphasis>lot</emphasis> faster than its “standard”
178 counterpart—we saw a threefold speedup on one example.
182 There are some restrictions on the use of primitive types:
184 <listitem><para>The main restriction
185 is that you can't pass a primitive value to a polymorphic
186 function or store one in a polymorphic data type. This rules out
187 things like <literal>[Int#]</literal> (i.e. lists of primitive
188 integers). The reason for this restriction is that polymorphic
189 arguments and constructor fields are assumed to be pointers: if an
190 unboxed integer is stored in one of these, the garbage collector would
191 attempt to follow it, leading to unpredictable space leaks. Or a
192 <function>seq</function> operation on the polymorphic component may
193 attempt to dereference the pointer, with disastrous results. Even
194 worse, the unboxed value might be larger than a pointer
195 (<literal>Double#</literal> for instance).
198 <listitem><para> You cannot define a newtype whose representation type
199 (the argument type of the data constructor) is an unboxed type. Thus,
205 <listitem><para> You cannot bind a variable with an unboxed type
206 in a <emphasis>top-level</emphasis> binding.
208 <listitem><para> You cannot bind a variable with an unboxed type
209 in a <emphasis>recursive</emphasis> binding.
211 <listitem><para> You may bind unboxed variables in a (non-recursive,
212 non-top-level) pattern binding, but any such variable causes the entire
214 to become strict. For example:
216 data Foo = Foo Int Int#
218 f x = let (Foo a b, w) = ..rhs.. in ..body..
220 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
222 is strict, and the program behaves as if you had written
224 data Foo = Foo Int Int#
226 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
235 <sect2 id="unboxed-tuples">
236 <title>Unboxed Tuples
240 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
241 they're available by default with <option>-fglasgow-exts</option>. An
242 unboxed tuple looks like this:
254 where <literal>e_1..e_n</literal> are expressions of any
255 type (primitive or non-primitive). The type of an unboxed tuple looks
260 Unboxed tuples are used for functions that need to return multiple
261 values, but they avoid the heap allocation normally associated with
262 using fully-fledged tuples. When an unboxed tuple is returned, the
263 components are put directly into registers or on the stack; the
264 unboxed tuple itself does not have a composite representation. Many
265 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
267 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
268 tuples to avoid unnecessary allocation during sequences of operations.
272 There are some pretty stringent restrictions on the use of unboxed tuples:
277 Values of unboxed tuple types are subject to the same restrictions as
278 other unboxed types; i.e. they may not be stored in polymorphic data
279 structures or passed to polymorphic functions.
286 No variable can have an unboxed tuple type, nor may a constructor or function
287 argument have an unboxed tuple type. The following are all illegal:
291 data Foo = Foo (# Int, Int #)
293 f :: (# Int, Int #) -> (# Int, Int #)
296 g :: (# Int, Int #) -> Int
299 h x = let y = (# x,x #) in ...
306 The typical use of unboxed tuples is simply to return multiple values,
307 binding those multiple results with a <literal>case</literal> expression, thus:
309 f x y = (# x+1, y-1 #)
310 g x = case f x x of { (# a, b #) -> a + b }
312 You can have an unboxed tuple in a pattern binding, thus
314 f x = let (# p,q #) = h x in ..body..
316 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
317 the resulting binding is lazy like any other Haskell pattern binding. The
318 above example desugars like this:
320 f x = let t = case h x o f{ (# p,q #) -> (p,q)
325 Indeed, the bindings can even be recursive.
332 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
334 <sect1 id="syntax-extns">
335 <title>Syntactic extensions</title>
337 <sect2 id="magic-hash">
338 <title>The magic hash</title>
339 <para>The language extension <option>-XMagicHash</option> allows "#" as a
340 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
341 a valid type constructor or data constructor.</para>
343 <para>The hash sign does not change sematics at all. We tend to use variable
344 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
345 but there is no requirement to do so; they are just plain ordinary variables.
346 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
347 For example, to bring <literal>Int#</literal> into scope you must
348 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
349 the <option>-XMagicHash</option> extension
350 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
351 that is now in scope.</para>
352 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
354 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
355 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
356 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
357 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
358 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
359 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
360 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
361 is a <literal>Word#</literal>. </para> </listitem>
362 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
363 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
368 <sect2 id="new-qualified-operators">
369 <title>New qualified operator syntax</title>
371 <para>A new syntax for referencing qualified operators is
372 planned to be introduced by Haskell', and is enabled in GHC
374 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
375 option. In the new syntax, the prefix form of a qualified
377 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
378 (in Haskell 98 this would
379 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
380 and the infix form is
381 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
382 (in Haskell 98 this would
383 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
386 add x y = Prelude.(+) x y
387 subtract y = (`Prelude.(-)` y)
389 The new form of qualified operators is intended to regularise
390 the syntax by eliminating odd cases
391 like <literal>Prelude..</literal>. For example,
392 when <literal>NewQualifiedOperators</literal> is on, it is possible to
393 write the enerated sequence <literal>[Monday..]</literal>
394 without spaces, whereas in Haskell 98 this would be a
395 reference to the operator ‘<literal>.</literal>‘
396 from module <literal>Monday</literal>.</para>
398 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
399 98 syntax for qualified operators is not accepted, so this
400 option may cause existing Haskell 98 code to break.</para>
405 <!-- ====================== HIERARCHICAL MODULES ======================= -->
408 <sect2 id="hierarchical-modules">
409 <title>Hierarchical Modules</title>
411 <para>GHC supports a small extension to the syntax of module
412 names: a module name is allowed to contain a dot
413 <literal>‘.’</literal>. This is also known as the
414 “hierarchical module namespace” extension, because
415 it extends the normally flat Haskell module namespace into a
416 more flexible hierarchy of modules.</para>
418 <para>This extension has very little impact on the language
419 itself; modules names are <emphasis>always</emphasis> fully
420 qualified, so you can just think of the fully qualified module
421 name as <quote>the module name</quote>. In particular, this
422 means that the full module name must be given after the
423 <literal>module</literal> keyword at the beginning of the
424 module; for example, the module <literal>A.B.C</literal> must
427 <programlisting>module A.B.C</programlisting>
430 <para>It is a common strategy to use the <literal>as</literal>
431 keyword to save some typing when using qualified names with
432 hierarchical modules. For example:</para>
435 import qualified Control.Monad.ST.Strict as ST
438 <para>For details on how GHC searches for source and interface
439 files in the presence of hierarchical modules, see <xref
440 linkend="search-path"/>.</para>
442 <para>GHC comes with a large collection of libraries arranged
443 hierarchically; see the accompanying <ulink
444 url="../libraries/index.html">library
445 documentation</ulink>. More libraries to install are available
447 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
450 <!-- ====================== PATTERN GUARDS ======================= -->
452 <sect2 id="pattern-guards">
453 <title>Pattern guards</title>
456 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
457 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
461 Suppose we have an abstract data type of finite maps, with a
465 lookup :: FiniteMap -> Int -> Maybe Int
468 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
469 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
473 clunky env var1 var2 | ok1 && ok2 = val1 + val2
474 | otherwise = var1 + var2
485 The auxiliary functions are
489 maybeToBool :: Maybe a -> Bool
490 maybeToBool (Just x) = True
491 maybeToBool Nothing = False
493 expectJust :: Maybe a -> a
494 expectJust (Just x) = x
495 expectJust Nothing = error "Unexpected Nothing"
499 What is <function>clunky</function> doing? The guard <literal>ok1 &&
500 ok2</literal> checks that both lookups succeed, using
501 <function>maybeToBool</function> to convert the <function>Maybe</function>
502 types to booleans. The (lazily evaluated) <function>expectJust</function>
503 calls extract the values from the results of the lookups, and binds the
504 returned values to <varname>val1</varname> and <varname>val2</varname>
505 respectively. If either lookup fails, then clunky takes the
506 <literal>otherwise</literal> case and returns the sum of its arguments.
510 This is certainly legal Haskell, but it is a tremendously verbose and
511 un-obvious way to achieve the desired effect. Arguably, a more direct way
512 to write clunky would be to use case expressions:
516 clunky env var1 var2 = case lookup env var1 of
518 Just val1 -> case lookup env var2 of
520 Just val2 -> val1 + val2
526 This is a bit shorter, but hardly better. Of course, we can rewrite any set
527 of pattern-matching, guarded equations as case expressions; that is
528 precisely what the compiler does when compiling equations! The reason that
529 Haskell provides guarded equations is because they allow us to write down
530 the cases we want to consider, one at a time, independently of each other.
531 This structure is hidden in the case version. Two of the right-hand sides
532 are really the same (<function>fail</function>), and the whole expression
533 tends to become more and more indented.
537 Here is how I would write clunky:
542 | Just val1 <- lookup env var1
543 , Just val2 <- lookup env var2
545 ...other equations for clunky...
549 The semantics should be clear enough. The qualifiers are matched in order.
550 For a <literal><-</literal> qualifier, which I call a pattern guard, the
551 right hand side is evaluated and matched against the pattern on the left.
552 If the match fails then the whole guard fails and the next equation is
553 tried. If it succeeds, then the appropriate binding takes place, and the
554 next qualifier is matched, in the augmented environment. Unlike list
555 comprehensions, however, the type of the expression to the right of the
556 <literal><-</literal> is the same as the type of the pattern to its
557 left. The bindings introduced by pattern guards scope over all the
558 remaining guard qualifiers, and over the right hand side of the equation.
562 Just as with list comprehensions, boolean expressions can be freely mixed
563 with among the pattern guards. For example:
574 Haskell's current guards therefore emerge as a special case, in which the
575 qualifier list has just one element, a boolean expression.
579 <!-- ===================== View patterns =================== -->
581 <sect2 id="view-patterns">
586 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
587 More information and examples of view patterns can be found on the
588 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
593 View patterns are somewhat like pattern guards that can be nested inside
594 of other patterns. They are a convenient way of pattern-matching
595 against values of abstract types. For example, in a programming language
596 implementation, we might represent the syntax of the types of the
605 view :: Type -> TypeView
607 -- additional operations for constructing Typ's ...
610 The representation of Typ is held abstract, permitting implementations
611 to use a fancy representation (e.g., hash-consing to manage sharing).
613 Without view patterns, using this signature a little inconvenient:
615 size :: Typ -> Integer
616 size t = case view t of
618 Arrow t1 t2 -> size t1 + size t2
621 It is necessary to iterate the case, rather than using an equational
622 function definition. And the situation is even worse when the matching
623 against <literal>t</literal> is buried deep inside another pattern.
627 View patterns permit calling the view function inside the pattern and
628 matching against the result:
630 size (view -> Unit) = 1
631 size (view -> Arrow t1 t2) = size t1 + size t2
634 That is, we add a new form of pattern, written
635 <replaceable>expression</replaceable> <literal>-></literal>
636 <replaceable>pattern</replaceable> that means "apply the expression to
637 whatever we're trying to match against, and then match the result of
638 that application against the pattern". The expression can be any Haskell
639 expression of function type, and view patterns can be used wherever
644 The semantics of a pattern <literal>(</literal>
645 <replaceable>exp</replaceable> <literal>-></literal>
646 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
652 <para>The variables bound by the view pattern are the variables bound by
653 <replaceable>pat</replaceable>.
657 Any variables in <replaceable>exp</replaceable> are bound occurrences,
658 but variables bound "to the left" in a pattern are in scope. This
659 feature permits, for example, one argument to a function to be used in
660 the view of another argument. For example, the function
661 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
662 written using view patterns as follows:
665 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
666 ...other equations for clunky...
671 More precisely, the scoping rules are:
675 In a single pattern, variables bound by patterns to the left of a view
676 pattern expression are in scope. For example:
678 example :: Maybe ((String -> Integer,Integer), String) -> Bool
679 example Just ((f,_), f -> 4) = True
682 Additionally, in function definitions, variables bound by matching earlier curried
683 arguments may be used in view pattern expressions in later arguments:
685 example :: (String -> Integer) -> String -> Bool
686 example f (f -> 4) = True
688 That is, the scoping is the same as it would be if the curried arguments
689 were collected into a tuple.
695 In mutually recursive bindings, such as <literal>let</literal>,
696 <literal>where</literal>, or the top level, view patterns in one
697 declaration may not mention variables bound by other declarations. That
698 is, each declaration must be self-contained. For example, the following
699 program is not allowed:
706 restriction in the future; the only cost is that type checking patterns
707 would get a little more complicated.)
717 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
718 <replaceable>T1</replaceable> <literal>-></literal>
719 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
720 a <replaceable>T2</replaceable>, then the whole view pattern matches a
721 <replaceable>T1</replaceable>.
724 <listitem><para> Matching: To the equations in Section 3.17.3 of the
725 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
726 Report</ulink>, add the following:
728 case v of { (e -> p) -> e1 ; _ -> e2 }
730 case (e v) of { p -> e1 ; _ -> e2 }
732 That is, to match a variable <replaceable>v</replaceable> against a pattern
733 <literal>(</literal> <replaceable>exp</replaceable>
734 <literal>-></literal> <replaceable>pat</replaceable>
735 <literal>)</literal>, evaluate <literal>(</literal>
736 <replaceable>exp</replaceable> <replaceable> v</replaceable>
737 <literal>)</literal> and match the result against
738 <replaceable>pat</replaceable>.
741 <listitem><para> Efficiency: When the same view function is applied in
742 multiple branches of a function definition or a case expression (e.g.,
743 in <literal>size</literal> above), GHC makes an attempt to collect these
744 applications into a single nested case expression, so that the view
745 function is only applied once. Pattern compilation in GHC follows the
746 matrix algorithm described in Chapter 4 of <ulink
747 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
748 Implementation of Functional Programming Languages</ulink>. When the
749 top rows of the first column of a matrix are all view patterns with the
750 "same" expression, these patterns are transformed into a single nested
751 case. This includes, for example, adjacent view patterns that line up
754 f ((view -> A, p1), p2) = e1
755 f ((view -> B, p3), p4) = e2
759 <para> The current notion of when two view pattern expressions are "the
760 same" is very restricted: it is not even full syntactic equality.
761 However, it does include variables, literals, applications, and tuples;
762 e.g., two instances of <literal>view ("hi", "there")</literal> will be
763 collected. However, the current implementation does not compare up to
764 alpha-equivalence, so two instances of <literal>(x, view x ->
765 y)</literal> will not be coalesced.
775 <!-- ===================== Recursive do-notation =================== -->
777 <sect2 id="mdo-notation">
778 <title>The recursive do-notation
781 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
782 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
783 by Levent Erkok, John Launchbury,
784 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
785 This paper is essential reading for anyone making non-trivial use of mdo-notation,
786 and we do not repeat it here.
789 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
790 that is, the variables bound in a do-expression are visible only in the textually following
791 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
792 group. It turns out that several applications can benefit from recursive bindings in
793 the do-notation, and this extension provides the necessary syntactic support.
796 Here is a simple (yet contrived) example:
799 import Control.Monad.Fix
801 justOnes = mdo xs <- Just (1:xs)
805 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
809 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
812 class Monad m => MonadFix m where
813 mfix :: (a -> m a) -> m a
816 The function <literal>mfix</literal>
817 dictates how the required recursion operation should be performed. For example,
818 <literal>justOnes</literal> desugars as follows:
820 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
822 For full details of the way in which mdo is typechecked and desugared, see
823 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
824 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
827 If recursive bindings are required for a monad,
828 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
829 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
830 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
831 for Haskell's internal state monad (strict and lazy, respectively).
834 Here are some important points in using the recursive-do notation:
837 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
838 than <literal>do</literal>).
842 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
843 <literal>-fglasgow-exts</literal>.
847 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
848 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
849 be distinct (Section 3.3 of the paper).
853 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
854 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
855 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
856 and improve termination (Section 3.2 of the paper).
862 Historical note: The old implementation of the mdo-notation (and most
863 of the existing documents) used the name
864 <literal>MonadRec</literal> for the class and the corresponding library.
865 This name is not supported by GHC.
871 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
873 <sect2 id="parallel-list-comprehensions">
874 <title>Parallel List Comprehensions</title>
875 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
877 <indexterm><primary>parallel list comprehensions</primary>
880 <para>Parallel list comprehensions are a natural extension to list
881 comprehensions. List comprehensions can be thought of as a nice
882 syntax for writing maps and filters. Parallel comprehensions
883 extend this to include the zipWith family.</para>
885 <para>A parallel list comprehension has multiple independent
886 branches of qualifier lists, each separated by a `|' symbol. For
887 example, the following zips together two lists:</para>
890 [ (x, y) | x <- xs | y <- ys ]
893 <para>The behavior of parallel list comprehensions follows that of
894 zip, in that the resulting list will have the same length as the
895 shortest branch.</para>
897 <para>We can define parallel list comprehensions by translation to
898 regular comprehensions. Here's the basic idea:</para>
900 <para>Given a parallel comprehension of the form: </para>
903 [ e | p1 <- e11, p2 <- e12, ...
904 | q1 <- e21, q2 <- e22, ...
909 <para>This will be translated to: </para>
912 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
913 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
918 <para>where `zipN' is the appropriate zip for the given number of
923 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
925 <sect2 id="generalised-list-comprehensions">
926 <title>Generalised (SQL-Like) List Comprehensions</title>
927 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
929 <indexterm><primary>extended list comprehensions</primary>
931 <indexterm><primary>group</primary></indexterm>
932 <indexterm><primary>sql</primary></indexterm>
935 <para>Generalised list comprehensions are a further enhancement to the
936 list comprehension syntatic sugar to allow operations such as sorting
937 and grouping which are familiar from SQL. They are fully described in the
938 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
939 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
940 except that the syntax we use differs slightly from the paper.</para>
941 <para>Here is an example:
943 employees = [ ("Simon", "MS", 80)
944 , ("Erik", "MS", 100)
946 , ("Gordon", "Ed", 45)
947 , ("Paul", "Yale", 60)]
949 output = [ (the dept, sum salary)
950 | (name, dept, salary) <- employees
952 , then sortWith by (sum salary)
955 In this example, the list <literal>output</literal> would take on
959 [("Yale", 60), ("Ed", 85), ("MS", 180)]
962 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
963 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
964 function that is exported by <literal>GHC.Exts</literal>.)</para>
966 <para>There are five new forms of comprehension qualifier,
967 all introduced by the (existing) keyword <literal>then</literal>:
975 This statement requires that <literal>f</literal> have the type <literal>
976 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
977 motivating example, as this form is used to apply <literal>take 5</literal>.
988 This form is similar to the previous one, but allows you to create a function
989 which will be passed as the first argument to f. As a consequence f must have
990 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
991 from the type, this function lets f "project out" some information
992 from the elements of the list it is transforming.</para>
994 <para>An example is shown in the opening example, where <literal>sortWith</literal>
995 is supplied with a function that lets it find out the <literal>sum salary</literal>
996 for any item in the list comprehension it transforms.</para>
1004 then group by e using f
1007 <para>This is the most general of the grouping-type statements. In this form,
1008 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1009 As with the <literal>then f by e</literal> case above, the first argument
1010 is a function supplied to f by the compiler which lets it compute e on every
1011 element of the list being transformed. However, unlike the non-grouping case,
1012 f additionally partitions the list into a number of sublists: this means that
1013 at every point after this statement, binders occurring before it in the comprehension
1014 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1015 this, let's look at an example:</para>
1018 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1019 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1020 groupRuns f = groupBy (\x y -> f x == f y)
1022 output = [ (the x, y)
1023 | x <- ([1..3] ++ [1..2])
1025 , then group by x using groupRuns ]
1028 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1031 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1034 <para>Note that we have used the <literal>the</literal> function to change the type
1035 of x from a list to its original numeric type. The variable y, in contrast, is left
1036 unchanged from the list form introduced by the grouping.</para>
1046 <para>This form of grouping is essentially the same as the one described above. However,
1047 since no function to use for the grouping has been supplied it will fall back on the
1048 <literal>groupWith</literal> function defined in
1049 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1050 is the form of the group statement that we made use of in the opening example.</para>
1061 <para>With this form of the group statement, f is required to simply have the type
1062 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1063 comprehension so far directly. An example of this form is as follows:</para>
1069 , then group using inits]
1072 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1075 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1083 <!-- ===================== REBINDABLE SYNTAX =================== -->
1085 <sect2 id="rebindable-syntax">
1086 <title>Rebindable syntax and the implicit Prelude import</title>
1088 <para><indexterm><primary>-XNoImplicitPrelude
1089 option</primary></indexterm> GHC normally imports
1090 <filename>Prelude.hi</filename> files for you. If you'd
1091 rather it didn't, then give it a
1092 <option>-XNoImplicitPrelude</option> option. The idea is
1093 that you can then import a Prelude of your own. (But don't
1094 call it <literal>Prelude</literal>; the Haskell module
1095 namespace is flat, and you must not conflict with any
1096 Prelude module.)</para>
1098 <para>Suppose you are importing a Prelude of your own
1099 in order to define your own numeric class
1100 hierarchy. It completely defeats that purpose if the
1101 literal "1" means "<literal>Prelude.fromInteger
1102 1</literal>", which is what the Haskell Report specifies.
1103 So the <option>-XNoImplicitPrelude</option>
1104 flag <emphasis>also</emphasis> causes
1105 the following pieces of built-in syntax to refer to
1106 <emphasis>whatever is in scope</emphasis>, not the Prelude
1110 <para>An integer literal <literal>368</literal> means
1111 "<literal>fromInteger (368::Integer)</literal>", rather than
1112 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1115 <listitem><para>Fractional literals are handed in just the same way,
1116 except that the translation is
1117 <literal>fromRational (3.68::Rational)</literal>.
1120 <listitem><para>The equality test in an overloaded numeric pattern
1121 uses whatever <literal>(==)</literal> is in scope.
1124 <listitem><para>The subtraction operation, and the
1125 greater-than-or-equal test, in <literal>n+k</literal> patterns
1126 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1130 <para>Negation (e.g. "<literal>- (f x)</literal>")
1131 means "<literal>negate (f x)</literal>", both in numeric
1132 patterns, and expressions.
1136 <para>"Do" notation is translated using whatever
1137 functions <literal>(>>=)</literal>,
1138 <literal>(>>)</literal>, and <literal>fail</literal>,
1139 are in scope (not the Prelude
1140 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1141 comprehensions, are unaffected. </para></listitem>
1145 notation (see <xref linkend="arrow-notation"/>)
1146 uses whatever <literal>arr</literal>,
1147 <literal>(>>>)</literal>, <literal>first</literal>,
1148 <literal>app</literal>, <literal>(|||)</literal> and
1149 <literal>loop</literal> functions are in scope. But unlike the
1150 other constructs, the types of these functions must match the
1151 Prelude types very closely. Details are in flux; if you want
1155 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1156 even if that is a little unexpected. For example, the
1157 static semantics of the literal <literal>368</literal>
1158 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1159 <literal>fromInteger</literal> to have any of the types:
1161 fromInteger :: Integer -> Integer
1162 fromInteger :: forall a. Foo a => Integer -> a
1163 fromInteger :: Num a => a -> Integer
1164 fromInteger :: Integer -> Bool -> Bool
1168 <para>Be warned: this is an experimental facility, with
1169 fewer checks than usual. Use <literal>-dcore-lint</literal>
1170 to typecheck the desugared program. If Core Lint is happy
1171 you should be all right.</para>
1175 <sect2 id="postfix-operators">
1176 <title>Postfix operators</title>
1179 The <option>-XPostfixOperators</option> flag enables a small
1180 extension to the syntax of left operator sections, which allows you to
1181 define postfix operators. The extension is this: the left section
1185 is equivalent (from the point of view of both type checking and execution) to the expression
1189 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1190 The strict Haskell 98 interpretation is that the section is equivalent to
1194 That is, the operator must be a function of two arguments. GHC allows it to
1195 take only one argument, and that in turn allows you to write the function
1198 <para>The extension does not extend to the left-hand side of function
1199 definitions; you must define such a function in prefix form.</para>
1203 <sect2 id="disambiguate-fields">
1204 <title>Record field disambiguation</title>
1206 In record construction and record pattern matching
1207 it is entirely unambiguous which field is referred to, even if there are two different
1208 data types in scope with a common field name. For example:
1211 data S = MkS { x :: Int, y :: Bool }
1216 data T = MkT { x :: Int }
1218 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1220 ok2 n = MkT { x = n+1 } -- Unambiguous
1222 bad1 k = k { x = 3 } -- Ambiguous
1223 bad2 k = x k -- Ambiguous
1225 Even though there are two <literal>x</literal>'s in scope,
1226 it is clear that the <literal>x</literal> in the pattern in the
1227 definition of <literal>ok1</literal> can only mean the field
1228 <literal>x</literal> from type <literal>S</literal>. Similarly for
1229 the function <literal>ok2</literal>. However, in the record update
1230 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1231 it is not clear which of the two types is intended.
1234 Haskell 98 regards all four as ambiguous, but with the
1235 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1236 the former two. The rules are precisely the same as those for instance
1237 declarations in Haskell 98, where the method names on the left-hand side
1238 of the method bindings in an instance declaration refer unambiguously
1239 to the method of that class (provided they are in scope at all), even
1240 if there are other variables in scope with the same name.
1241 This reduces the clutter of qualified names when you import two
1242 records from different modules that use the same field name.
1246 <!-- ===================== Record puns =================== -->
1248 <sect2 id="record-puns">
1253 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1257 When using records, it is common to write a pattern that binds a
1258 variable with the same name as a record field, such as:
1261 data C = C {a :: Int}
1267 Record punning permits the variable name to be elided, so one can simply
1274 to mean the same pattern as above. That is, in a record pattern, the
1275 pattern <literal>a</literal> expands into the pattern <literal>a =
1276 a</literal> for the same name <literal>a</literal>.
1280 Note that puns and other patterns can be mixed in the same record:
1282 data C = C {a :: Int, b :: Int}
1283 f (C {a, b = 4}) = a
1285 and that puns can be used wherever record patterns occur (e.g. in
1286 <literal>let</literal> bindings or at the top-level).
1290 Record punning can also be used in an expression, writing, for example,
1296 let a = 1 in C {a = a}
1299 Note that this expansion is purely syntactic, so the record pun
1300 expression refers to the nearest enclosing variable that is spelled the
1301 same as the field name.
1306 <!-- ===================== Record wildcards =================== -->
1308 <sect2 id="record-wildcards">
1309 <title>Record wildcards
1313 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1317 For records with many fields, it can be tiresome to write out each field
1318 individually in a record pattern, as in
1320 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1321 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1326 Record wildcard syntax permits a (<literal>..</literal>) in a record
1327 pattern, where each elided field <literal>f</literal> is replaced by the
1328 pattern <literal>f = f</literal>. For example, the above pattern can be
1331 f (C {a = 1, ..}) = b + c + d
1336 Note that wildcards can be mixed with other patterns, including puns
1337 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1338 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1339 wherever record patterns occur, including in <literal>let</literal>
1340 bindings and at the top-level. For example, the top-level binding
1344 defines <literal>b</literal>, <literal>c</literal>, and
1345 <literal>d</literal>.
1349 Record wildcards can also be used in expressions, writing, for example,
1352 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1358 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1361 Note that this expansion is purely syntactic, so the record wildcard
1362 expression refers to the nearest enclosing variables that are spelled
1363 the same as the omitted field names.
1368 <!-- ===================== Local fixity declarations =================== -->
1370 <sect2 id="local-fixity-declarations">
1371 <title>Local Fixity Declarations
1374 <para>A careful reading of the Haskell 98 Report reveals that fixity
1375 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1376 <literal>infixr</literal>) are permitted to appear inside local bindings
1377 such those introduced by <literal>let</literal> and
1378 <literal>where</literal>. However, the Haskell Report does not specify
1379 the semantics of such bindings very precisely.
1382 <para>In GHC, a fixity declaration may accompany a local binding:
1389 and the fixity declaration applies wherever the binding is in scope.
1390 For example, in a <literal>let</literal>, it applies in the right-hand
1391 sides of other <literal>let</literal>-bindings and the body of the
1392 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1393 expressions (<xref linkend="mdo-notation"/>), the local fixity
1394 declarations of a <literal>let</literal> statement scope over other
1395 statements in the group, just as the bound name does.
1399 Moreover, a local fixity declaration *must* accompany a local binding of
1400 that name: it is not possible to revise the fixity of name bound
1403 let infixr 9 $ in ...
1406 Because local fixity declarations are technically Haskell 98, no flag is
1407 necessary to enable them.
1411 <sect2 id="package-imports">
1412 <title>Package-qualified imports</title>
1414 <para>With the <option>-XPackageImports</option> flag, GHC allows
1415 import declarations to be qualified by the package name that the
1416 module is intended to be imported from. For example:</para>
1419 import "network" Network.Socket
1422 <para>would import the module <literal>Network.Socket</literal> from
1423 the package <literal>network</literal> (any version). This may
1424 be used to disambiguate an import when the same module is
1425 available from multiple packages, or is present in both the
1426 current package being built and an external package.</para>
1428 <para>Note: you probably don't need to use this feature, it was
1429 added mainly so that we can build backwards-compatible versions of
1430 packages when APIs change. It can lead to fragile dependencies in
1431 the common case: modules occasionally move from one package to
1432 another, rendering any package-qualified imports broken.</para>
1435 <sect2 id="syntax-stolen">
1436 <title>Summary of stolen syntax</title>
1438 <para>Turning on an option that enables special syntax
1439 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1440 to compile, perhaps because it uses a variable name which has
1441 become a reserved word. This section lists the syntax that is
1442 "stolen" by language extensions.
1444 notation and nonterminal names from the Haskell 98 lexical syntax
1445 (see the Haskell 98 Report).
1446 We only list syntax changes here that might affect
1447 existing working programs (i.e. "stolen" syntax). Many of these
1448 extensions will also enable new context-free syntax, but in all
1449 cases programs written to use the new syntax would not be
1450 compilable without the option enabled.</para>
1452 <para>There are two classes of special
1457 <para>New reserved words and symbols: character sequences
1458 which are no longer available for use as identifiers in the
1462 <para>Other special syntax: sequences of characters that have
1463 a different meaning when this particular option is turned
1468 The following syntax is stolen:
1473 <literal>forall</literal>
1474 <indexterm><primary><literal>forall</literal></primary></indexterm>
1477 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1478 <option>-XLiberalTypeSynonyms</option>,
1479 <option>-XRank2Types</option>,
1480 <option>-XRankNTypes</option>,
1481 <option>-XPolymorphicComponents</option>,
1482 <option>-XExistentialQuantification</option>
1488 <literal>mdo</literal>
1489 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1492 Stolen by: <option>-XRecursiveDo</option>,
1498 <literal>foreign</literal>
1499 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1502 Stolen by: <option>-XForeignFunctionInterface</option>,
1508 <literal>rec</literal>,
1509 <literal>proc</literal>, <literal>-<</literal>,
1510 <literal>>-</literal>, <literal>-<<</literal>,
1511 <literal>>>-</literal>, and <literal>(|</literal>,
1512 <literal>|)</literal> brackets
1513 <indexterm><primary><literal>proc</literal></primary></indexterm>
1516 Stolen by: <option>-XArrows</option>,
1522 <literal>?<replaceable>varid</replaceable></literal>,
1523 <literal>%<replaceable>varid</replaceable></literal>
1524 <indexterm><primary>implicit parameters</primary></indexterm>
1527 Stolen by: <option>-XImplicitParams</option>,
1533 <literal>[|</literal>,
1534 <literal>[e|</literal>, <literal>[p|</literal>,
1535 <literal>[d|</literal>, <literal>[t|</literal>,
1536 <literal>$(</literal>,
1537 <literal>$<replaceable>varid</replaceable></literal>
1538 <indexterm><primary>Template Haskell</primary></indexterm>
1541 Stolen by: <option>-XTemplateHaskell</option>,
1547 <literal>[:<replaceable>varid</replaceable>|</literal>
1548 <indexterm><primary>quasi-quotation</primary></indexterm>
1551 Stolen by: <option>-XQuasiQuotes</option>,
1557 <replaceable>varid</replaceable>{<literal>#</literal>},
1558 <replaceable>char</replaceable><literal>#</literal>,
1559 <replaceable>string</replaceable><literal>#</literal>,
1560 <replaceable>integer</replaceable><literal>#</literal>,
1561 <replaceable>float</replaceable><literal>#</literal>,
1562 <replaceable>float</replaceable><literal>##</literal>,
1563 <literal>(#</literal>, <literal>#)</literal>,
1566 Stolen by: <option>-XMagicHash</option>,
1575 <!-- TYPE SYSTEM EXTENSIONS -->
1576 <sect1 id="data-type-extensions">
1577 <title>Extensions to data types and type synonyms</title>
1579 <sect2 id="nullary-types">
1580 <title>Data types with no constructors</title>
1582 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1583 a data type with no constructors. For example:</para>
1587 data T a -- T :: * -> *
1590 <para>Syntactically, the declaration lacks the "= constrs" part. The
1591 type can be parameterised over types of any kind, but if the kind is
1592 not <literal>*</literal> then an explicit kind annotation must be used
1593 (see <xref linkend="kinding"/>).</para>
1595 <para>Such data types have only one value, namely bottom.
1596 Nevertheless, they can be useful when defining "phantom types".</para>
1599 <sect2 id="infix-tycons">
1600 <title>Infix type constructors, classes, and type variables</title>
1603 GHC allows type constructors, classes, and type variables to be operators, and
1604 to be written infix, very much like expressions. More specifically:
1607 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1608 The lexical syntax is the same as that for data constructors.
1611 Data type and type-synonym declarations can be written infix, parenthesised
1612 if you want further arguments. E.g.
1614 data a :*: b = Foo a b
1615 type a :+: b = Either a b
1616 class a :=: b where ...
1618 data (a :**: b) x = Baz a b x
1619 type (a :++: b) y = Either (a,b) y
1623 Types, and class constraints, can be written infix. For example
1626 f :: (a :=: b) => a -> b
1630 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1631 The lexical syntax is the same as that for variable operators, excluding "(.)",
1632 "(!)", and "(*)". In a binding position, the operator must be
1633 parenthesised. For example:
1635 type T (+) = Int + Int
1639 liftA2 :: Arrow (~>)
1640 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1646 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1647 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1650 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1651 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1652 sets the fixity for a data constructor and the corresponding type constructor. For example:
1656 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1657 and similarly for <literal>:*:</literal>.
1658 <literal>Int `a` Bool</literal>.
1661 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1668 <sect2 id="type-synonyms">
1669 <title>Liberalised type synonyms</title>
1672 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1673 on individual synonym declarations.
1674 With the <option>-XLiberalTypeSynonyms</option> extension,
1675 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1676 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1679 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1680 in a type synonym, thus:
1682 type Discard a = forall b. Show b => a -> b -> (a, String)
1687 g :: Discard Int -> (Int,String) -- A rank-2 type
1694 If you also use <option>-XUnboxedTuples</option>,
1695 you can write an unboxed tuple in a type synonym:
1697 type Pr = (# Int, Int #)
1705 You can apply a type synonym to a forall type:
1707 type Foo a = a -> a -> Bool
1709 f :: Foo (forall b. b->b)
1711 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1713 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1718 You can apply a type synonym to a partially applied type synonym:
1720 type Generic i o = forall x. i x -> o x
1723 foo :: Generic Id []
1725 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1727 foo :: forall x. x -> [x]
1735 GHC currently does kind checking before expanding synonyms (though even that
1739 After expanding type synonyms, GHC does validity checking on types, looking for
1740 the following mal-formedness which isn't detected simply by kind checking:
1743 Type constructor applied to a type involving for-alls.
1746 Unboxed tuple on left of an arrow.
1749 Partially-applied type synonym.
1753 this will be rejected:
1755 type Pr = (# Int, Int #)
1760 because GHC does not allow unboxed tuples on the left of a function arrow.
1765 <sect2 id="existential-quantification">
1766 <title>Existentially quantified data constructors
1770 The idea of using existential quantification in data type declarations
1771 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1772 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1773 London, 1991). It was later formalised by Laufer and Odersky
1774 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1775 TOPLAS, 16(5), pp1411-1430, 1994).
1776 It's been in Lennart
1777 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1778 proved very useful. Here's the idea. Consider the declaration:
1784 data Foo = forall a. MkFoo a (a -> Bool)
1791 The data type <literal>Foo</literal> has two constructors with types:
1797 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1804 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1805 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1806 For example, the following expression is fine:
1812 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1818 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1819 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1820 isUpper</function> packages a character with a compatible function. These
1821 two things are each of type <literal>Foo</literal> and can be put in a list.
1825 What can we do with a value of type <literal>Foo</literal>?. In particular,
1826 what happens when we pattern-match on <function>MkFoo</function>?
1832 f (MkFoo val fn) = ???
1838 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1839 are compatible, the only (useful) thing we can do with them is to
1840 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1847 f (MkFoo val fn) = fn val
1853 What this allows us to do is to package heterogeneous values
1854 together with a bunch of functions that manipulate them, and then treat
1855 that collection of packages in a uniform manner. You can express
1856 quite a bit of object-oriented-like programming this way.
1859 <sect3 id="existential">
1860 <title>Why existential?
1864 What has this to do with <emphasis>existential</emphasis> quantification?
1865 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1871 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1877 But Haskell programmers can safely think of the ordinary
1878 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1879 adding a new existential quantification construct.
1884 <sect3 id="existential-with-context">
1885 <title>Existentials and type classes</title>
1888 An easy extension is to allow
1889 arbitrary contexts before the constructor. For example:
1895 data Baz = forall a. Eq a => Baz1 a a
1896 | forall b. Show b => Baz2 b (b -> b)
1902 The two constructors have the types you'd expect:
1908 Baz1 :: forall a. Eq a => a -> a -> Baz
1909 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1915 But when pattern matching on <function>Baz1</function> the matched values can be compared
1916 for equality, and when pattern matching on <function>Baz2</function> the first matched
1917 value can be converted to a string (as well as applying the function to it).
1918 So this program is legal:
1925 f (Baz1 p q) | p == q = "Yes"
1927 f (Baz2 v fn) = show (fn v)
1933 Operationally, in a dictionary-passing implementation, the
1934 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1935 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1936 extract it on pattern matching.
1941 <sect3 id="existential-records">
1942 <title>Record Constructors</title>
1945 GHC allows existentials to be used with records syntax as well. For example:
1948 data Counter a = forall self. NewCounter
1950 , _inc :: self -> self
1951 , _display :: self -> IO ()
1955 Here <literal>tag</literal> is a public field, with a well-typed selector
1956 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1957 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1958 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1959 compile-time error. In other words, <emphasis>GHC defines a record selector function
1960 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1961 (This example used an underscore in the fields for which record selectors
1962 will not be defined, but that is only programming style; GHC ignores them.)
1966 To make use of these hidden fields, we need to create some helper functions:
1969 inc :: Counter a -> Counter a
1970 inc (NewCounter x i d t) = NewCounter
1971 { _this = i x, _inc = i, _display = d, tag = t }
1973 display :: Counter a -> IO ()
1974 display NewCounter{ _this = x, _display = d } = d x
1977 Now we can define counters with different underlying implementations:
1980 counterA :: Counter String
1981 counterA = NewCounter
1982 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1984 counterB :: Counter String
1985 counterB = NewCounter
1986 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1989 display (inc counterA) -- prints "1"
1990 display (inc (inc counterB)) -- prints "##"
1993 At the moment, record update syntax is only supported for Haskell 98 data types,
1994 so the following function does <emphasis>not</emphasis> work:
1997 -- This is invalid; use explicit NewCounter instead for now
1998 setTag :: Counter a -> a -> Counter a
1999 setTag obj t = obj{ tag = t }
2008 <title>Restrictions</title>
2011 There are several restrictions on the ways in which existentially-quantified
2012 constructors can be use.
2021 When pattern matching, each pattern match introduces a new,
2022 distinct, type for each existential type variable. These types cannot
2023 be unified with any other type, nor can they escape from the scope of
2024 the pattern match. For example, these fragments are incorrect:
2032 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2033 is the result of <function>f1</function>. One way to see why this is wrong is to
2034 ask what type <function>f1</function> has:
2038 f1 :: Foo -> a -- Weird!
2042 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2047 f1 :: forall a. Foo -> a -- Wrong!
2051 The original program is just plain wrong. Here's another sort of error
2055 f2 (Baz1 a b) (Baz1 p q) = a==q
2059 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2060 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2061 from the two <function>Baz1</function> constructors.
2069 You can't pattern-match on an existentially quantified
2070 constructor in a <literal>let</literal> or <literal>where</literal> group of
2071 bindings. So this is illegal:
2075 f3 x = a==b where { Baz1 a b = x }
2078 Instead, use a <literal>case</literal> expression:
2081 f3 x = case x of Baz1 a b -> a==b
2084 In general, you can only pattern-match
2085 on an existentially-quantified constructor in a <literal>case</literal> expression or
2086 in the patterns of a function definition.
2088 The reason for this restriction is really an implementation one.
2089 Type-checking binding groups is already a nightmare without
2090 existentials complicating the picture. Also an existential pattern
2091 binding at the top level of a module doesn't make sense, because it's
2092 not clear how to prevent the existentially-quantified type "escaping".
2093 So for now, there's a simple-to-state restriction. We'll see how
2101 You can't use existential quantification for <literal>newtype</literal>
2102 declarations. So this is illegal:
2106 newtype T = forall a. Ord a => MkT a
2110 Reason: a value of type <literal>T</literal> must be represented as a
2111 pair of a dictionary for <literal>Ord t</literal> and a value of type
2112 <literal>t</literal>. That contradicts the idea that
2113 <literal>newtype</literal> should have no concrete representation.
2114 You can get just the same efficiency and effect by using
2115 <literal>data</literal> instead of <literal>newtype</literal>. If
2116 there is no overloading involved, then there is more of a case for
2117 allowing an existentially-quantified <literal>newtype</literal>,
2118 because the <literal>data</literal> version does carry an
2119 implementation cost, but single-field existentially quantified
2120 constructors aren't much use. So the simple restriction (no
2121 existential stuff on <literal>newtype</literal>) stands, unless there
2122 are convincing reasons to change it.
2130 You can't use <literal>deriving</literal> to define instances of a
2131 data type with existentially quantified data constructors.
2133 Reason: in most cases it would not make sense. For example:;
2136 data T = forall a. MkT [a] deriving( Eq )
2139 To derive <literal>Eq</literal> in the standard way we would need to have equality
2140 between the single component of two <function>MkT</function> constructors:
2144 (MkT a) == (MkT b) = ???
2147 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2148 It's just about possible to imagine examples in which the derived instance
2149 would make sense, but it seems altogether simpler simply to prohibit such
2150 declarations. Define your own instances!
2161 <!-- ====================== Generalised algebraic data types ======================= -->
2163 <sect2 id="gadt-style">
2164 <title>Declaring data types with explicit constructor signatures</title>
2166 <para>GHC allows you to declare an algebraic data type by
2167 giving the type signatures of constructors explicitly. For example:
2171 Just :: a -> Maybe a
2173 The form is called a "GADT-style declaration"
2174 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2175 can only be declared using this form.</para>
2176 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2177 For example, these two declarations are equivalent:
2179 data Foo = forall a. MkFoo a (a -> Bool)
2180 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2183 <para>Any data type that can be declared in standard Haskell-98 syntax
2184 can also be declared using GADT-style syntax.
2185 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2186 they treat class constraints on the data constructors differently.
2187 Specifically, if the constructor is given a type-class context, that
2188 context is made available by pattern matching. For example:
2191 MkSet :: Eq a => [a] -> Set a
2193 makeSet :: Eq a => [a] -> Set a
2194 makeSet xs = MkSet (nub xs)
2196 insert :: a -> Set a -> Set a
2197 insert a (MkSet as) | a `elem` as = MkSet as
2198 | otherwise = MkSet (a:as)
2200 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2201 gives rise to a <literal>(Eq a)</literal>
2202 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2203 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2204 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2205 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2206 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2207 In the example, the equality dictionary is used to satisfy the equality constraint
2208 generated by the call to <literal>elem</literal>, so that the type of
2209 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2212 For example, one possible application is to reify dictionaries:
2214 data NumInst a where
2215 MkNumInst :: Num a => NumInst a
2217 intInst :: NumInst Int
2220 plus :: NumInst a -> a -> a -> a
2221 plus MkNumInst p q = p + q
2223 Here, a value of type <literal>NumInst a</literal> is equivalent
2224 to an explicit <literal>(Num a)</literal> dictionary.
2227 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2228 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2232 = Num a => MkNumInst (NumInst a)
2234 Notice that, unlike the situation when declaring an existential, there is
2235 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2236 data type's universally quantified type variable <literal>a</literal>.
2237 A constructor may have both universal and existential type variables: for example,
2238 the following two declarations are equivalent:
2241 = forall b. (Num a, Eq b) => MkT1 a b
2243 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2246 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2247 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2248 In Haskell 98 the definition
2250 data Eq a => Set' a = MkSet' [a]
2252 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2253 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2254 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2255 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2256 GHC's behaviour is much more useful, as well as much more intuitive.
2260 The rest of this section gives further details about GADT-style data
2265 The result type of each data constructor must begin with the type constructor being defined.
2266 If the result type of all constructors
2267 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2268 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2269 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2273 The type signature of
2274 each constructor is independent, and is implicitly universally quantified as usual.
2275 Different constructors may have different universally-quantified type variables
2276 and different type-class constraints.
2277 For example, this is fine:
2280 T1 :: Eq b => b -> T b
2281 T2 :: (Show c, Ix c) => c -> [c] -> T c
2286 Unlike a Haskell-98-style
2287 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2288 have no scope. Indeed, one can write a kind signature instead:
2290 data Set :: * -> * where ...
2292 or even a mixture of the two:
2294 data Foo a :: (* -> *) -> * where ...
2296 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2299 data Foo a (b :: * -> *) where ...
2305 You can use strictness annotations, in the obvious places
2306 in the constructor type:
2309 Lit :: !Int -> Term Int
2310 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2311 Pair :: Term a -> Term b -> Term (a,b)
2316 You can use a <literal>deriving</literal> clause on a GADT-style data type
2317 declaration. For example, these two declarations are equivalent
2319 data Maybe1 a where {
2320 Nothing1 :: Maybe1 a ;
2321 Just1 :: a -> Maybe1 a
2322 } deriving( Eq, Ord )
2324 data Maybe2 a = Nothing2 | Just2 a
2330 You can use record syntax on a GADT-style data type declaration:
2334 Adult { name :: String, children :: [Person] } :: Person
2335 Child { name :: String } :: Person
2337 As usual, for every constructor that has a field <literal>f</literal>, the type of
2338 field <literal>f</literal> must be the same (modulo alpha conversion).
2341 At the moment, record updates are not yet possible with GADT-style declarations,
2342 so support is limited to record construction, selection and pattern matching.
2345 aPerson = Adult { name = "Fred", children = [] }
2347 shortName :: Person -> Bool
2348 hasChildren (Adult { children = kids }) = not (null kids)
2349 hasChildren (Child {}) = False
2354 As in the case of existentials declared using the Haskell-98-like record syntax
2355 (<xref linkend="existential-records"/>),
2356 record-selector functions are generated only for those fields that have well-typed
2358 Here is the example of that section, in GADT-style syntax:
2360 data Counter a where
2361 NewCounter { _this :: self
2362 , _inc :: self -> self
2363 , _display :: self -> IO ()
2368 As before, only one selector function is generated here, that for <literal>tag</literal>.
2369 Nevertheless, you can still use all the field names in pattern matching and record construction.
2371 </itemizedlist></para>
2375 <title>Generalised Algebraic Data Types (GADTs)</title>
2377 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2378 by allowing constructors to have richer return types. Here is an example:
2381 Lit :: Int -> Term Int
2382 Succ :: Term Int -> Term Int
2383 IsZero :: Term Int -> Term Bool
2384 If :: Term Bool -> Term a -> Term a -> Term a
2385 Pair :: Term a -> Term b -> Term (a,b)
2387 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2388 case with ordinary data types. This generality allows us to
2389 write a well-typed <literal>eval</literal> function
2390 for these <literal>Terms</literal>:
2394 eval (Succ t) = 1 + eval t
2395 eval (IsZero t) = eval t == 0
2396 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2397 eval (Pair e1 e2) = (eval e1, eval e2)
2399 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2400 For example, in the right hand side of the equation
2405 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2406 A precise specification of the type rules is beyond what this user manual aspires to,
2407 but the design closely follows that described in
2409 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2410 unification-based type inference for GADTs</ulink>,
2412 The general principle is this: <emphasis>type refinement is only carried out
2413 based on user-supplied type annotations</emphasis>.
2414 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2415 and lots of obscure error messages will
2416 occur. However, the refinement is quite general. For example, if we had:
2418 eval :: Term a -> a -> a
2419 eval (Lit i) j = i+j
2421 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2422 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2423 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2426 These and many other examples are given in papers by Hongwei Xi, and
2427 Tim Sheard. There is a longer introduction
2428 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2430 <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
2431 may use different notation to that implemented in GHC.
2434 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2435 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2438 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2439 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2440 The result type of each constructor must begin with the type constructor being defined,
2441 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2442 For example, in the <literal>Term</literal> data
2443 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2444 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2449 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2450 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2451 whose result type is not just <literal>T a b</literal>.
2455 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2456 an ordinary data type.
2460 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2464 Lit { val :: Int } :: Term Int
2465 Succ { num :: Term Int } :: Term Int
2466 Pred { num :: Term Int } :: Term Int
2467 IsZero { arg :: Term Int } :: Term Bool
2468 Pair { arg1 :: Term a
2471 If { cnd :: Term Bool
2476 However, for GADTs there is the following additional constraint:
2477 every constructor that has a field <literal>f</literal> must have
2478 the same result type (modulo alpha conversion)
2479 Hence, in the above example, we cannot merge the <literal>num</literal>
2480 and <literal>arg</literal> fields above into a
2481 single name. Although their field types are both <literal>Term Int</literal>,
2482 their selector functions actually have different types:
2485 num :: Term Int -> Term Int
2486 arg :: Term Bool -> Term Int
2491 When pattern-matching against data constructors drawn from a GADT,
2492 for example in a <literal>case</literal> expression, the following rules apply:
2494 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2495 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2496 <listitem><para>The type of any free variable mentioned in any of
2497 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2499 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2500 way to ensure that a variable a rigid type is to give it a type signature.
2501 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2502 Simple unification-based type inference for GADTs
2503 </ulink>. The criteria implemented by GHC are given in the Appendix.
2513 <!-- ====================== End of Generalised algebraic data types ======================= -->
2515 <sect1 id="deriving">
2516 <title>Extensions to the "deriving" mechanism</title>
2518 <sect2 id="deriving-inferred">
2519 <title>Inferred context for deriving clauses</title>
2522 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2525 data T0 f a = MkT0 a deriving( Eq )
2526 data T1 f a = MkT1 (f a) deriving( Eq )
2527 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2529 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2531 instance Eq a => Eq (T0 f a) where ...
2532 instance Eq (f a) => Eq (T1 f a) where ...
2533 instance Eq (f (f a)) => Eq (T2 f a) where ...
2535 The first of these is obviously fine. The second is still fine, although less obviously.
2536 The third is not Haskell 98, and risks losing termination of instances.
2539 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2540 each constraint in the inferred instance context must consist only of type variables,
2541 with no repetitions.
2544 This rule is applied regardless of flags. If you want a more exotic context, you can write
2545 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2549 <sect2 id="stand-alone-deriving">
2550 <title>Stand-alone deriving declarations</title>
2553 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2555 data Foo a = Bar a | Baz String
2557 deriving instance Eq a => Eq (Foo a)
2559 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2560 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2561 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2562 exactly as you would in an ordinary instance declaration.
2563 (In contrast the context is inferred in a <literal>deriving</literal> clause
2564 attached to a data type declaration.)
2566 A <literal>deriving instance</literal> declaration
2567 must obey the same rules concerning form and termination as ordinary instance declarations,
2568 controlled by the same flags; see <xref linkend="instance-decls"/>.
2571 Unlike a <literal>deriving</literal>
2572 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2573 than the data type (assuming you also use
2574 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2577 data Foo a = Bar a | Baz String
2579 deriving instance Eq a => Eq (Foo [a])
2580 deriving instance Eq a => Eq (Foo (Maybe a))
2582 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2583 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2586 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2587 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2590 newtype Foo a = MkFoo (State Int a)
2592 deriving instance MonadState Int Foo
2594 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2595 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2601 <sect2 id="deriving-typeable">
2602 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2605 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2606 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2607 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2608 classes <literal>Eq</literal>, <literal>Ord</literal>,
2609 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2612 GHC extends this list with two more classes that may be automatically derived
2613 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2614 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2615 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2616 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2618 <para>An instance of <literal>Typeable</literal> can only be derived if the
2619 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2620 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2622 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2623 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2625 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2626 are used, and only <literal>Typeable1</literal> up to
2627 <literal>Typeable7</literal> are provided in the library.)
2628 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2629 class, whose kind suits that of the data type constructor, and
2630 then writing the data type instance by hand.
2634 <sect2 id="newtype-deriving">
2635 <title>Generalised derived instances for newtypes</title>
2638 When you define an abstract type using <literal>newtype</literal>, you may want
2639 the new type to inherit some instances from its representation. In
2640 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2641 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2642 other classes you have to write an explicit instance declaration. For
2643 example, if you define
2646 newtype Dollars = Dollars Int
2649 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2650 explicitly define an instance of <literal>Num</literal>:
2653 instance Num Dollars where
2654 Dollars a + Dollars b = Dollars (a+b)
2657 All the instance does is apply and remove the <literal>newtype</literal>
2658 constructor. It is particularly galling that, since the constructor
2659 doesn't appear at run-time, this instance declaration defines a
2660 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2661 dictionary, only slower!
2665 <sect3> <title> Generalising the deriving clause </title>
2667 GHC now permits such instances to be derived instead,
2668 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2671 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2674 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2675 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2676 derives an instance declaration of the form
2679 instance Num Int => Num Dollars
2682 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2686 We can also derive instances of constructor classes in a similar
2687 way. For example, suppose we have implemented state and failure monad
2688 transformers, such that
2691 instance Monad m => Monad (State s m)
2692 instance Monad m => Monad (Failure m)
2694 In Haskell 98, we can define a parsing monad by
2696 type Parser tok m a = State [tok] (Failure m) a
2699 which is automatically a monad thanks to the instance declarations
2700 above. With the extension, we can make the parser type abstract,
2701 without needing to write an instance of class <literal>Monad</literal>, via
2704 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2707 In this case the derived instance declaration is of the form
2709 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2712 Notice that, since <literal>Monad</literal> is a constructor class, the
2713 instance is a <emphasis>partial application</emphasis> of the new type, not the
2714 entire left hand side. We can imagine that the type declaration is
2715 "eta-converted" to generate the context of the instance
2720 We can even derive instances of multi-parameter classes, provided the
2721 newtype is the last class parameter. In this case, a ``partial
2722 application'' of the class appears in the <literal>deriving</literal>
2723 clause. For example, given the class
2726 class StateMonad s m | m -> s where ...
2727 instance Monad m => StateMonad s (State s m) where ...
2729 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2731 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2732 deriving (Monad, StateMonad [tok])
2735 The derived instance is obtained by completing the application of the
2736 class to the new type:
2739 instance StateMonad [tok] (State [tok] (Failure m)) =>
2740 StateMonad [tok] (Parser tok m)
2745 As a result of this extension, all derived instances in newtype
2746 declarations are treated uniformly (and implemented just by reusing
2747 the dictionary for the representation type), <emphasis>except</emphasis>
2748 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2749 the newtype and its representation.
2753 <sect3> <title> A more precise specification </title>
2755 Derived instance declarations are constructed as follows. Consider the
2756 declaration (after expansion of any type synonyms)
2759 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2765 The <literal>ci</literal> are partial applications of
2766 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2767 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2770 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2773 The type <literal>t</literal> is an arbitrary type.
2776 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2777 nor in the <literal>ci</literal>, and
2780 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2781 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2782 should not "look through" the type or its constructor. You can still
2783 derive these classes for a newtype, but it happens in the usual way, not
2784 via this new mechanism.
2787 Then, for each <literal>ci</literal>, the derived instance
2790 instance ci t => ci (T v1...vk)
2792 As an example which does <emphasis>not</emphasis> work, consider
2794 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2796 Here we cannot derive the instance
2798 instance Monad (State s m) => Monad (NonMonad m)
2801 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2802 and so cannot be "eta-converted" away. It is a good thing that this
2803 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2804 not, in fact, a monad --- for the same reason. Try defining
2805 <literal>>>=</literal> with the correct type: you won't be able to.
2809 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2810 important, since we can only derive instances for the last one. If the
2811 <literal>StateMonad</literal> class above were instead defined as
2814 class StateMonad m s | m -> s where ...
2817 then we would not have been able to derive an instance for the
2818 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2819 classes usually have one "main" parameter for which deriving new
2820 instances is most interesting.
2822 <para>Lastly, all of this applies only for classes other than
2823 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2824 and <literal>Data</literal>, for which the built-in derivation applies (section
2825 4.3.3. of the Haskell Report).
2826 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2827 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2828 the standard method is used or the one described here.)
2835 <!-- TYPE SYSTEM EXTENSIONS -->
2836 <sect1 id="type-class-extensions">
2837 <title>Class and instances declarations</title>
2839 <sect2 id="multi-param-type-classes">
2840 <title>Class declarations</title>
2843 This section, and the next one, documents GHC's type-class extensions.
2844 There's lots of background in the paper <ulink
2845 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2846 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2847 Jones, Erik Meijer).
2850 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2854 <title>Multi-parameter type classes</title>
2856 Multi-parameter type classes are permitted. For example:
2860 class Collection c a where
2861 union :: c a -> c a -> c a
2869 <title>The superclasses of a class declaration</title>
2872 There are no restrictions on the context in a class declaration
2873 (which introduces superclasses), except that the class hierarchy must
2874 be acyclic. So these class declarations are OK:
2878 class Functor (m k) => FiniteMap m k where
2881 class (Monad m, Monad (t m)) => Transform t m where
2882 lift :: m a -> (t m) a
2888 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2889 of "acyclic" involves only the superclass relationships. For example,
2895 op :: D b => a -> b -> b
2898 class C a => D a where { ... }
2902 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2903 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2904 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2911 <sect3 id="class-method-types">
2912 <title>Class method types</title>
2915 Haskell 98 prohibits class method types to mention constraints on the
2916 class type variable, thus:
2919 fromList :: [a] -> s a
2920 elem :: Eq a => a -> s a -> Bool
2922 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2923 contains the constraint <literal>Eq a</literal>, constrains only the
2924 class type variable (in this case <literal>a</literal>).
2925 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2932 <sect2 id="functional-dependencies">
2933 <title>Functional dependencies
2936 <para> Functional dependencies are implemented as described by Mark Jones
2937 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2938 In Proceedings of the 9th European Symposium on Programming,
2939 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2943 Functional dependencies are introduced by a vertical bar in the syntax of a
2944 class declaration; e.g.
2946 class (Monad m) => MonadState s m | m -> s where ...
2948 class Foo a b c | a b -> c where ...
2950 There should be more documentation, but there isn't (yet). Yell if you need it.
2953 <sect3><title>Rules for functional dependencies </title>
2955 In a class declaration, all of the class type variables must be reachable (in the sense
2956 mentioned in <xref linkend="type-restrictions"/>)
2957 from the free variables of each method type.
2961 class Coll s a where
2963 insert :: s -> a -> s
2966 is not OK, because the type of <literal>empty</literal> doesn't mention
2967 <literal>a</literal>. Functional dependencies can make the type variable
2970 class Coll s a | s -> a where
2972 insert :: s -> a -> s
2975 Alternatively <literal>Coll</literal> might be rewritten
2978 class Coll s a where
2980 insert :: s a -> a -> s a
2984 which makes the connection between the type of a collection of
2985 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2986 Occasionally this really doesn't work, in which case you can split the
2994 class CollE s => Coll s a where
2995 insert :: s -> a -> s
3002 <title>Background on functional dependencies</title>
3004 <para>The following description of the motivation and use of functional dependencies is taken
3005 from the Hugs user manual, reproduced here (with minor changes) by kind
3006 permission of Mark Jones.
3009 Consider the following class, intended as part of a
3010 library for collection types:
3012 class Collects e ce where
3014 insert :: e -> ce -> ce
3015 member :: e -> ce -> Bool
3017 The type variable e used here represents the element type, while ce is the type
3018 of the container itself. Within this framework, we might want to define
3019 instances of this class for lists or characteristic functions (both of which
3020 can be used to represent collections of any equality type), bit sets (which can
3021 be used to represent collections of characters), or hash tables (which can be
3022 used to represent any collection whose elements have a hash function). Omitting
3023 standard implementation details, this would lead to the following declarations:
3025 instance Eq e => Collects e [e] where ...
3026 instance Eq e => Collects e (e -> Bool) where ...
3027 instance Collects Char BitSet where ...
3028 instance (Hashable e, Collects a ce)
3029 => Collects e (Array Int ce) where ...
3031 All this looks quite promising; we have a class and a range of interesting
3032 implementations. Unfortunately, there are some serious problems with the class
3033 declaration. First, the empty function has an ambiguous type:
3035 empty :: Collects e ce => ce
3037 By "ambiguous" we mean that there is a type variable e that appears on the left
3038 of the <literal>=></literal> symbol, but not on the right. The problem with
3039 this is that, according to the theoretical foundations of Haskell overloading,
3040 we cannot guarantee a well-defined semantics for any term with an ambiguous
3044 We can sidestep this specific problem by removing the empty member from the
3045 class declaration. However, although the remaining members, insert and member,
3046 do not have ambiguous types, we still run into problems when we try to use
3047 them. For example, consider the following two functions:
3049 f x y = insert x . insert y
3052 for which GHC infers the following types:
3054 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3055 g :: (Collects Bool c, Collects Char c) => c -> c
3057 Notice that the type for f allows the two parameters x and y to be assigned
3058 different types, even though it attempts to insert each of the two values, one
3059 after the other, into the same collection. If we're trying to model collections
3060 that contain only one type of value, then this is clearly an inaccurate
3061 type. Worse still, the definition for g is accepted, without causing a type
3062 error. As a result, the error in this code will not be flagged at the point
3063 where it appears. Instead, it will show up only when we try to use g, which
3064 might even be in a different module.
3067 <sect4><title>An attempt to use constructor classes</title>
3070 Faced with the problems described above, some Haskell programmers might be
3071 tempted to use something like the following version of the class declaration:
3073 class Collects e c where
3075 insert :: e -> c e -> c e
3076 member :: e -> c e -> Bool
3078 The key difference here is that we abstract over the type constructor c that is
3079 used to form the collection type c e, and not over that collection type itself,
3080 represented by ce in the original class declaration. This avoids the immediate
3081 problems that we mentioned above: empty has type <literal>Collects e c => c
3082 e</literal>, which is not ambiguous.
3085 The function f from the previous section has a more accurate type:
3087 f :: (Collects e c) => e -> e -> c e -> c e
3089 The function g from the previous section is now rejected with a type error as
3090 we would hope because the type of f does not allow the two arguments to have
3092 This, then, is an example of a multiple parameter class that does actually work
3093 quite well in practice, without ambiguity problems.
3094 There is, however, a catch. This version of the Collects class is nowhere near
3095 as general as the original class seemed to be: only one of the four instances
3096 for <literal>Collects</literal>
3097 given above can be used with this version of Collects because only one of
3098 them---the instance for lists---has a collection type that can be written in
3099 the form c e, for some type constructor c, and element type e.
3103 <sect4><title>Adding functional dependencies</title>
3106 To get a more useful version of the Collects class, Hugs provides a mechanism
3107 that allows programmers to specify dependencies between the parameters of a
3108 multiple parameter class (For readers with an interest in theoretical
3109 foundations and previous work: The use of dependency information can be seen
3110 both as a generalization of the proposal for `parametric type classes' that was
3111 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3112 later framework for "improvement" of qualified types. The
3113 underlying ideas are also discussed in a more theoretical and abstract setting
3114 in a manuscript [implparam], where they are identified as one point in a
3115 general design space for systems of implicit parameterization.).
3117 To start with an abstract example, consider a declaration such as:
3119 class C a b where ...
3121 which tells us simply that C can be thought of as a binary relation on types
3122 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3123 included in the definition of classes to add information about dependencies
3124 between parameters, as in the following examples:
3126 class D a b | a -> b where ...
3127 class E a b | a -> b, b -> a where ...
3129 The notation <literal>a -> b</literal> used here between the | and where
3130 symbols --- not to be
3131 confused with a function type --- indicates that the a parameter uniquely
3132 determines the b parameter, and might be read as "a determines b." Thus D is
3133 not just a relation, but actually a (partial) function. Similarly, from the two
3134 dependencies that are included in the definition of E, we can see that E
3135 represents a (partial) one-one mapping between types.
3138 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3139 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3140 m>=0, meaning that the y parameters are uniquely determined by the x
3141 parameters. Spaces can be used as separators if more than one variable appears
3142 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3143 annotated with multiple dependencies using commas as separators, as in the
3144 definition of E above. Some dependencies that we can write in this notation are
3145 redundant, and will be rejected because they don't serve any useful
3146 purpose, and may instead indicate an error in the program. Examples of
3147 dependencies like this include <literal>a -> a </literal>,
3148 <literal>a -> a a </literal>,
3149 <literal>a -> </literal>, etc. There can also be
3150 some redundancy if multiple dependencies are given, as in
3151 <literal>a->b</literal>,
3152 <literal>b->c </literal>, <literal>a->c </literal>, and
3153 in which some subset implies the remaining dependencies. Examples like this are
3154 not treated as errors. Note that dependencies appear only in class
3155 declarations, and not in any other part of the language. In particular, the
3156 syntax for instance declarations, class constraints, and types is completely
3160 By including dependencies in a class declaration, we provide a mechanism for
3161 the programmer to specify each multiple parameter class more precisely. The
3162 compiler, on the other hand, is responsible for ensuring that the set of
3163 instances that are in scope at any given point in the program is consistent
3164 with any declared dependencies. For example, the following pair of instance
3165 declarations cannot appear together in the same scope because they violate the
3166 dependency for D, even though either one on its own would be acceptable:
3168 instance D Bool Int where ...
3169 instance D Bool Char where ...
3171 Note also that the following declaration is not allowed, even by itself:
3173 instance D [a] b where ...
3175 The problem here is that this instance would allow one particular choice of [a]
3176 to be associated with more than one choice for b, which contradicts the
3177 dependency specified in the definition of D. More generally, this means that,
3178 in any instance of the form:
3180 instance D t s where ...
3182 for some particular types t and s, the only variables that can appear in s are
3183 the ones that appear in t, and hence, if the type t is known, then s will be
3184 uniquely determined.
3187 The benefit of including dependency information is that it allows us to define
3188 more general multiple parameter classes, without ambiguity problems, and with
3189 the benefit of more accurate types. To illustrate this, we return to the
3190 collection class example, and annotate the original definition of <literal>Collects</literal>
3191 with a simple dependency:
3193 class Collects e ce | ce -> e where
3195 insert :: e -> ce -> ce
3196 member :: e -> ce -> Bool
3198 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3199 determined by the type of the collection ce. Note that both parameters of
3200 Collects are of kind *; there are no constructor classes here. Note too that
3201 all of the instances of Collects that we gave earlier can be used
3202 together with this new definition.
3205 What about the ambiguity problems that we encountered with the original
3206 definition? The empty function still has type Collects e ce => ce, but it is no
3207 longer necessary to regard that as an ambiguous type: Although the variable e
3208 does not appear on the right of the => symbol, the dependency for class
3209 Collects tells us that it is uniquely determined by ce, which does appear on
3210 the right of the => symbol. Hence the context in which empty is used can still
3211 give enough information to determine types for both ce and e, without
3212 ambiguity. More generally, we need only regard a type as ambiguous if it
3213 contains a variable on the left of the => that is not uniquely determined
3214 (either directly or indirectly) by the variables on the right.
3217 Dependencies also help to produce more accurate types for user defined
3218 functions, and hence to provide earlier detection of errors, and less cluttered
3219 types for programmers to work with. Recall the previous definition for a
3222 f x y = insert x y = insert x . insert y
3224 for which we originally obtained a type:
3226 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3228 Given the dependency information that we have for Collects, however, we can
3229 deduce that a and b must be equal because they both appear as the second
3230 parameter in a Collects constraint with the same first parameter c. Hence we
3231 can infer a shorter and more accurate type for f:
3233 f :: (Collects a c) => a -> a -> c -> c
3235 In a similar way, the earlier definition of g will now be flagged as a type error.
3238 Although we have given only a few examples here, it should be clear that the
3239 addition of dependency information can help to make multiple parameter classes
3240 more useful in practice, avoiding ambiguity problems, and allowing more general
3241 sets of instance declarations.
3247 <sect2 id="instance-decls">
3248 <title>Instance declarations</title>
3250 <para>An instance declaration has the form
3252 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 ...
3254 The part before the "<literal>=></literal>" is the
3255 <emphasis>context</emphasis>, while the part after the
3256 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3259 <sect3 id="flexible-instance-head">
3260 <title>Relaxed rules for the instance head</title>
3263 In Haskell 98 the head of an instance declaration
3264 must be of the form <literal>C (T a1 ... an)</literal>, where
3265 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3266 and the <literal>a1 ... an</literal> are distinct type variables.
3267 GHC relaxes these rules in two ways.
3271 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3272 declaration to mention arbitrary nested types.
3273 For example, this becomes a legal instance declaration
3275 instance C (Maybe Int) where ...
3277 See also the <link linkend="instance-overlap">rules on overlap</link>.
3280 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3281 synonyms. As always, using a type synonym is just shorthand for
3282 writing the RHS of the type synonym definition. For example:
3286 type Point = (Int,Int)
3287 instance C Point where ...
3288 instance C [Point] where ...
3292 is legal. However, if you added
3296 instance C (Int,Int) where ...
3300 as well, then the compiler will complain about the overlapping
3301 (actually, identical) instance declarations. As always, type synonyms
3302 must be fully applied. You cannot, for example, write:
3306 instance Monad P where ...
3314 <sect3 id="instance-rules">
3315 <title>Relaxed rules for instance contexts</title>
3317 <para>In Haskell 98, the assertions in the context of the instance declaration
3318 must be of the form <literal>C a</literal> where <literal>a</literal>
3319 is a type variable that occurs in the head.
3323 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3324 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3325 With this flag the context of the instance declaration can each consist of arbitrary
3326 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3330 The Paterson Conditions: for each assertion in the context
3332 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3333 <listitem><para>The assertion has fewer constructors and variables (taken together
3334 and counting repetitions) than the head</para></listitem>
3338 <listitem><para>The Coverage Condition. For each functional dependency,
3339 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3340 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3341 every type variable in
3342 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3343 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3344 substitution mapping each type variable in the class declaration to the
3345 corresponding type in the instance declaration.
3348 These restrictions ensure that context reduction terminates: each reduction
3349 step makes the problem smaller by at least one
3350 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3351 if you give the <option>-XUndecidableInstances</option>
3352 flag (<xref linkend="undecidable-instances"/>).
3353 You can find lots of background material about the reason for these
3354 restrictions in the paper <ulink
3355 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3356 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3359 For example, these are OK:
3361 instance C Int [a] -- Multiple parameters
3362 instance Eq (S [a]) -- Structured type in head
3364 -- Repeated type variable in head
3365 instance C4 a a => C4 [a] [a]
3366 instance Stateful (ST s) (MutVar s)
3368 -- Head can consist of type variables only
3370 instance (Eq a, Show b) => C2 a b
3372 -- Non-type variables in context
3373 instance Show (s a) => Show (Sized s a)
3374 instance C2 Int a => C3 Bool [a]
3375 instance C2 Int a => C3 [a] b
3379 -- Context assertion no smaller than head
3380 instance C a => C a where ...
3381 -- (C b b) has more more occurrences of b than the head
3382 instance C b b => Foo [b] where ...
3387 The same restrictions apply to instances generated by
3388 <literal>deriving</literal> clauses. Thus the following is accepted:
3390 data MinHeap h a = H a (h a)
3393 because the derived instance
3395 instance (Show a, Show (h a)) => Show (MinHeap h a)
3397 conforms to the above rules.
3401 A useful idiom permitted by the above rules is as follows.
3402 If one allows overlapping instance declarations then it's quite
3403 convenient to have a "default instance" declaration that applies if
3404 something more specific does not:
3412 <sect3 id="undecidable-instances">
3413 <title>Undecidable instances</title>
3416 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3417 For example, sometimes you might want to use the following to get the
3418 effect of a "class synonym":
3420 class (C1 a, C2 a, C3 a) => C a where { }
3422 instance (C1 a, C2 a, C3 a) => C a where { }
3424 This allows you to write shorter signatures:
3430 f :: (C1 a, C2 a, C3 a) => ...
3432 The restrictions on functional dependencies (<xref
3433 linkend="functional-dependencies"/>) are particularly troublesome.
3434 It is tempting to introduce type variables in the context that do not appear in
3435 the head, something that is excluded by the normal rules. For example:
3437 class HasConverter a b | a -> b where
3440 data Foo a = MkFoo a
3442 instance (HasConverter a b,Show b) => Show (Foo a) where
3443 show (MkFoo value) = show (convert value)
3445 This is dangerous territory, however. Here, for example, is a program that would make the
3450 instance F [a] [[a]]
3451 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3453 Similarly, it can be tempting to lift the coverage condition:
3455 class Mul a b c | a b -> c where
3456 (.*.) :: a -> b -> c
3458 instance Mul Int Int Int where (.*.) = (*)
3459 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3460 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3462 The third instance declaration does not obey the coverage condition;
3463 and indeed the (somewhat strange) definition:
3465 f = \ b x y -> if b then x .*. [y] else y
3467 makes instance inference go into a loop, because it requires the constraint
3468 <literal>(Mul a [b] b)</literal>.
3471 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3472 the experimental flag <option>-XUndecidableInstances</option>
3473 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3474 both the Paterson Conditions and the Coverage Condition
3475 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3476 fixed-depth recursion stack. If you exceed the stack depth you get a
3477 sort of backtrace, and the opportunity to increase the stack depth
3478 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3484 <sect3 id="instance-overlap">
3485 <title>Overlapping instances</title>
3487 In general, <emphasis>GHC requires that that it be unambiguous which instance
3489 should be used to resolve a type-class constraint</emphasis>. This behaviour
3490 can be modified by two flags: <option>-XOverlappingInstances</option>
3491 <indexterm><primary>-XOverlappingInstances
3492 </primary></indexterm>
3493 and <option>-XIncoherentInstances</option>
3494 <indexterm><primary>-XIncoherentInstances
3495 </primary></indexterm>, as this section discusses. Both these
3496 flags are dynamic flags, and can be set on a per-module basis, using
3497 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3499 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3500 it tries to match every instance declaration against the
3502 by instantiating the head of the instance declaration. For example, consider
3505 instance context1 => C Int a where ... -- (A)
3506 instance context2 => C a Bool where ... -- (B)
3507 instance context3 => C Int [a] where ... -- (C)
3508 instance context4 => C Int [Int] where ... -- (D)
3510 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3511 but (C) and (D) do not. When matching, GHC takes
3512 no account of the context of the instance declaration
3513 (<literal>context1</literal> etc).
3514 GHC's default behaviour is that <emphasis>exactly one instance must match the
3515 constraint it is trying to resolve</emphasis>.
3516 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3517 including both declarations (A) and (B), say); an error is only reported if a
3518 particular constraint matches more than one.
3522 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3523 more than one instance to match, provided there is a most specific one. For
3524 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3525 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3526 most-specific match, the program is rejected.
3529 However, GHC is conservative about committing to an overlapping instance. For example:
3534 Suppose that from the RHS of <literal>f</literal> we get the constraint
3535 <literal>C Int [b]</literal>. But
3536 GHC does not commit to instance (C), because in a particular
3537 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3538 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3539 So GHC rejects the program.
3540 (If you add the flag <option>-XIncoherentInstances</option>,
3541 GHC will instead pick (C), without complaining about
3542 the problem of subsequent instantiations.)
3545 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3546 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3547 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3548 it instead. In this case, GHC will refrain from
3549 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3550 as before) but, rather than rejecting the program, it will infer the type
3552 f :: C Int [b] => [b] -> [b]
3554 That postpones the question of which instance to pick to the
3555 call site for <literal>f</literal>
3556 by which time more is known about the type <literal>b</literal>.
3557 You can write this type signature yourself if you use the
3558 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3562 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3566 instance Foo [b] where
3569 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3570 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3571 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3572 declaration. The solution is to postpone the choice by adding the constraint to the context
3573 of the instance declaration, thus:
3575 instance C Int [b] => Foo [b] where
3578 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3581 The willingness to be overlapped or incoherent is a property of
3582 the <emphasis>instance declaration</emphasis> itself, controlled by the
3583 presence or otherwise of the <option>-XOverlappingInstances</option>
3584 and <option>-XIncoherentInstances</option> flags when that module is
3585 being defined. Neither flag is required in a module that imports and uses the
3586 instance declaration. Specifically, during the lookup process:
3589 An instance declaration is ignored during the lookup process if (a) a more specific
3590 match is found, and (b) the instance declaration was compiled with
3591 <option>-XOverlappingInstances</option>. The flag setting for the
3592 more-specific instance does not matter.
3595 Suppose an instance declaration does not match the constraint being looked up, but
3596 does unify with it, so that it might match when the constraint is further
3597 instantiated. Usually GHC will regard this as a reason for not committing to
3598 some other constraint. But if the instance declaration was compiled with
3599 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3600 check for that declaration.
3603 These rules make it possible for a library author to design a library that relies on
3604 overlapping instances without the library client having to know.
3607 If an instance declaration is compiled without
3608 <option>-XOverlappingInstances</option>,
3609 then that instance can never be overlapped. This could perhaps be
3610 inconvenient. Perhaps the rule should instead say that the
3611 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3612 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3613 at a usage site should be permitted regardless of how the instance declarations
3614 are compiled, if the <option>-XOverlappingInstances</option> flag is
3615 used at the usage site. (Mind you, the exact usage site can occasionally be
3616 hard to pin down.) We are interested to receive feedback on these points.
3618 <para>The <option>-XIncoherentInstances</option> flag implies the
3619 <option>-XOverlappingInstances</option> flag, but not vice versa.
3627 <sect2 id="overloaded-strings">
3628 <title>Overloaded string literals
3632 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3633 string literal has type <literal>String</literal>, but with overloaded string
3634 literals enabled (with <literal>-XOverloadedStrings</literal>)
3635 a string literal has type <literal>(IsString a) => a</literal>.
3638 This means that the usual string syntax can be used, e.g., for packed strings
3639 and other variations of string like types. String literals behave very much
3640 like integer literals, i.e., they can be used in both expressions and patterns.
3641 If used in a pattern the literal with be replaced by an equality test, in the same
3642 way as an integer literal is.
3645 The class <literal>IsString</literal> is defined as:
3647 class IsString a where
3648 fromString :: String -> a
3650 The only predefined instance is the obvious one to make strings work as usual:
3652 instance IsString [Char] where
3655 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3656 it explicitly (for example, to give an instance declaration for it), you can import it
3657 from module <literal>GHC.Exts</literal>.
3660 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3664 Each type in a default declaration must be an
3665 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3669 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3670 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3671 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3672 <emphasis>or</emphasis> <literal>IsString</literal>.
3681 import GHC.Exts( IsString(..) )
3683 newtype MyString = MyString String deriving (Eq, Show)
3684 instance IsString MyString where
3685 fromString = MyString
3687 greet :: MyString -> MyString
3688 greet "hello" = "world"
3692 print $ greet "hello"
3693 print $ greet "fool"
3697 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3698 to work since it gets translated into an equality comparison.
3704 <sect1 id="type-families">
3705 <title>Type families</title>
3708 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3709 facilitate type-level
3710 programming. Type families are a generalisation of <firstterm>associated
3711 data types</firstterm>
3712 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3713 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3714 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3715 Symposium on Principles of Programming Languages (POPL'05)”, pages
3716 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3717 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3718 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3720 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3721 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3722 themselves are described in the paper “<ulink
3723 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3724 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3726 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3727 13th ACM SIGPLAN International Conference on Functional
3728 Programming”, ACM Press, pages 51-62, 2008. Type families
3729 essentially provide type-indexed data types and named functions on types,
3730 which are useful for generic programming and highly parameterised library
3731 interfaces as well as interfaces with enhanced static information, much like
3732 dependent types. They might also be regarded as an alternative to functional
3733 dependencies, but provide a more functional style of type-level programming
3734 than the relational style of functional dependencies.
3737 Indexed type families, or type families for short, are type constructors that
3738 represent sets of types. Set members are denoted by supplying the type family
3739 constructor with type parameters, which are called <firstterm>type
3740 indices</firstterm>. The
3741 difference between vanilla parametrised type constructors and family
3742 constructors is much like between parametrically polymorphic functions and
3743 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3744 behave the same at all type instances, whereas class methods can change their
3745 behaviour in dependence on the class type parameters. Similarly, vanilla type
3746 constructors imply the same data representation for all type instances, but
3747 family constructors can have varying representation types for varying type
3751 Indexed type families come in two flavours: <firstterm>data
3752 families</firstterm> and <firstterm>type synonym
3753 families</firstterm>. They are the indexed family variants of algebraic
3754 data types and type synonyms, respectively. The instances of data families
3755 can be data types and newtypes.
3758 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3759 Additional information on the use of type families in GHC is available on
3760 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3761 Haskell wiki page on type families</ulink>.
3764 <sect2 id="data-families">
3765 <title>Data families</title>
3768 Data families appear in two flavours: (1) they can be defined on the
3770 or (2) they can appear inside type classes (in which case they are known as
3771 associated types). The former is the more general variant, as it lacks the
3772 requirement for the type-indexes to coincide with the class
3773 parameters. However, the latter can lead to more clearly structured code and
3774 compiler warnings if some type instances were - possibly accidentally -
3775 omitted. In the following, we always discuss the general toplevel form first
3776 and then cover the additional constraints placed on associated types.
3779 <sect3 id="data-family-declarations">
3780 <title>Data family declarations</title>
3783 Indexed data families are introduced by a signature, such as
3785 data family GMap k :: * -> *
3787 The special <literal>family</literal> distinguishes family from standard
3788 data declarations. The result kind annotation is optional and, as
3789 usual, defaults to <literal>*</literal> if omitted. An example is
3793 Named arguments can also be given explicit kind signatures if needed.
3795 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3796 declarations] named arguments are entirely optional, so that we can
3797 declare <literal>Array</literal> alternatively with
3799 data family Array :: * -> *
3803 <sect4 id="assoc-data-family-decl">
3804 <title>Associated data family declarations</title>
3806 When a data family is declared as part of a type class, we drop
3807 the <literal>family</literal> special. The <literal>GMap</literal>
3808 declaration takes the following form
3810 class GMapKey k where
3811 data GMap k :: * -> *
3814 In contrast to toplevel declarations, named arguments must be used for
3815 all type parameters that are to be used as type-indexes. Moreover,
3816 the argument names must be class parameters. Each class parameter may
3817 only be used at most once per associated type, but some may be omitted
3818 and they may be in an order other than in the class head. Hence, the
3819 following contrived example is admissible:
3828 <sect3 id="data-instance-declarations">
3829 <title>Data instance declarations</title>
3832 Instance declarations of data and newtype families are very similar to
3833 standard data and newtype declarations. The only two differences are
3834 that the keyword <literal>data</literal> or <literal>newtype</literal>
3835 is followed by <literal>instance</literal> and that some or all of the
3836 type arguments can be non-variable types, but may not contain forall
3837 types or type synonym families. However, data families are generally
3838 allowed in type parameters, and type synonyms are allowed as long as
3839 they are fully applied and expand to a type that is itself admissible -
3840 exactly as this is required for occurrences of type synonyms in class
3841 instance parameters. For example, the <literal>Either</literal>
3842 instance for <literal>GMap</literal> is
3844 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3846 In this example, the declaration has only one variant. In general, it
3850 Data and newtype instance declarations are only legit when an
3851 appropriate family declaration is in scope - just like class instances
3852 require the class declaration to be visible. Moreover, each instance
3853 declaration has to conform to the kind determined by its family
3854 declaration. This implies that the number of parameters of an instance
3855 declaration matches the arity determined by the kind of the family.
3856 Although, all data families are declared with
3857 the <literal>data</literal> keyword, instances can be
3858 either <literal>data</literal> or <literal>newtype</literal>s, or a mix
3862 Even if type families are defined as toplevel declarations, functions
3863 that perform different computations for different family instances still
3864 need to be defined as methods of type classes. In particular, the
3865 following is not possible:
3868 data instance T Int = A
3869 data instance T Char = B
3870 nonsence :: T a -> Int
3871 nonsence A = 1 -- WRONG: These two equations together...
3872 nonsence B = 2 -- ...will produce a type error.
3874 Given the functionality provided by GADTs (Generalised Algebraic Data
3875 Types), it might seem as if a definition, such as the above, should be
3876 feasible. However, type families are - in contrast to GADTs - are
3877 <emphasis>open;</emphasis> i.e., new instances can always be added,
3879 modules. Supporting pattern matching across different data instances
3880 would require a form of extensible case construct.
3883 <sect4 id="assoc-data-inst">
3884 <title>Associated data instances</title>
3886 When an associated data family instance is declared within a type
3887 class instance, we drop the <literal>instance</literal> keyword in the
3888 family instance. So, the <literal>Either</literal> instance
3889 for <literal>GMap</literal> becomes:
3891 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
3892 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3895 The most important point about associated family instances is that the
3896 type indexes corresponding to class parameters must be identical to
3897 the type given in the instance head; here this is the first argument
3898 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
3899 which coincides with the only class parameter. Any parameters to the
3900 family constructor that do not correspond to class parameters, need to
3901 be variables in every instance; here this is the
3902 variable <literal>v</literal>.
3905 Instances for an associated family can only appear as part of
3906 instances declarations of the class in which the family was declared -
3907 just as with the equations of the methods of a class. Also in
3908 correspondence to how methods are handled, declarations of associated
3909 types can be omitted in class instances. If an associated family
3910 instance is omitted, the corresponding instance type is not inhabited;
3911 i.e., only diverging expressions, such
3912 as <literal>undefined</literal>, can assume the type.
3916 <sect4 id="scoping-class-params">
3917 <title>Scoping of class parameters</title>
3919 In the case of multi-parameter type classes, the visibility of class
3920 parameters in the right-hand side of associated family instances
3921 depends <emphasis>solely</emphasis> on the parameters of the data
3922 family. As an example, consider the simple class declaration
3927 Only one of the two class parameters is a parameter to the data
3928 family. Hence, the following instance declaration is invalid:
3930 instance C [c] d where
3931 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
3933 Here, the right-hand side of the data instance mentions the type
3934 variable <literal>d</literal> that does not occur in its left-hand
3935 side. We cannot admit such data instances as they would compromise
3940 <sect4 id="family-class-inst">
3941 <title>Type class instances of family instances</title>
3943 Type class instances of instances of data families can be defined as
3944 usual, and in particular data instance declarations can
3945 have <literal>deriving</literal> clauses. For example, we can write
3947 data GMap () v = GMapUnit (Maybe v)
3950 which implicitly defines an instance of the form
3952 instance Show v => Show (GMap () v) where ...
3956 Note that class instances are always for
3957 particular <emphasis>instances</emphasis> of a data family and never
3958 for an entire family as a whole. This is for essentially the same
3959 reasons that we cannot define a toplevel function that performs
3960 pattern matching on the data constructors
3961 of <emphasis>different</emphasis> instances of a single type family.
3962 It would require a form of extensible case construct.
3966 <sect4 id="data-family-overlap">
3967 <title>Overlap of data instances</title>
3969 The instance declarations of a data family used in a single program
3970 may not overlap at all, independent of whether they are associated or
3971 not. In contrast to type class instances, this is not only a matter
3972 of consistency, but one of type safety.
3978 <sect3 id="data-family-import-export">
3979 <title>Import and export</title>
3982 The association of data constructors with type families is more dynamic
3983 than that is the case with standard data and newtype declarations. In
3984 the standard case, the notation <literal>T(..)</literal> in an import or
3985 export list denotes the type constructor and all the data constructors
3986 introduced in its declaration. However, a family declaration never
3987 introduces any data constructors; instead, data constructors are
3988 introduced by family instances. As a result, which data constructors
3989 are associated with a type family depends on the currently visible
3990 instance declarations for that family. Consequently, an import or
3991 export item of the form <literal>T(..)</literal> denotes the family
3992 constructor and all currently visible data constructors - in the case of
3993 an export item, these may be either imported or defined in the current
3994 module. The treatment of import and export items that explicitly list
3995 data constructors, such as <literal>GMap(GMapEither)</literal>, is
3999 <sect4 id="data-family-impexp-assoc">
4000 <title>Associated families</title>
4002 As expected, an import or export item of the
4003 form <literal>C(..)</literal> denotes all of the class' methods and
4004 associated types. However, when associated types are explicitly
4005 listed as subitems of a class, we need some new syntax, as uppercase
4006 identifiers as subitems are usually data constructors, not type
4007 constructors. To clarify that we denote types here, each associated
4008 type name needs to be prefixed by the keyword <literal>type</literal>.
4009 So for example, when explicitly listing the components of
4010 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4011 GMap, empty, lookup, insert)</literal>.
4015 <sect4 id="data-family-impexp-examples">
4016 <title>Examples</title>
4018 Assuming our running <literal>GMapKey</literal> class example, let us
4019 look at some export lists and their meaning:
4022 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4023 just the class name.</para>
4026 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4027 Exports the class, the associated type <literal>GMap</literal>
4029 functions <literal>empty</literal>, <literal>lookup</literal>,
4030 and <literal>insert</literal>. None of the data constructors is
4034 <para><literal>module GMap (GMapKey(..), GMap(..))
4035 where...</literal>: As before, but also exports all the data
4036 constructors <literal>GMapInt</literal>,
4037 <literal>GMapChar</literal>,
4038 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4039 and <literal>GMapUnit</literal>.</para>
4042 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4043 GMap(..)) where...</literal>: As before.</para>
4046 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4047 where...</literal>: As before.</para>
4052 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4053 both the class <literal>GMapKey</literal> as well as its associated
4054 type <literal>GMap</literal>. However, you cannot
4055 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4056 sub-component specifications cannot be nested. To
4057 specify <literal>GMap</literal>'s data constructors, you have to list
4062 <sect4 id="data-family-impexp-instances">
4063 <title>Instances</title>
4065 Family instances are implicitly exported, just like class instances.
4066 However, this applies only to the heads of instances, not to the data
4067 constructors an instance defines.
4075 <sect2 id="synonym-families">
4076 <title>Synonym families</title>
4079 Type families appear in two flavours: (1) they can be defined on the
4080 toplevel or (2) they can appear inside type classes (in which case they
4081 are known as associated type synonyms). The former is the more general
4082 variant, as it lacks the requirement for the type-indexes to coincide with
4083 the class parameters. However, the latter can lead to more clearly
4084 structured code and compiler warnings if some type instances were -
4085 possibly accidentally - omitted. In the following, we always discuss the
4086 general toplevel form first and then cover the additional constraints
4087 placed on associated types.
4090 <sect3 id="type-family-declarations">
4091 <title>Type family declarations</title>
4094 Indexed type families are introduced by a signature, such as
4096 type family Elem c :: *
4098 The special <literal>family</literal> distinguishes family from standard
4099 type declarations. The result kind annotation is optional and, as
4100 usual, defaults to <literal>*</literal> if omitted. An example is
4104 Parameters can also be given explicit kind signatures if needed. We
4105 call the number of parameters in a type family declaration, the family's
4106 arity, and all applications of a type family must be fully saturated
4107 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4108 and it implies that the kind of a type family is not sufficient to
4109 determine a family's arity, and hence in general, also insufficient to
4110 determine whether a type family application is well formed. As an
4111 example, consider the following declaration:
4113 type family F a b :: * -> * -- F's arity is 2,
4114 -- although it's overall kind is * -> * -> * -> *
4116 Given this declaration the following are examples of well-formed and
4119 F Char [Int] -- OK! Kind: * -> *
4120 F Char [Int] Bool -- OK! Kind: *
4121 F IO Bool -- WRONG: kind mismatch in the first argument
4122 F Bool -- WRONG: unsaturated application
4126 <sect4 id="assoc-type-family-decl">
4127 <title>Associated type family declarations</title>
4129 When a type family is declared as part of a type class, we drop
4130 the <literal>family</literal> special. The <literal>Elem</literal>
4131 declaration takes the following form
4133 class Collects ce where
4137 The argument names of the type family must be class parameters. Each
4138 class parameter may only be used at most once per associated type, but
4139 some may be omitted and they may be in an order other than in the
4140 class head. Hence, the following contrived example is admissible:
4145 These rules are exactly as for associated data families.
4150 <sect3 id="type-instance-declarations">
4151 <title>Type instance declarations</title>
4153 Instance declarations of type families are very similar to standard type
4154 synonym declarations. The only two differences are that the
4155 keyword <literal>type</literal> is followed
4156 by <literal>instance</literal> and that some or all of the type
4157 arguments can be non-variable types, but may not contain forall types or
4158 type synonym families. However, data families are generally allowed, and
4159 type synonyms are allowed as long as they are fully applied and expand
4160 to a type that is admissible - these are the exact same requirements as
4161 for data instances. For example, the <literal>[e]</literal> instance
4162 for <literal>Elem</literal> is
4164 type instance Elem [e] = e
4168 Type family instance declarations are only legitimate when an
4169 appropriate family declaration is in scope - just like class instances
4170 require the class declaration to be visible. Moreover, each instance
4171 declaration has to conform to the kind determined by its family
4172 declaration, and the number of type parameters in an instance
4173 declaration must match the number of type parameters in the family
4174 declaration. Finally, the right-hand side of a type instance must be a
4175 monotype (i.e., it may not include foralls) and after the expansion of
4176 all saturated vanilla type synonyms, no synonyms, except family synonyms
4177 may remain. Here are some examples of admissible and illegal type
4180 type family F a :: *
4181 type instance F [Int] = Int -- OK!
4182 type instance F String = Char -- OK!
4183 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4184 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4185 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4187 type family G a b :: * -> *
4188 type instance G Int = (,) -- WRONG: must be two type parameters
4189 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4193 <sect4 id="assoc-type-instance">
4194 <title>Associated type instance declarations</title>
4196 When an associated family instance is declared within a type class
4197 instance, we drop the <literal>instance</literal> keyword in the family
4198 instance. So, the <literal>[e]</literal> instance
4199 for <literal>Elem</literal> becomes:
4201 instance (Eq (Elem [e])) => Collects ([e]) where
4205 The most important point about associated family instances is that the
4206 type indexes corresponding to class parameters must be identical to the
4207 type given in the instance head; here this is <literal>[e]</literal>,
4208 which coincides with the only class parameter.
4211 Instances for an associated family can only appear as part of instances
4212 declarations of the class in which the family was declared - just as
4213 with the equations of the methods of a class. Also in correspondence to
4214 how methods are handled, declarations of associated types can be omitted
4215 in class instances. If an associated family instance is omitted, the
4216 corresponding instance type is not inhabited; i.e., only diverging
4217 expressions, such as <literal>undefined</literal>, can assume the type.
4221 <sect4 id="type-family-overlap">
4222 <title>Overlap of type synonym instances</title>
4224 The instance declarations of a type family used in a single program
4225 may only overlap if the right-hand sides of the overlapping instances
4226 coincide for the overlapping types. More formally, two instance
4227 declarations overlap if there is a substitution that makes the
4228 left-hand sides of the instances syntactically the same. Whenever
4229 that is the case, the right-hand sides of the instances must also be
4230 syntactically equal under the same substitution. This condition is
4231 independent of whether the type family is associated or not, and it is
4232 not only a matter of consistency, but one of type safety.
4235 Here are two example to illustrate the condition under which overlap
4238 type instance F (a, Int) = [a]
4239 type instance F (Int, b) = [b] -- overlap permitted
4241 type instance G (a, Int) = [a]
4242 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4247 <sect4 id="type-family-decidability">
4248 <title>Decidability of type synonym instances</title>
4250 In order to guarantee that type inference in the presence of type
4251 families decidable, we need to place a number of additional
4252 restrictions on the formation of type instance declarations (c.f.,
4253 Definition 5 (Relaxed Conditions) of “<ulink
4254 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4255 Checking with Open Type Functions</ulink>”). Instance
4256 declarations have the general form
4258 type instance F t1 .. tn = t
4260 where we require that for every type family application <literal>(G s1
4261 .. sm)</literal> in <literal>t</literal>,
4264 <para><literal>s1 .. sm</literal> do not contain any type family
4265 constructors,</para>
4268 <para>the total number of symbols (data type constructors and type
4269 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4270 in <literal>t1 .. tn</literal>, and</para>
4273 <para>for every type
4274 variable <literal>a</literal>, <literal>a</literal> occurs
4275 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4276 .. tn</literal>.</para>
4279 These restrictions are easily verified and ensure termination of type
4280 inference. However, they are not sufficient to guarantee completeness
4281 of type inference in the presence of, so called, ''loopy equalities'',
4282 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4283 a type variable is underneath a family application and data
4284 constructor application - see the above mentioned paper for details.
4287 If the option <option>-XUndecidableInstances</option> is passed to the
4288 compiler, the above restrictions are not enforced and it is on the
4289 programmer to ensure termination of the normalisation of type families
4290 during type inference.
4295 <sect3 id-="equality-constraints">
4296 <title>Equality constraints</title>
4298 Type context can include equality constraints of the form <literal>t1 ~
4299 t2</literal>, which denote that the types <literal>t1</literal>
4300 and <literal>t2</literal> need to be the same. In the presence of type
4301 families, whether two types are equal cannot generally be decided
4302 locally. Hence, the contexts of function signatures may include
4303 equality constraints, as in the following example:
4305 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4307 where we require that the element type of <literal>c1</literal>
4308 and <literal>c2</literal> are the same. In general, the
4309 types <literal>t1</literal> and <literal>t2</literal> of an equality
4310 constraint may be arbitrary monotypes; i.e., they may not contain any
4311 quantifiers, independent of whether higher-rank types are otherwise
4315 Equality constraints can also appear in class and instance contexts.
4316 The former enable a simple translation of programs using functional
4317 dependencies into programs using family synonyms instead. The general
4318 idea is to rewrite a class declaration of the form
4320 class C a b | a -> b
4324 class (F a ~ b) => C a b where
4327 That is, we represent every functional dependency (FD) <literal>a1 .. an
4328 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4329 superclass context equality <literal>F a1 .. an ~ b</literal>,
4330 essentially giving a name to the functional dependency. In class
4331 instances, we define the type instances of FD families in accordance
4332 with the class head. Method signatures are not affected by that
4336 NB: Equalities in superclass contexts are not fully implemented in
4341 <sect3 id-="ty-fams-in-instances">
4342 <title>Type families and instance declarations</title>
4343 <para>Type families require us to extend the rules for
4344 the form of instance heads, which are given
4345 in <xref linkend="flexible-instance-head"/>.
4348 <listitem><para>Data type families may appear in an instance head</para></listitem>
4349 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4351 The reason for the latter restriction is that there is no way to check for. Consider
4354 type instance F Bool = Int
4361 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4362 The situation is especially bad because the type instance for <literal>F Bool</literal>
4363 might be in another module, or even in a module that is not yet written.
4370 <sect1 id="other-type-extensions">
4371 <title>Other type system extensions</title>
4373 <sect2 id="type-restrictions">
4374 <title>Type signatures</title>
4376 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4378 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4379 that the type-class constraints in a type signature must have the
4380 form <emphasis>(class type-variable)</emphasis> or
4381 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4382 With <option>-XFlexibleContexts</option>
4383 these type signatures are perfectly OK
4386 g :: Ord (T a ()) => ...
4390 GHC imposes the following restrictions on the constraints in a type signature.
4394 forall tv1..tvn (c1, ...,cn) => type
4397 (Here, we write the "foralls" explicitly, although the Haskell source
4398 language omits them; in Haskell 98, all the free type variables of an
4399 explicit source-language type signature are universally quantified,
4400 except for the class type variables in a class declaration. However,
4401 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4410 <emphasis>Each universally quantified type variable
4411 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4413 A type variable <literal>a</literal> is "reachable" if it appears
4414 in the same constraint as either a type variable free in
4415 <literal>type</literal>, or another reachable type variable.
4416 A value with a type that does not obey
4417 this reachability restriction cannot be used without introducing
4418 ambiguity; that is why the type is rejected.
4419 Here, for example, is an illegal type:
4423 forall a. Eq a => Int
4427 When a value with this type was used, the constraint <literal>Eq tv</literal>
4428 would be introduced where <literal>tv</literal> is a fresh type variable, and
4429 (in the dictionary-translation implementation) the value would be
4430 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4431 can never know which instance of <literal>Eq</literal> to use because we never
4432 get any more information about <literal>tv</literal>.
4436 that the reachability condition is weaker than saying that <literal>a</literal> is
4437 functionally dependent on a type variable free in
4438 <literal>type</literal> (see <xref
4439 linkend="functional-dependencies"/>). The reason for this is there
4440 might be a "hidden" dependency, in a superclass perhaps. So
4441 "reachable" is a conservative approximation to "functionally dependent".
4442 For example, consider:
4444 class C a b | a -> b where ...
4445 class C a b => D a b where ...
4446 f :: forall a b. D a b => a -> a
4448 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4449 but that is not immediately apparent from <literal>f</literal>'s type.
4455 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4456 universally quantified type variables <literal>tvi</literal></emphasis>.
4458 For example, this type is OK because <literal>C a b</literal> mentions the
4459 universally quantified type variable <literal>b</literal>:
4463 forall a. C a b => burble
4467 The next type is illegal because the constraint <literal>Eq b</literal> does not
4468 mention <literal>a</literal>:
4472 forall a. Eq b => burble
4476 The reason for this restriction is milder than the other one. The
4477 excluded types are never useful or necessary (because the offending
4478 context doesn't need to be witnessed at this point; it can be floated
4479 out). Furthermore, floating them out increases sharing. Lastly,
4480 excluding them is a conservative choice; it leaves a patch of
4481 territory free in case we need it later.
4495 <sect2 id="implicit-parameters">
4496 <title>Implicit parameters</title>
4498 <para> Implicit parameters are implemented as described in
4499 "Implicit parameters: dynamic scoping with static types",
4500 J Lewis, MB Shields, E Meijer, J Launchbury,
4501 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4505 <para>(Most of the following, still rather incomplete, documentation is
4506 due to Jeff Lewis.)</para>
4508 <para>Implicit parameter support is enabled with the option
4509 <option>-XImplicitParams</option>.</para>
4512 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4513 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4514 context. In Haskell, all variables are statically bound. Dynamic
4515 binding of variables is a notion that goes back to Lisp, but was later
4516 discarded in more modern incarnations, such as Scheme. Dynamic binding
4517 can be very confusing in an untyped language, and unfortunately, typed
4518 languages, in particular Hindley-Milner typed languages like Haskell,
4519 only support static scoping of variables.
4522 However, by a simple extension to the type class system of Haskell, we
4523 can support dynamic binding. Basically, we express the use of a
4524 dynamically bound variable as a constraint on the type. These
4525 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4526 function uses a dynamically-bound variable <literal>?x</literal>
4527 of type <literal>t'</literal>". For
4528 example, the following expresses the type of a sort function,
4529 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4531 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4533 The dynamic binding constraints are just a new form of predicate in the type class system.
4536 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4537 where <literal>x</literal> is
4538 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4539 Use of this construct also introduces a new
4540 dynamic-binding constraint in the type of the expression.
4541 For example, the following definition
4542 shows how we can define an implicitly parameterized sort function in
4543 terms of an explicitly parameterized <literal>sortBy</literal> function:
4545 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4547 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4553 <title>Implicit-parameter type constraints</title>
4555 Dynamic binding constraints behave just like other type class
4556 constraints in that they are automatically propagated. Thus, when a
4557 function is used, its implicit parameters are inherited by the
4558 function that called it. For example, our <literal>sort</literal> function might be used
4559 to pick out the least value in a list:
4561 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4562 least xs = head (sort xs)
4564 Without lifting a finger, the <literal>?cmp</literal> parameter is
4565 propagated to become a parameter of <literal>least</literal> as well. With explicit
4566 parameters, the default is that parameters must always be explicit
4567 propagated. With implicit parameters, the default is to always
4571 An implicit-parameter type constraint differs from other type class constraints in the
4572 following way: All uses of a particular implicit parameter must have
4573 the same type. This means that the type of <literal>(?x, ?x)</literal>
4574 is <literal>(?x::a) => (a,a)</literal>, and not
4575 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4579 <para> You can't have an implicit parameter in the context of a class or instance
4580 declaration. For example, both these declarations are illegal:
4582 class (?x::Int) => C a where ...
4583 instance (?x::a) => Foo [a] where ...
4585 Reason: exactly which implicit parameter you pick up depends on exactly where
4586 you invoke a function. But the ``invocation'' of instance declarations is done
4587 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4588 Easiest thing is to outlaw the offending types.</para>
4590 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4592 f :: (?x :: [a]) => Int -> Int
4595 g :: (Read a, Show a) => String -> String
4598 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4599 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4600 quite unambiguous, and fixes the type <literal>a</literal>.
4605 <title>Implicit-parameter bindings</title>
4608 An implicit parameter is <emphasis>bound</emphasis> using the standard
4609 <literal>let</literal> or <literal>where</literal> binding forms.
4610 For example, we define the <literal>min</literal> function by binding
4611 <literal>cmp</literal>.
4614 min = let ?cmp = (<=) in least
4618 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4619 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4620 (including in a list comprehension, or do-notation, or pattern guards),
4621 or a <literal>where</literal> clause.
4622 Note the following points:
4625 An implicit-parameter binding group must be a
4626 collection of simple bindings to implicit-style variables (no
4627 function-style bindings, and no type signatures); these bindings are
4628 neither polymorphic or recursive.
4631 You may not mix implicit-parameter bindings with ordinary bindings in a
4632 single <literal>let</literal>
4633 expression; use two nested <literal>let</literal>s instead.
4634 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4638 You may put multiple implicit-parameter bindings in a
4639 single binding group; but they are <emphasis>not</emphasis> treated
4640 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4641 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4642 parameter. The bindings are not nested, and may be re-ordered without changing
4643 the meaning of the program.
4644 For example, consider:
4646 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4648 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4649 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4651 f :: (?x::Int) => Int -> Int
4659 <sect3><title>Implicit parameters and polymorphic recursion</title>
4662 Consider these two definitions:
4665 len1 xs = let ?acc = 0 in len_acc1 xs
4668 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4673 len2 xs = let ?acc = 0 in len_acc2 xs
4675 len_acc2 :: (?acc :: Int) => [a] -> Int
4677 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4679 The only difference between the two groups is that in the second group
4680 <literal>len_acc</literal> is given a type signature.
4681 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4682 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4683 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4684 has a type signature, the recursive call is made to the
4685 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4686 as an implicit parameter. So we get the following results in GHCi:
4693 Adding a type signature dramatically changes the result! This is a rather
4694 counter-intuitive phenomenon, worth watching out for.
4698 <sect3><title>Implicit parameters and monomorphism</title>
4700 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4701 Haskell Report) to implicit parameters. For example, consider:
4709 Since the binding for <literal>y</literal> falls under the Monomorphism
4710 Restriction it is not generalised, so the type of <literal>y</literal> is
4711 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4712 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4713 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4714 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4715 <literal>y</literal> in the body of the <literal>let</literal> will see the
4716 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4717 <literal>14</literal>.
4722 <!-- ======================= COMMENTED OUT ========================
4724 We intend to remove linear implicit parameters, so I'm at least removing
4725 them from the 6.6 user manual
4727 <sect2 id="linear-implicit-parameters">
4728 <title>Linear implicit parameters</title>
4730 Linear implicit parameters are an idea developed by Koen Claessen,
4731 Mark Shields, and Simon PJ. They address the long-standing
4732 problem that monads seem over-kill for certain sorts of problem, notably:
4735 <listitem> <para> distributing a supply of unique names </para> </listitem>
4736 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4737 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4741 Linear implicit parameters are just like ordinary implicit parameters,
4742 except that they are "linear"; that is, they cannot be copied, and
4743 must be explicitly "split" instead. Linear implicit parameters are
4744 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4745 (The '/' in the '%' suggests the split!)
4750 import GHC.Exts( Splittable )
4752 data NameSupply = ...
4754 splitNS :: NameSupply -> (NameSupply, NameSupply)
4755 newName :: NameSupply -> Name
4757 instance Splittable NameSupply where
4761 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4762 f env (Lam x e) = Lam x' (f env e)
4765 env' = extend env x x'
4766 ...more equations for f...
4768 Notice that the implicit parameter %ns is consumed
4770 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4771 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4775 So the translation done by the type checker makes
4776 the parameter explicit:
4778 f :: NameSupply -> Env -> Expr -> Expr
4779 f ns env (Lam x e) = Lam x' (f ns1 env e)
4781 (ns1,ns2) = splitNS ns
4783 env = extend env x x'
4785 Notice the call to 'split' introduced by the type checker.
4786 How did it know to use 'splitNS'? Because what it really did
4787 was to introduce a call to the overloaded function 'split',
4788 defined by the class <literal>Splittable</literal>:
4790 class Splittable a where
4793 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4794 split for name supplies. But we can simply write
4800 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4802 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4803 <literal>GHC.Exts</literal>.
4808 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4809 are entirely distinct implicit parameters: you
4810 can use them together and they won't interfere with each other. </para>
4813 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4815 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4816 in the context of a class or instance declaration. </para></listitem>
4820 <sect3><title>Warnings</title>
4823 The monomorphism restriction is even more important than usual.
4824 Consider the example above:
4826 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4827 f env (Lam x e) = Lam x' (f env e)
4830 env' = extend env x x'
4832 If we replaced the two occurrences of x' by (newName %ns), which is
4833 usually a harmless thing to do, we get:
4835 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4836 f env (Lam x e) = Lam (newName %ns) (f env e)
4838 env' = extend env x (newName %ns)
4840 But now the name supply is consumed in <emphasis>three</emphasis> places
4841 (the two calls to newName,and the recursive call to f), so
4842 the result is utterly different. Urk! We don't even have
4846 Well, this is an experimental change. With implicit
4847 parameters we have already lost beta reduction anyway, and
4848 (as John Launchbury puts it) we can't sensibly reason about
4849 Haskell programs without knowing their typing.
4854 <sect3><title>Recursive functions</title>
4855 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4858 foo :: %x::T => Int -> [Int]
4860 foo n = %x : foo (n-1)
4862 where T is some type in class Splittable.</para>
4864 Do you get a list of all the same T's or all different T's
4865 (assuming that split gives two distinct T's back)?
4867 If you supply the type signature, taking advantage of polymorphic
4868 recursion, you get what you'd probably expect. Here's the
4869 translated term, where the implicit param is made explicit:
4872 foo x n = let (x1,x2) = split x
4873 in x1 : foo x2 (n-1)
4875 But if you don't supply a type signature, GHC uses the Hindley
4876 Milner trick of using a single monomorphic instance of the function
4877 for the recursive calls. That is what makes Hindley Milner type inference
4878 work. So the translation becomes
4882 foom n = x : foom (n-1)
4886 Result: 'x' is not split, and you get a list of identical T's. So the
4887 semantics of the program depends on whether or not foo has a type signature.
4890 You may say that this is a good reason to dislike linear implicit parameters
4891 and you'd be right. That is why they are an experimental feature.
4897 ================ END OF Linear Implicit Parameters commented out -->
4899 <sect2 id="kinding">
4900 <title>Explicitly-kinded quantification</title>
4903 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4904 to give the kind explicitly as (machine-checked) documentation,
4905 just as it is nice to give a type signature for a function. On some occasions,
4906 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4907 John Hughes had to define the data type:
4909 data Set cxt a = Set [a]
4910 | Unused (cxt a -> ())
4912 The only use for the <literal>Unused</literal> constructor was to force the correct
4913 kind for the type variable <literal>cxt</literal>.
4916 GHC now instead allows you to specify the kind of a type variable directly, wherever
4917 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4920 This flag enables kind signatures in the following places:
4922 <listitem><para><literal>data</literal> declarations:
4924 data Set (cxt :: * -> *) a = Set [a]
4925 </screen></para></listitem>
4926 <listitem><para><literal>type</literal> declarations:
4928 type T (f :: * -> *) = f Int
4929 </screen></para></listitem>
4930 <listitem><para><literal>class</literal> declarations:
4932 class (Eq a) => C (f :: * -> *) a where ...
4933 </screen></para></listitem>
4934 <listitem><para><literal>forall</literal>'s in type signatures:
4936 f :: forall (cxt :: * -> *). Set cxt Int
4937 </screen></para></listitem>
4942 The parentheses are required. Some of the spaces are required too, to
4943 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4944 will get a parse error, because "<literal>::*->*</literal>" is a
4945 single lexeme in Haskell.
4949 As part of the same extension, you can put kind annotations in types
4952 f :: (Int :: *) -> Int
4953 g :: forall a. a -> (a :: *)
4957 atype ::= '(' ctype '::' kind ')
4959 The parentheses are required.
4964 <sect2 id="universal-quantification">
4965 <title>Arbitrary-rank polymorphism
4969 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4970 allows us to say exactly what this means. For example:
4978 g :: forall b. (b -> b)
4980 The two are treated identically.
4984 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4985 explicit universal quantification in
4987 For example, all the following types are legal:
4989 f1 :: forall a b. a -> b -> a
4990 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4992 f2 :: (forall a. a->a) -> Int -> Int
4993 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4995 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4997 f4 :: Int -> (forall a. a -> a)
4999 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5000 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5001 The <literal>forall</literal> makes explicit the universal quantification that
5002 is implicitly added by Haskell.
5005 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5006 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5007 shows, the polymorphic type on the left of the function arrow can be overloaded.
5010 The function <literal>f3</literal> has a rank-3 type;
5011 it has rank-2 types on the left of a function arrow.
5014 GHC has three flags to control higher-rank types:
5017 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5020 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5023 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5024 That is, you can nest <literal>forall</literal>s
5025 arbitrarily deep in function arrows.
5026 In particular, a forall-type (also called a "type scheme"),
5027 including an operational type class context, is legal:
5029 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5030 of a function arrow </para> </listitem>
5031 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5032 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5033 field type signatures.</para> </listitem>
5034 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5035 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5039 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5040 a type variable any more!
5049 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5050 the types of the constructor arguments. Here are several examples:
5056 data T a = T1 (forall b. b -> b -> b) a
5058 data MonadT m = MkMonad { return :: forall a. a -> m a,
5059 bind :: forall a b. m a -> (a -> m b) -> m b
5062 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5068 The constructors have rank-2 types:
5074 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5075 MkMonad :: forall m. (forall a. a -> m a)
5076 -> (forall a b. m a -> (a -> m b) -> m b)
5078 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5084 Notice that you don't need to use a <literal>forall</literal> if there's an
5085 explicit context. For example in the first argument of the
5086 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5087 prefixed to the argument type. The implicit <literal>forall</literal>
5088 quantifies all type variables that are not already in scope, and are
5089 mentioned in the type quantified over.
5093 As for type signatures, implicit quantification happens for non-overloaded
5094 types too. So if you write this:
5097 data T a = MkT (Either a b) (b -> b)
5100 it's just as if you had written this:
5103 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5106 That is, since the type variable <literal>b</literal> isn't in scope, it's
5107 implicitly universally quantified. (Arguably, it would be better
5108 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5109 where that is what is wanted. Feedback welcomed.)
5113 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5114 the constructor to suitable values, just as usual. For example,
5125 a3 = MkSwizzle reverse
5128 a4 = let r x = Just x
5135 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5136 mkTs f x y = [T1 f x, T1 f y]
5142 The type of the argument can, as usual, be more general than the type
5143 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5144 does not need the <literal>Ord</literal> constraint.)
5148 When you use pattern matching, the bound variables may now have
5149 polymorphic types. For example:
5155 f :: T a -> a -> (a, Char)
5156 f (T1 w k) x = (w k x, w 'c' 'd')
5158 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5159 g (MkSwizzle s) xs f = s (map f (s xs))
5161 h :: MonadT m -> [m a] -> m [a]
5162 h m [] = return m []
5163 h m (x:xs) = bind m x $ \y ->
5164 bind m (h m xs) $ \ys ->
5171 In the function <function>h</function> we use the record selectors <literal>return</literal>
5172 and <literal>bind</literal> to extract the polymorphic bind and return functions
5173 from the <literal>MonadT</literal> data structure, rather than using pattern
5179 <title>Type inference</title>
5182 In general, type inference for arbitrary-rank types is undecidable.
5183 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5184 to get a decidable algorithm by requiring some help from the programmer.
5185 We do not yet have a formal specification of "some help" but the rule is this:
5188 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5189 provides an explicit polymorphic type for x, or GHC's type inference will assume
5190 that x's type has no foralls in it</emphasis>.
5193 What does it mean to "provide" an explicit type for x? You can do that by
5194 giving a type signature for x directly, using a pattern type signature
5195 (<xref linkend="scoped-type-variables"/>), thus:
5197 \ f :: (forall a. a->a) -> (f True, f 'c')
5199 Alternatively, you can give a type signature to the enclosing
5200 context, which GHC can "push down" to find the type for the variable:
5202 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5204 Here the type signature on the expression can be pushed inwards
5205 to give a type signature for f. Similarly, and more commonly,
5206 one can give a type signature for the function itself:
5208 h :: (forall a. a->a) -> (Bool,Char)
5209 h f = (f True, f 'c')
5211 You don't need to give a type signature if the lambda bound variable
5212 is a constructor argument. Here is an example we saw earlier:
5214 f :: T a -> a -> (a, Char)
5215 f (T1 w k) x = (w k x, w 'c' 'd')
5217 Here we do not need to give a type signature to <literal>w</literal>, because
5218 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5225 <sect3 id="implicit-quant">
5226 <title>Implicit quantification</title>
5229 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5230 user-written types, if and only if there is no explicit <literal>forall</literal>,
5231 GHC finds all the type variables mentioned in the type that are not already
5232 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5236 f :: forall a. a -> a
5243 h :: forall b. a -> b -> b
5249 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5252 f :: (a -> a) -> Int
5254 f :: forall a. (a -> a) -> Int
5256 f :: (forall a. a -> a) -> Int
5259 g :: (Ord a => a -> a) -> Int
5260 -- MEANS the illegal type
5261 g :: forall a. (Ord a => a -> a) -> Int
5263 g :: (forall a. Ord a => a -> a) -> Int
5265 The latter produces an illegal type, which you might think is silly,
5266 but at least the rule is simple. If you want the latter type, you
5267 can write your for-alls explicitly. Indeed, doing so is strongly advised
5274 <sect2 id="impredicative-polymorphism">
5275 <title>Impredicative polymorphism
5277 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5278 enabled with <option>-XImpredicativeTypes</option>.
5280 that you can call a polymorphic function at a polymorphic type, and
5281 parameterise data structures over polymorphic types. For example:
5283 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5284 f (Just g) = Just (g [3], g "hello")
5287 Notice here that the <literal>Maybe</literal> type is parameterised by the
5288 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5291 <para>The technical details of this extension are described in the paper
5292 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5293 type inference for higher-rank types and impredicativity</ulink>,
5294 which appeared at ICFP 2006.
5298 <sect2 id="scoped-type-variables">
5299 <title>Lexically scoped type variables
5303 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5304 which some type signatures are simply impossible to write. For example:
5306 f :: forall a. [a] -> [a]
5312 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
5313 the entire definition of <literal>f</literal>.
5314 In particular, it is in scope at the type signature for <varname>ys</varname>.
5315 In Haskell 98 it is not possible to declare
5316 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5317 it becomes possible to do so.
5319 <para>Lexically-scoped type variables are enabled by
5320 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5322 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5323 variables work, compared to earlier releases. Read this section
5327 <title>Overview</title>
5329 <para>The design follows the following principles
5331 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5332 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5333 design.)</para></listitem>
5334 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5335 type variables. This means that every programmer-written type signature
5336 (including one that contains free scoped type variables) denotes a
5337 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5338 checker, and no inference is involved.</para></listitem>
5339 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5340 changing the program.</para></listitem>
5344 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5346 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5347 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5348 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5349 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5353 In Haskell, a programmer-written type signature is implicitly quantified over
5354 its free type variables (<ulink
5355 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5357 of the Haskell Report).
5358 Lexically scoped type variables affect this implicit quantification rules
5359 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5360 quantified. For example, if type variable <literal>a</literal> is in scope,
5363 (e :: a -> a) means (e :: a -> a)
5364 (e :: b -> b) means (e :: forall b. b->b)
5365 (e :: a -> b) means (e :: forall b. a->b)
5373 <sect3 id="decl-type-sigs">
5374 <title>Declaration type signatures</title>
5375 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5376 quantification (using <literal>forall</literal>) brings into scope the
5377 explicitly-quantified
5378 type variables, in the definition of the named function. For example:
5380 f :: forall a. [a] -> [a]
5381 f (x:xs) = xs ++ [ x :: a ]
5383 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5384 the definition of "<literal>f</literal>".
5386 <para>This only happens if:
5388 <listitem><para> The quantification in <literal>f</literal>'s type
5389 signature is explicit. For example:
5392 g (x:xs) = xs ++ [ x :: a ]
5394 This program will be rejected, because "<literal>a</literal>" does not scope
5395 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5396 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5397 quantification rules.
5399 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5400 not a pattern binding.
5403 f1 :: forall a. [a] -> [a]
5404 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5406 f2 :: forall a. [a] -> [a]
5407 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5409 f3 :: forall a. [a] -> [a]
5410 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5412 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5413 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5414 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5415 the type signature brings <literal>a</literal> into scope.
5421 <sect3 id="exp-type-sigs">
5422 <title>Expression type signatures</title>
5424 <para>An expression type signature that has <emphasis>explicit</emphasis>
5425 quantification (using <literal>forall</literal>) brings into scope the
5426 explicitly-quantified
5427 type variables, in the annotated expression. For example:
5429 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5431 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5432 type variable <literal>s</literal> into scope, in the annotated expression
5433 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5438 <sect3 id="pattern-type-sigs">
5439 <title>Pattern type signatures</title>
5441 A type signature may occur in any pattern; this is a <emphasis>pattern type
5442 signature</emphasis>.
5445 -- f and g assume that 'a' is already in scope
5446 f = \(x::Int, y::a) -> x
5448 h ((x,y) :: (Int,Bool)) = (y,x)
5450 In the case where all the type variables in the pattern type signature are
5451 already in scope (i.e. bound by the enclosing context), matters are simple: the
5452 signature simply constrains the type of the pattern in the obvious way.
5455 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5456 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5457 that are already in scope. For example:
5459 f :: forall a. [a] -> (Int, [a])
5462 (ys::[a], n) = (reverse xs, length xs) -- OK
5463 zs::[a] = xs ++ ys -- OK
5465 Just (v::b) = ... -- Not OK; b is not in scope
5467 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5468 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5472 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5473 type signature may mention a type variable that is not in scope; in this case,
5474 <emphasis>the signature brings that type variable into scope</emphasis>.
5475 This is particularly important for existential data constructors. For example:
5477 data T = forall a. MkT [a]
5480 k (MkT [t::a]) = MkT t3
5484 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5485 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5486 because it is bound by the pattern match. GHC's rule is that in this situation
5487 (and only then), a pattern type signature can mention a type variable that is
5488 not already in scope; the effect is to bring it into scope, standing for the
5489 existentially-bound type variable.
5492 When a pattern type signature binds a type variable in this way, GHC insists that the
5493 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5494 This means that any user-written type signature always stands for a completely known type.
5497 If all this seems a little odd, we think so too. But we must have
5498 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5499 could not name existentially-bound type variables in subsequent type signatures.
5502 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5503 signature is allowed to mention a lexical variable that is not already in
5505 For example, both <literal>f</literal> and <literal>g</literal> would be
5506 illegal if <literal>a</literal> was not already in scope.
5512 <!-- ==================== Commented out part about result type signatures
5514 <sect3 id="result-type-sigs">
5515 <title>Result type signatures</title>
5518 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5521 {- f assumes that 'a' is already in scope -}
5522 f x y :: [a] = [x,y,x]
5524 g = \ x :: [Int] -> [3,4]
5526 h :: forall a. [a] -> a
5530 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5531 the result of the function. Similarly, the body of the lambda in the RHS of
5532 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5533 alternative in <literal>h</literal> is <literal>a</literal>.
5535 <para> A result type signature never brings new type variables into scope.</para>
5537 There are a couple of syntactic wrinkles. First, notice that all three
5538 examples would parse quite differently with parentheses:
5540 {- f assumes that 'a' is already in scope -}
5541 f x (y :: [a]) = [x,y,x]
5543 g = \ (x :: [Int]) -> [3,4]
5545 h :: forall a. [a] -> a
5549 Now the signature is on the <emphasis>pattern</emphasis>; and
5550 <literal>h</literal> would certainly be ill-typed (since the pattern
5551 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5553 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5554 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5555 token or a parenthesised type of some sort). To see why,
5556 consider how one would parse this:
5565 <sect3 id="cls-inst-scoped-tyvars">
5566 <title>Class and instance declarations</title>
5569 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5570 scope over the methods defined in the <literal>where</literal> part. For example:
5588 <sect2 id="typing-binds">
5589 <title>Generalised typing of mutually recursive bindings</title>
5592 The Haskell Report specifies that a group of bindings (at top level, or in a
5593 <literal>let</literal> or <literal>where</literal>) should be sorted into
5594 strongly-connected components, and then type-checked in dependency order
5595 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5596 Report, Section 4.5.1</ulink>).
5597 As each group is type-checked, any binders of the group that
5599 an explicit type signature are put in the type environment with the specified
5601 and all others are monomorphic until the group is generalised
5602 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5605 <para>Following a suggestion of Mark Jones, in his paper
5606 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5608 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5610 <emphasis>the dependency analysis ignores references to variables that have an explicit
5611 type signature</emphasis>.
5612 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5613 typecheck. For example, consider:
5615 f :: Eq a => a -> Bool
5616 f x = (x == x) || g True || g "Yes"
5618 g y = (y <= y) || f True
5620 This is rejected by Haskell 98, but under Jones's scheme the definition for
5621 <literal>g</literal> is typechecked first, separately from that for
5622 <literal>f</literal>,
5623 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5624 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5625 type is generalised, to get
5627 g :: Ord a => a -> Bool
5629 Now, the definition for <literal>f</literal> is typechecked, with this type for
5630 <literal>g</literal> in the type environment.
5634 The same refined dependency analysis also allows the type signatures of
5635 mutually-recursive functions to have different contexts, something that is illegal in
5636 Haskell 98 (Section 4.5.2, last sentence). With
5637 <option>-XRelaxedPolyRec</option>
5638 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5639 type signatures; in practice this means that only variables bound by the same
5640 pattern binding must have the same context. For example, this is fine:
5642 f :: Eq a => a -> Bool
5643 f x = (x == x) || g True
5645 g :: Ord a => a -> Bool
5646 g y = (y <= y) || f True
5652 <!-- ==================== End of type system extensions ================= -->
5654 <!-- ====================== TEMPLATE HASKELL ======================= -->
5656 <sect1 id="template-haskell">
5657 <title>Template Haskell</title>
5659 <para>Template Haskell allows you to do compile-time meta-programming in
5662 the main technical innovations is discussed in "<ulink
5663 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5664 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5667 There is a Wiki page about
5668 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5669 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5673 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5674 Haskell library reference material</ulink>
5675 (look for module <literal>Language.Haskell.TH</literal>).
5676 Many changes to the original design are described in
5677 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5678 Notes on Template Haskell version 2</ulink>.
5679 Not all of these changes are in GHC, however.
5682 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5683 as a worked example to help get you started.
5687 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5688 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5693 <title>Syntax</title>
5695 <para> Template Haskell has the following new syntactic
5696 constructions. You need to use the flag
5697 <option>-XTemplateHaskell</option>
5698 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5699 </indexterm>to switch these syntactic extensions on
5700 (<option>-XTemplateHaskell</option> is no longer implied by
5701 <option>-fglasgow-exts</option>).</para>
5705 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5706 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5707 There must be no space between the "$" and the identifier or parenthesis. This use
5708 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5709 of "." as an infix operator. If you want the infix operator, put spaces around it.
5711 <para> A splice can occur in place of
5713 <listitem><para> an expression; the spliced expression must
5714 have type <literal>Q Exp</literal></para></listitem>
5715 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5718 Inside a splice you can can only call functions defined in imported modules,
5719 not functions defined elsewhere in the same module.</listitem>
5723 A expression quotation is written in Oxford brackets, thus:
5725 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5726 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5727 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5728 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5729 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5730 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5731 </itemizedlist></para></listitem>
5734 A quasi-quotation can appear in either a pattern context or an
5735 expression context and is also written in Oxford brackets:
5737 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5738 where the "..." is an arbitrary string; a full description of the
5739 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5740 </itemizedlist></para></listitem>
5743 A name can be quoted with either one or two prefix single quotes:
5745 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5746 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5747 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5749 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5750 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5753 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5754 may also be given as an argument to the <literal>reify</literal> function.
5760 (Compared to the original paper, there are many differences of detail.
5761 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5762 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5763 Type splices are not implemented, and neither are pattern splices or quotations.
5767 <sect2> <title> Using Template Haskell </title>
5771 The data types and monadic constructor functions for Template Haskell are in the library
5772 <literal>Language.Haskell.THSyntax</literal>.
5776 You can only run a function at compile time if it is imported from another module. That is,
5777 you can't define a function in a module, and call it from within a splice in the same module.
5778 (It would make sense to do so, but it's hard to implement.)
5782 You can only run a function at compile time if it is imported
5783 from another module <emphasis>that is not part of a mutually-recursive group of modules
5784 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5785 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5786 splice is to be run.</para>
5788 For example, when compiling module A,
5789 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5790 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5794 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5797 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5798 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5799 compiles and runs a program, and then looks at the result. So it's important that
5800 the program it compiles produces results whose representations are identical to
5801 those of the compiler itself.
5805 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5806 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5811 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5812 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5813 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5820 -- Import our template "pr"
5821 import Printf ( pr )
5823 -- The splice operator $ takes the Haskell source code
5824 -- generated at compile time by "pr" and splices it into
5825 -- the argument of "putStrLn".
5826 main = putStrLn ( $(pr "Hello") )
5832 -- Skeletal printf from the paper.
5833 -- It needs to be in a separate module to the one where
5834 -- you intend to use it.
5836 -- Import some Template Haskell syntax
5837 import Language.Haskell.TH
5839 -- Describe a format string
5840 data Format = D | S | L String
5842 -- Parse a format string. This is left largely to you
5843 -- as we are here interested in building our first ever
5844 -- Template Haskell program and not in building printf.
5845 parse :: String -> [Format]
5848 -- Generate Haskell source code from a parsed representation
5849 -- of the format string. This code will be spliced into
5850 -- the module which calls "pr", at compile time.
5851 gen :: [Format] -> Q Exp
5852 gen [D] = [| \n -> show n |]
5853 gen [S] = [| \s -> s |]
5854 gen [L s] = stringE s
5856 -- Here we generate the Haskell code for the splice
5857 -- from an input format string.
5858 pr :: String -> Q Exp
5859 pr s = gen (parse s)
5862 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5865 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5868 <para>Run "main.exe" and here is your output:</para>
5878 <title>Using Template Haskell with Profiling</title>
5879 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5881 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5882 interpreter to run the splice expressions. The bytecode interpreter
5883 runs the compiled expression on top of the same runtime on which GHC
5884 itself is running; this means that the compiled code referred to by
5885 the interpreted expression must be compatible with this runtime, and
5886 in particular this means that object code that is compiled for
5887 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5888 expression, because profiled object code is only compatible with the
5889 profiling version of the runtime.</para>
5891 <para>This causes difficulties if you have a multi-module program
5892 containing Template Haskell code and you need to compile it for
5893 profiling, because GHC cannot load the profiled object code and use it
5894 when executing the splices. Fortunately GHC provides a workaround.
5895 The basic idea is to compile the program twice:</para>
5899 <para>Compile the program or library first the normal way, without
5900 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5903 <para>Then compile it again with <option>-prof</option>, and
5904 additionally use <option>-osuf
5905 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5906 to name the object files differently (you can choose any suffix
5907 that isn't the normal object suffix here). GHC will automatically
5908 load the object files built in the first step when executing splice
5909 expressions. If you omit the <option>-osuf</option> flag when
5910 building with <option>-prof</option> and Template Haskell is used,
5911 GHC will emit an error message. </para>
5916 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5917 <para>Quasi-quotation allows patterns and expressions to be written using
5918 programmer-defined concrete syntax; the motivation behind the extension and
5919 several examples are documented in
5920 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5921 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5922 2007). The example below shows how to write a quasiquoter for a simple
5923 expression language.</para>
5926 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5927 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5928 functions for quoting expressions and patterns, respectively. The first argument
5929 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5930 context of the quasi-quotation statement determines which of the two parsers is
5931 called: if the quasi-quotation occurs in an expression context, the expression
5932 parser is called, and if it occurs in a pattern context, the pattern parser is
5936 Note that in the example we make use of an antiquoted
5937 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5938 (this syntax for anti-quotation was defined by the parser's
5939 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5940 integer value argument of the constructor <literal>IntExpr</literal> when
5941 pattern matching. Please see the referenced paper for further details regarding
5942 anti-quotation as well as the description of a technique that uses SYB to
5943 leverage a single parser of type <literal>String -> a</literal> to generate both
5944 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5945 pattern parser that returns a value of type <literal>Q Pat</literal>.
5948 <para>In general, a quasi-quote has the form
5949 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5950 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5951 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5952 can be arbitrary, and may contain newlines.
5955 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5956 the example, <literal>expr</literal> cannot be defined
5957 in <literal>Main.hs</literal> where it is used, but must be imported.
5968 main = do { print $ eval [$expr|1 + 2|]
5970 { [$expr|'int:n|] -> print n
5979 import qualified Language.Haskell.TH as TH
5980 import Language.Haskell.TH.Quasi
5982 data Expr = IntExpr Integer
5983 | AntiIntExpr String
5984 | BinopExpr BinOp Expr Expr
5986 deriving(Show, Typeable, Data)
5992 deriving(Show, Typeable, Data)
5994 eval :: Expr -> Integer
5995 eval (IntExpr n) = n
5996 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6003 expr = QuasiQuoter parseExprExp parseExprPat
6005 -- Parse an Expr, returning its representation as
6006 -- either a Q Exp or a Q Pat. See the referenced paper
6007 -- for how to use SYB to do this by writing a single
6008 -- parser of type String -> Expr instead of two
6009 -- separate parsers.
6011 parseExprExp :: String -> Q Exp
6014 parseExprPat :: String -> Q Pat
6018 <para>Now run the compiler:
6021 $ ghc --make -XQuasiQuotes Main.hs -o main
6024 <para>Run "main" and here is your output:</para>
6036 <!-- ===================== Arrow notation =================== -->
6038 <sect1 id="arrow-notation">
6039 <title>Arrow notation
6042 <para>Arrows are a generalization of monads introduced by John Hughes.
6043 For more details, see
6048 “Generalising Monads to Arrows”,
6049 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6050 pp67–111, May 2000.
6051 The paper that introduced arrows: a friendly introduction, motivated with
6052 programming examples.
6058 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6059 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6060 Introduced the notation described here.
6066 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6067 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6074 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6075 John Hughes, in <citetitle>5th International Summer School on
6076 Advanced Functional Programming</citetitle>,
6077 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6079 This paper includes another introduction to the notation,
6080 with practical examples.
6086 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6087 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6088 A terse enumeration of the formal rules used
6089 (extracted from comments in the source code).
6095 The arrows web page at
6096 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6101 With the <option>-XArrows</option> flag, GHC supports the arrow
6102 notation described in the second of these papers,
6103 translating it using combinators from the
6104 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6106 What follows is a brief introduction to the notation;
6107 it won't make much sense unless you've read Hughes's paper.
6110 <para>The extension adds a new kind of expression for defining arrows:
6112 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6113 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6115 where <literal>proc</literal> is a new keyword.
6116 The variables of the pattern are bound in the body of the
6117 <literal>proc</literal>-expression,
6118 which is a new sort of thing called a <firstterm>command</firstterm>.
6119 The syntax of commands is as follows:
6121 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6122 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6123 | <replaceable>cmd</replaceable><superscript>0</superscript>
6125 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6126 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6127 infix operators as for expressions, and
6129 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6130 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6131 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6132 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6133 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6134 | <replaceable>fcmd</replaceable>
6136 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6137 | ( <replaceable>cmd</replaceable> )
6138 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6140 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6141 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6142 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6143 | <replaceable>cmd</replaceable>
6145 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6146 except that the bodies are commands instead of expressions.
6150 Commands produce values, but (like monadic computations)
6151 may yield more than one value,
6152 or none, and may do other things as well.
6153 For the most part, familiarity with monadic notation is a good guide to
6155 However the values of expressions, even monadic ones,
6156 are determined by the values of the variables they contain;
6157 this is not necessarily the case for commands.
6161 A simple example of the new notation is the expression
6163 proc x -> f -< x+1
6165 We call this a <firstterm>procedure</firstterm> or
6166 <firstterm>arrow abstraction</firstterm>.
6167 As with a lambda expression, the variable <literal>x</literal>
6168 is a new variable bound within the <literal>proc</literal>-expression.
6169 It refers to the input to the arrow.
6170 In the above example, <literal>-<</literal> is not an identifier but an
6171 new reserved symbol used for building commands from an expression of arrow
6172 type and an expression to be fed as input to that arrow.
6173 (The weird look will make more sense later.)
6174 It may be read as analogue of application for arrows.
6175 The above example is equivalent to the Haskell expression
6177 arr (\ x -> x+1) >>> f
6179 That would make no sense if the expression to the left of
6180 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6181 More generally, the expression to the left of <literal>-<</literal>
6182 may not involve any <firstterm>local variable</firstterm>,
6183 i.e. a variable bound in the current arrow abstraction.
6184 For such a situation there is a variant <literal>-<<</literal>, as in
6186 proc x -> f x -<< x+1
6188 which is equivalent to
6190 arr (\ x -> (f x, x+1)) >>> app
6192 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6194 Such an arrow is equivalent to a monad, so if you're using this form
6195 you may find a monadic formulation more convenient.
6199 <title>do-notation for commands</title>
6202 Another form of command is a form of <literal>do</literal>-notation.
6203 For example, you can write
6212 You can read this much like ordinary <literal>do</literal>-notation,
6213 but with commands in place of monadic expressions.
6214 The first line sends the value of <literal>x+1</literal> as an input to
6215 the arrow <literal>f</literal>, and matches its output against
6216 <literal>y</literal>.
6217 In the next line, the output is discarded.
6218 The arrow <function>returnA</function> is defined in the
6219 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6220 module as <literal>arr id</literal>.
6221 The above example is treated as an abbreviation for
6223 arr (\ x -> (x, x)) >>>
6224 first (arr (\ x -> x+1) >>> f) >>>
6225 arr (\ (y, x) -> (y, (x, y))) >>>
6226 first (arr (\ y -> 2*y) >>> g) >>>
6228 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6229 first (arr (\ (x, z) -> x*z) >>> h) >>>
6230 arr (\ (t, z) -> t+z) >>>
6233 Note that variables not used later in the composition are projected out.
6234 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6236 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6237 module, this reduces to
6239 arr (\ x -> (x+1, x)) >>>
6241 arr (\ (y, x) -> (2*y, (x, y))) >>>
6243 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6245 arr (\ (t, z) -> t+z)
6247 which is what you might have written by hand.
6248 With arrow notation, GHC keeps track of all those tuples of variables for you.
6252 Note that although the above translation suggests that
6253 <literal>let</literal>-bound variables like <literal>z</literal> must be
6254 monomorphic, the actual translation produces Core,
6255 so polymorphic variables are allowed.
6259 It's also possible to have mutually recursive bindings,
6260 using the new <literal>rec</literal> keyword, as in the following example:
6262 counter :: ArrowCircuit a => a Bool Int
6263 counter = proc reset -> do
6264 rec output <- returnA -< if reset then 0 else next
6265 next <- delay 0 -< output+1
6266 returnA -< output
6268 The translation of such forms uses the <function>loop</function> combinator,
6269 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6275 <title>Conditional commands</title>
6278 In the previous example, we used a conditional expression to construct the
6280 Sometimes we want to conditionally execute different commands, as in
6287 which is translated to
6289 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6290 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6292 Since the translation uses <function>|||</function>,
6293 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6297 There are also <literal>case</literal> commands, like
6303 y <- h -< (x1, x2)
6307 The syntax is the same as for <literal>case</literal> expressions,
6308 except that the bodies of the alternatives are commands rather than expressions.
6309 The translation is similar to that of <literal>if</literal> commands.
6315 <title>Defining your own control structures</title>
6318 As we're seen, arrow notation provides constructs,
6319 modelled on those for expressions,
6320 for sequencing, value recursion and conditionals.
6321 But suitable combinators,
6322 which you can define in ordinary Haskell,
6323 may also be used to build new commands out of existing ones.
6324 The basic idea is that a command defines an arrow from environments to values.
6325 These environments assign values to the free local variables of the command.
6326 Thus combinators that produce arrows from arrows
6327 may also be used to build commands from commands.
6328 For example, the <literal>ArrowChoice</literal> class includes a combinator
6330 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6332 so we can use it to build commands:
6334 expr' = proc x -> do
6337 symbol Plus -< ()
6338 y <- term -< ()
6341 symbol Minus -< ()
6342 y <- term -< ()
6345 (The <literal>do</literal> on the first line is needed to prevent the first
6346 <literal><+> ...</literal> from being interpreted as part of the
6347 expression on the previous line.)
6348 This is equivalent to
6350 expr' = (proc x -> returnA -< x)
6351 <+> (proc x -> do
6352 symbol Plus -< ()
6353 y <- term -< ()
6355 <+> (proc x -> do
6356 symbol Minus -< ()
6357 y <- term -< ()
6360 It is essential that this operator be polymorphic in <literal>e</literal>
6361 (representing the environment input to the command
6362 and thence to its subcommands)
6363 and satisfy the corresponding naturality property
6365 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6367 at least for strict <literal>k</literal>.
6368 (This should be automatic if you're not using <function>seq</function>.)
6369 This ensures that environments seen by the subcommands are environments
6370 of the whole command,
6371 and also allows the translation to safely trim these environments.
6372 The operator must also not use any variable defined within the current
6377 We could define our own operator
6379 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6380 untilA body cond = proc x ->
6381 b <- cond -< x
6382 if b then returnA -< ()
6385 untilA body cond -< x
6387 and use it in the same way.
6388 Of course this infix syntax only makes sense for binary operators;
6389 there is also a more general syntax involving special brackets:
6393 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6400 <title>Primitive constructs</title>
6403 Some operators will need to pass additional inputs to their subcommands.
6404 For example, in an arrow type supporting exceptions,
6405 the operator that attaches an exception handler will wish to pass the
6406 exception that occurred to the handler.
6407 Such an operator might have a type
6409 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6411 where <literal>Ex</literal> is the type of exceptions handled.
6412 You could then use this with arrow notation by writing a command
6414 body `handleA` \ ex -> handler
6416 so that if an exception is raised in the command <literal>body</literal>,
6417 the variable <literal>ex</literal> is bound to the value of the exception
6418 and the command <literal>handler</literal>,
6419 which typically refers to <literal>ex</literal>, is entered.
6420 Though the syntax here looks like a functional lambda,
6421 we are talking about commands, and something different is going on.
6422 The input to the arrow represented by a command consists of values for
6423 the free local variables in the command, plus a stack of anonymous values.
6424 In all the prior examples, this stack was empty.
6425 In the second argument to <function>handleA</function>,
6426 this stack consists of one value, the value of the exception.
6427 The command form of lambda merely gives this value a name.
6432 the values on the stack are paired to the right of the environment.
6433 So operators like <function>handleA</function> that pass
6434 extra inputs to their subcommands can be designed for use with the notation
6435 by pairing the values with the environment in this way.
6436 More precisely, the type of each argument of the operator (and its result)
6437 should have the form
6439 a (...(e,t1), ... tn) t
6441 where <replaceable>e</replaceable> is a polymorphic variable
6442 (representing the environment)
6443 and <replaceable>ti</replaceable> are the types of the values on the stack,
6444 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6445 The polymorphic variable <replaceable>e</replaceable> must not occur in
6446 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6447 <replaceable>t</replaceable>.
6448 However the arrows involved need not be the same.
6449 Here are some more examples of suitable operators:
6451 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6452 runReader :: ... => a e c -> a' (e,State) c
6453 runState :: ... => a e c -> a' (e,State) (c,State)
6455 We can supply the extra input required by commands built with the last two
6456 by applying them to ordinary expressions, as in
6460 (|runReader (do { ... })|) s
6462 which adds <literal>s</literal> to the stack of inputs to the command
6463 built using <function>runReader</function>.
6467 The command versions of lambda abstraction and application are analogous to
6468 the expression versions.
6469 In particular, the beta and eta rules describe equivalences of commands.
6470 These three features (operators, lambda abstraction and application)
6471 are the core of the notation; everything else can be built using them,
6472 though the results would be somewhat clumsy.
6473 For example, we could simulate <literal>do</literal>-notation by defining
6475 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6476 u `bind` f = returnA &&& u >>> f
6478 bind_ :: Arrow a => a e b -> a e c -> a e c
6479 u `bind_` f = u `bind` (arr fst >>> f)
6481 We could simulate <literal>if</literal> by defining
6483 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6484 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6491 <title>Differences with the paper</title>
6496 <para>Instead of a single form of arrow application (arrow tail) with two
6497 translations, the implementation provides two forms
6498 <quote><literal>-<</literal></quote> (first-order)
6499 and <quote><literal>-<<</literal></quote> (higher-order).
6504 <para>User-defined operators are flagged with banana brackets instead of
6505 a new <literal>form</literal> keyword.
6514 <title>Portability</title>
6517 Although only GHC implements arrow notation directly,
6518 there is also a preprocessor
6520 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6521 that translates arrow notation into Haskell 98
6522 for use with other Haskell systems.
6523 You would still want to check arrow programs with GHC;
6524 tracing type errors in the preprocessor output is not easy.
6525 Modules intended for both GHC and the preprocessor must observe some
6526 additional restrictions:
6531 The module must import
6532 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6538 The preprocessor cannot cope with other Haskell extensions.
6539 These would have to go in separate modules.
6545 Because the preprocessor targets Haskell (rather than Core),
6546 <literal>let</literal>-bound variables are monomorphic.
6557 <!-- ==================== BANG PATTERNS ================= -->
6559 <sect1 id="bang-patterns">
6560 <title>Bang patterns
6561 <indexterm><primary>Bang patterns</primary></indexterm>
6563 <para>GHC supports an extension of pattern matching called <emphasis>bang
6564 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
6566 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6567 prime feature description</ulink> contains more discussion and examples
6568 than the material below.
6571 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6574 <sect2 id="bang-patterns-informal">
6575 <title>Informal description of bang patterns
6578 The main idea is to add a single new production to the syntax of patterns:
6582 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6583 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6588 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6589 whereas without the bang it would be lazy.
6590 Bang patterns can be nested of course:
6594 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6595 <literal>y</literal>.
6596 A bang only really has an effect if it precedes a variable or wild-card pattern:
6601 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
6602 forces evaluation anyway does nothing.
6604 Bang patterns work in <literal>case</literal> expressions too, of course:
6606 g5 x = let y = f x in body
6607 g6 x = case f x of { y -> body }
6608 g7 x = case f x of { !y -> body }
6610 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6611 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6612 result, and then evaluates <literal>body</literal>.
6614 Bang patterns work in <literal>let</literal> and <literal>where</literal>
6615 definitions too. For example:
6619 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
6620 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
6621 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
6622 in a function argument <literal>![x,y]</literal> means the
6623 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
6624 is part of the syntax of <literal>let</literal> bindings.
6629 <sect2 id="bang-patterns-sem">
6630 <title>Syntax and semantics
6634 We add a single new production to the syntax of patterns:
6638 There is one problem with syntactic ambiguity. Consider:
6642 Is this a definition of the infix function "<literal>(!)</literal>",
6643 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6644 ambiguity in favour of the latter. If you want to define
6645 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6650 The semantics of Haskell pattern matching is described in <ulink
6651 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6652 Section 3.17.2</ulink> of the Haskell Report. To this description add
6653 one extra item 10, saying:
6654 <itemizedlist><listitem><para>Matching
6655 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6656 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6657 <listitem><para>otherwise, <literal>pat</literal> is matched against
6658 <literal>v</literal></para></listitem>
6660 </para></listitem></itemizedlist>
6661 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6662 Section 3.17.3</ulink>, add a new case (t):
6664 case v of { !pat -> e; _ -> e' }
6665 = v `seq` case v of { pat -> e; _ -> e' }
6668 That leaves let expressions, whose translation is given in
6669 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6671 of the Haskell Report.
6672 In the translation box, first apply
6673 the following transformation: for each pattern <literal>pi</literal> that is of
6674 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6675 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6676 have a bang at the top, apply the rules in the existing box.
6678 <para>The effect of the let rule is to force complete matching of the pattern
6679 <literal>qi</literal> before evaluation of the body is begun. The bang is
6680 retained in the translated form in case <literal>qi</literal> is a variable,
6688 The let-binding can be recursive. However, it is much more common for
6689 the let-binding to be non-recursive, in which case the following law holds:
6690 <literal>(let !p = rhs in body)</literal>
6692 <literal>(case rhs of !p -> body)</literal>
6695 A pattern with a bang at the outermost level is not allowed at the top level of
6701 <!-- ==================== ASSERTIONS ================= -->
6703 <sect1 id="assertions">
6705 <indexterm><primary>Assertions</primary></indexterm>
6709 If you want to make use of assertions in your standard Haskell code, you
6710 could define a function like the following:
6716 assert :: Bool -> a -> a
6717 assert False x = error "assertion failed!"
6724 which works, but gives you back a less than useful error message --
6725 an assertion failed, but which and where?
6729 One way out is to define an extended <function>assert</function> function which also
6730 takes a descriptive string to include in the error message and
6731 perhaps combine this with the use of a pre-processor which inserts
6732 the source location where <function>assert</function> was used.
6736 Ghc offers a helping hand here, doing all of this for you. For every
6737 use of <function>assert</function> in the user's source:
6743 kelvinToC :: Double -> Double
6744 kelvinToC k = assert (k >= 0.0) (k+273.15)
6750 Ghc will rewrite this to also include the source location where the
6757 assert pred val ==> assertError "Main.hs|15" pred val
6763 The rewrite is only performed by the compiler when it spots
6764 applications of <function>Control.Exception.assert</function>, so you
6765 can still define and use your own versions of
6766 <function>assert</function>, should you so wish. If not, import
6767 <literal>Control.Exception</literal> to make use
6768 <function>assert</function> in your code.
6772 GHC ignores assertions when optimisation is turned on with the
6773 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6774 <literal>assert pred e</literal> will be rewritten to
6775 <literal>e</literal>. You can also disable assertions using the
6776 <option>-fignore-asserts</option>
6777 option<indexterm><primary><option>-fignore-asserts</option></primary>
6778 </indexterm>.</para>
6781 Assertion failures can be caught, see the documentation for the
6782 <literal>Control.Exception</literal> library for the details.
6788 <!-- =============================== PRAGMAS =========================== -->
6790 <sect1 id="pragmas">
6791 <title>Pragmas</title>
6793 <indexterm><primary>pragma</primary></indexterm>
6795 <para>GHC supports several pragmas, or instructions to the
6796 compiler placed in the source code. Pragmas don't normally affect
6797 the meaning of the program, but they might affect the efficiency
6798 of the generated code.</para>
6800 <para>Pragmas all take the form
6802 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6804 where <replaceable>word</replaceable> indicates the type of
6805 pragma, and is followed optionally by information specific to that
6806 type of pragma. Case is ignored in
6807 <replaceable>word</replaceable>. The various values for
6808 <replaceable>word</replaceable> that GHC understands are described
6809 in the following sections; any pragma encountered with an
6810 unrecognised <replaceable>word</replaceable> is (silently)
6811 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6812 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6814 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6815 pragma must precede the <literal>module</literal> keyword in the file.
6816 There can be as many file-header pragmas as you please, and they can be
6817 preceded or followed by comments.</para>
6819 <sect2 id="language-pragma">
6820 <title>LANGUAGE pragma</title>
6822 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6823 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6825 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6827 It is the intention that all Haskell compilers support the
6828 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6829 all extensions are supported by all compilers, of
6830 course. The <literal>LANGUAGE</literal> pragma should be used instead
6831 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6833 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6835 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6837 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6839 <para>Every language extension can also be turned into a command-line flag
6840 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6841 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6844 <para>A list of all supported language extensions can be obtained by invoking
6845 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6847 <para>Any extension from the <literal>Extension</literal> type defined in
6849 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6850 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6854 <sect2 id="options-pragma">
6855 <title>OPTIONS_GHC pragma</title>
6856 <indexterm><primary>OPTIONS_GHC</primary>
6858 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6861 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6862 additional options that are given to the compiler when compiling
6863 this source file. See <xref linkend="source-file-options"/> for
6866 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6867 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6870 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6872 <sect2 id="include-pragma">
6873 <title>INCLUDE pragma</title>
6875 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6876 of C header files that should be <literal>#include</literal>'d into
6877 the C source code generated by the compiler for the current module (if
6878 compiling via C). For example:</para>
6881 {-# INCLUDE "foo.h" #-}
6882 {-# INCLUDE <stdio.h> #-}</programlisting>
6884 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6886 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6887 to the <option>-#include</option> option (<xref
6888 linkend="options-C-compiler" />), because the
6889 <literal>INCLUDE</literal> pragma is understood by other
6890 compilers. Yet another alternative is to add the include file to each
6891 <literal>foreign import</literal> declaration in your code, but we
6892 don't recommend using this approach with GHC.</para>
6895 <sect2 id="warning-deprecated-pragma">
6896 <title>WARNING and DEPRECATED pragmas</title>
6897 <indexterm><primary>WARNING</primary></indexterm>
6898 <indexterm><primary>DEPRECATED</primary></indexterm>
6900 <para>The WARNING pragma allows you to attach an arbitrary warning
6901 to a particular function, class, or type.
6902 A DEPRECATED pragma lets you specify that
6903 a particular function, class, or type is deprecated.
6904 There are two ways of using these pragmas.
6908 <para>You can work on an entire module thus:</para>
6910 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6915 module Wibble {-# WARNING "This is an unstable interface." #-} where
6918 <para>When you compile any module that import
6919 <literal>Wibble</literal>, GHC will print the specified
6924 <para>You can attach a warning to a function, class, type, or data constructor, with the
6925 following top-level declarations:</para>
6927 {-# DEPRECATED f, C, T "Don't use these" #-}
6928 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6930 <para>When you compile any module that imports and uses any
6931 of the specified entities, GHC will print the specified
6933 <para> You can only attach to entities declared at top level in the module
6934 being compiled, and you can only use unqualified names in the list of
6935 entities. A capitalised name, such as <literal>T</literal>
6936 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6937 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6938 both are in scope. If both are in scope, there is currently no way to
6939 specify one without the other (c.f. fixities
6940 <xref linkend="infix-tycons"/>).</para>
6943 Warnings and deprecations are not reported for
6944 (a) uses within the defining module, and
6945 (b) uses in an export list.
6946 The latter reduces spurious complaints within a library
6947 in which one module gathers together and re-exports
6948 the exports of several others.
6950 <para>You can suppress the warnings with the flag
6951 <option>-fno-warn-warnings-deprecations</option>.</para>
6954 <sect2 id="inline-noinline-pragma">
6955 <title>INLINE and NOINLINE pragmas</title>
6957 <para>These pragmas control the inlining of function
6960 <sect3 id="inline-pragma">
6961 <title>INLINE pragma</title>
6962 <indexterm><primary>INLINE</primary></indexterm>
6964 <para>GHC (with <option>-O</option>, as always) tries to
6965 inline (or “unfold”) functions/values that are
6966 “small enough,” thus avoiding the call overhead
6967 and possibly exposing other more-wonderful optimisations.
6968 Normally, if GHC decides a function is “too
6969 expensive” to inline, it will not do so, nor will it
6970 export that unfolding for other modules to use.</para>
6972 <para>The sledgehammer you can bring to bear is the
6973 <literal>INLINE</literal><indexterm><primary>INLINE
6974 pragma</primary></indexterm> pragma, used thusly:</para>
6977 key_function :: Int -> String -> (Bool, Double)
6978 {-# INLINE key_function #-}
6981 <para>The major effect of an <literal>INLINE</literal> pragma
6982 is to declare a function's “cost” to be very low.
6983 The normal unfolding machinery will then be very keen to
6984 inline it. However, an <literal>INLINE</literal> pragma for a
6985 function "<literal>f</literal>" has a number of other effects:
6988 No functions are inlined into <literal>f</literal>. Otherwise
6989 GHC might inline a big function into <literal>f</literal>'s right hand side,
6990 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6993 The float-in, float-out, and common-sub-expression transformations are not
6994 applied to the body of <literal>f</literal>.
6997 An INLINE function is not worker/wrappered by strictness analysis.
6998 It's going to be inlined wholesale instead.
7001 All of these effects are aimed at ensuring that what gets inlined is
7002 exactly what you asked for, no more and no less.
7004 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7005 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7006 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7007 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7008 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7009 when there is no choice even an INLINE function can be selected, in which case
7010 the INLINE pragma is ignored.
7011 For example, for a self-recursive function, the loop breaker can only be the function
7012 itself, so an INLINE pragma is always ignored.</para>
7014 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7015 function can be put anywhere its type signature could be
7018 <para><literal>INLINE</literal> pragmas are a particularly
7020 <literal>then</literal>/<literal>return</literal> (or
7021 <literal>bind</literal>/<literal>unit</literal>) functions in
7022 a monad. For example, in GHC's own
7023 <literal>UniqueSupply</literal> monad code, we have:</para>
7026 {-# INLINE thenUs #-}
7027 {-# INLINE returnUs #-}
7030 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7031 linkend="noinline-pragma"/>).</para>
7033 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7034 so if you want your code to be HBC-compatible you'll have to surround
7035 the pragma with C pre-processor directives
7036 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7040 <sect3 id="noinline-pragma">
7041 <title>NOINLINE pragma</title>
7043 <indexterm><primary>NOINLINE</primary></indexterm>
7044 <indexterm><primary>NOTINLINE</primary></indexterm>
7046 <para>The <literal>NOINLINE</literal> pragma does exactly what
7047 you'd expect: it stops the named function from being inlined
7048 by the compiler. You shouldn't ever need to do this, unless
7049 you're very cautious about code size.</para>
7051 <para><literal>NOTINLINE</literal> is a synonym for
7052 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7053 specified by Haskell 98 as the standard way to disable
7054 inlining, so it should be used if you want your code to be
7058 <sect3 id="phase-control">
7059 <title>Phase control</title>
7061 <para> Sometimes you want to control exactly when in GHC's
7062 pipeline the INLINE pragma is switched on. Inlining happens
7063 only during runs of the <emphasis>simplifier</emphasis>. Each
7064 run of the simplifier has a different <emphasis>phase
7065 number</emphasis>; the phase number decreases towards zero.
7066 If you use <option>-dverbose-core2core</option> you'll see the
7067 sequence of phase numbers for successive runs of the
7068 simplifier. In an INLINE pragma you can optionally specify a
7072 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7073 <literal>f</literal>
7074 until phase <literal>k</literal>, but from phase
7075 <literal>k</literal> onwards be very keen to inline it.
7078 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7079 <literal>f</literal>
7080 until phase <literal>k</literal>, but from phase
7081 <literal>k</literal> onwards do not inline it.
7084 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7085 <literal>f</literal>
7086 until phase <literal>k</literal>, but from phase
7087 <literal>k</literal> onwards be willing to inline it (as if
7088 there was no pragma).
7091 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7092 <literal>f</literal>
7093 until phase <literal>k</literal>, but from phase
7094 <literal>k</literal> onwards do not inline it.
7097 The same information is summarised here:
7099 -- Before phase 2 Phase 2 and later
7100 {-# INLINE [2] f #-} -- No Yes
7101 {-# INLINE [~2] f #-} -- Yes No
7102 {-# NOINLINE [2] f #-} -- No Maybe
7103 {-# NOINLINE [~2] f #-} -- Maybe No
7105 {-# INLINE f #-} -- Yes Yes
7106 {-# NOINLINE f #-} -- No No
7108 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7109 function body is small, or it is applied to interesting-looking arguments etc).
7110 Another way to understand the semantics is this:
7112 <listitem><para>For both INLINE and NOINLINE, the phase number says
7113 when inlining is allowed at all.</para></listitem>
7114 <listitem><para>The INLINE pragma has the additional effect of making the
7115 function body look small, so that when inlining is allowed it is very likely to
7120 <para>The same phase-numbering control is available for RULES
7121 (<xref linkend="rewrite-rules"/>).</para>
7125 <sect2 id="line-pragma">
7126 <title>LINE pragma</title>
7128 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7129 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7130 <para>This pragma is similar to C's <literal>#line</literal>
7131 pragma, and is mainly for use in automatically generated Haskell
7132 code. It lets you specify the line number and filename of the
7133 original code; for example</para>
7135 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7137 <para>if you'd generated the current file from something called
7138 <filename>Foo.vhs</filename> and this line corresponds to line
7139 42 in the original. GHC will adjust its error messages to refer
7140 to the line/file named in the <literal>LINE</literal>
7145 <title>RULES pragma</title>
7147 <para>The RULES pragma lets you specify rewrite rules. It is
7148 described in <xref linkend="rewrite-rules"/>.</para>
7151 <sect2 id="specialize-pragma">
7152 <title>SPECIALIZE pragma</title>
7154 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7155 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7156 <indexterm><primary>overloading, death to</primary></indexterm>
7158 <para>(UK spelling also accepted.) For key overloaded
7159 functions, you can create extra versions (NB: more code space)
7160 specialised to particular types. Thus, if you have an
7161 overloaded function:</para>
7164 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7167 <para>If it is heavily used on lists with
7168 <literal>Widget</literal> keys, you could specialise it as
7172 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7175 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7176 be put anywhere its type signature could be put.</para>
7178 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7179 (a) a specialised version of the function and (b) a rewrite rule
7180 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7181 un-specialised function into a call to the specialised one.</para>
7183 <para>The type in a SPECIALIZE pragma can be any type that is less
7184 polymorphic than the type of the original function. In concrete terms,
7185 if the original function is <literal>f</literal> then the pragma
7187 {-# SPECIALIZE f :: <type> #-}
7189 is valid if and only if the definition
7191 f_spec :: <type>
7194 is valid. Here are some examples (where we only give the type signature
7195 for the original function, not its code):
7197 f :: Eq a => a -> b -> b
7198 {-# SPECIALISE f :: Int -> b -> b #-}
7200 g :: (Eq a, Ix b) => a -> b -> b
7201 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7203 h :: Eq a => a -> a -> a
7204 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7206 The last of these examples will generate a
7207 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7208 well. If you use this kind of specialisation, let us know how well it works.
7211 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7212 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7213 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7214 The <literal>INLINE</literal> pragma affects the specialised version of the
7215 function (only), and applies even if the function is recursive. The motivating
7218 -- A GADT for arrays with type-indexed representation
7220 ArrInt :: !Int -> ByteArray# -> Arr Int
7221 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7223 (!:) :: Arr e -> Int -> e
7224 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7225 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7226 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7227 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7229 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7230 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7231 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7232 the specialised function will be inlined. It has two calls to
7233 <literal>(!:)</literal>,
7234 both at type <literal>Int</literal>. Both these calls fire the first
7235 specialisation, whose body is also inlined. The result is a type-based
7236 unrolling of the indexing function.</para>
7237 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7238 on an ordinarily-recursive function.</para>
7240 <para>Note: In earlier versions of GHC, it was possible to provide your own
7241 specialised function for a given type:
7244 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7247 This feature has been removed, as it is now subsumed by the
7248 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7252 <sect2 id="specialize-instance-pragma">
7253 <title>SPECIALIZE instance pragma
7257 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7258 <indexterm><primary>overloading, death to</primary></indexterm>
7259 Same idea, except for instance declarations. For example:
7262 instance (Eq a) => Eq (Foo a) where {
7263 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7267 The pragma must occur inside the <literal>where</literal> part
7268 of the instance declaration.
7271 Compatible with HBC, by the way, except perhaps in the placement
7277 <sect2 id="unpack-pragma">
7278 <title>UNPACK pragma</title>
7280 <indexterm><primary>UNPACK</primary></indexterm>
7282 <para>The <literal>UNPACK</literal> indicates to the compiler
7283 that it should unpack the contents of a constructor field into
7284 the constructor itself, removing a level of indirection. For
7288 data T = T {-# UNPACK #-} !Float
7289 {-# UNPACK #-} !Float
7292 <para>will create a constructor <literal>T</literal> containing
7293 two unboxed floats. This may not always be an optimisation: if
7294 the <function>T</function> constructor is scrutinised and the
7295 floats passed to a non-strict function for example, they will
7296 have to be reboxed (this is done automatically by the
7299 <para>Unpacking constructor fields should only be used in
7300 conjunction with <option>-O</option>, in order to expose
7301 unfoldings to the compiler so the reboxing can be removed as
7302 often as possible. For example:</para>
7306 f (T f1 f2) = f1 + f2
7309 <para>The compiler will avoid reboxing <function>f1</function>
7310 and <function>f2</function> by inlining <function>+</function>
7311 on floats, but only when <option>-O</option> is on.</para>
7313 <para>Any single-constructor data is eligible for unpacking; for
7317 data T = T {-# UNPACK #-} !(Int,Int)
7320 <para>will store the two <literal>Int</literal>s directly in the
7321 <function>T</function> constructor, by flattening the pair.
7322 Multi-level unpacking is also supported:
7325 data T = T {-# UNPACK #-} !S
7326 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7329 will store two unboxed <literal>Int#</literal>s
7330 directly in the <function>T</function> constructor. The
7331 unpacker can see through newtypes, too.</para>
7333 <para>If a field cannot be unpacked, you will not get a warning,
7334 so it might be an idea to check the generated code with
7335 <option>-ddump-simpl</option>.</para>
7337 <para>See also the <option>-funbox-strict-fields</option> flag,
7338 which essentially has the effect of adding
7339 <literal>{-# UNPACK #-}</literal> to every strict
7340 constructor field.</para>
7343 <sect2 id="source-pragma">
7344 <title>SOURCE pragma</title>
7346 <indexterm><primary>SOURCE</primary></indexterm>
7347 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7348 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7354 <!-- ======================= REWRITE RULES ======================== -->
7356 <sect1 id="rewrite-rules">
7357 <title>Rewrite rules
7359 <indexterm><primary>RULES pragma</primary></indexterm>
7360 <indexterm><primary>pragma, RULES</primary></indexterm>
7361 <indexterm><primary>rewrite rules</primary></indexterm></title>
7364 The programmer can specify rewrite rules as part of the source program
7370 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7375 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7376 If you need more information, then <option>-ddump-rule-firings</option> shows you
7377 each individual rule firing in detail.
7381 <title>Syntax</title>
7384 From a syntactic point of view:
7390 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7391 may be generated by the layout rule).
7397 The layout rule applies in a pragma.
7398 Currently no new indentation level
7399 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7400 you must lay out the starting in the same column as the enclosing definitions.
7403 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7404 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7407 Furthermore, the closing <literal>#-}</literal>
7408 should start in a column to the right of the opening <literal>{-#</literal>.
7414 Each rule has a name, enclosed in double quotes. The name itself has
7415 no significance at all. It is only used when reporting how many times the rule fired.
7421 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7422 immediately after the name of the rule. Thus:
7425 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7428 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7429 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7438 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7439 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7440 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7441 by spaces, just like in a type <literal>forall</literal>.
7447 A pattern variable may optionally have a type signature.
7448 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7449 For example, here is the <literal>foldr/build</literal> rule:
7452 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7453 foldr k z (build g) = g k z
7456 Since <function>g</function> has a polymorphic type, it must have a type signature.
7463 The left hand side of a rule must consist of a top-level variable applied
7464 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7467 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7468 "wrong2" forall f. f True = True
7471 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7478 A rule does not need to be in the same module as (any of) the
7479 variables it mentions, though of course they need to be in scope.
7485 All rules are implicitly exported from the module, and are therefore
7486 in force in any module that imports the module that defined the rule, directly
7487 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7488 in force when compiling A.) The situation is very similar to that for instance
7496 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7497 any other flag settings. Furthermore, inside a RULE, the language extension
7498 <option>-XScopedTypeVariables</option> is automatically enabled; see
7499 <xref linkend="scoped-type-variables"/>.
7505 Like other pragmas, RULE pragmas are always checked for scope errors, and
7506 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7507 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7508 if the <option>-fenable-rewrite-rules</option> flag is
7509 on (see <xref linkend="rule-semantics"/>).
7518 <sect2 id="rule-semantics">
7519 <title>Semantics</title>
7522 From a semantic point of view:
7527 Rules are enabled (that is, used during optimisation)
7528 by the <option>-fenable-rewrite-rules</option> flag.
7529 This flag is implied by <option>-O</option>, and may be switched
7530 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7531 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7532 may not do what you expect, though, because without <option>-O</option> GHC
7533 ignores all optimisation information in interface files;
7534 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7535 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7536 has no effect on parsing or typechecking.
7542 Rules are regarded as left-to-right rewrite rules.
7543 When GHC finds an expression that is a substitution instance of the LHS
7544 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7545 By "a substitution instance" we mean that the LHS can be made equal to the
7546 expression by substituting for the pattern variables.
7553 GHC makes absolutely no attempt to verify that the LHS and RHS
7554 of a rule have the same meaning. That is undecidable in general, and
7555 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7562 GHC makes no attempt to make sure that the rules are confluent or
7563 terminating. For example:
7566 "loop" forall x y. f x y = f y x
7569 This rule will cause the compiler to go into an infinite loop.
7576 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7582 GHC currently uses a very simple, syntactic, matching algorithm
7583 for matching a rule LHS with an expression. It seeks a substitution
7584 which makes the LHS and expression syntactically equal modulo alpha
7585 conversion. The pattern (rule), but not the expression, is eta-expanded if
7586 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7587 But not beta conversion (that's called higher-order matching).
7591 Matching is carried out on GHC's intermediate language, which includes
7592 type abstractions and applications. So a rule only matches if the
7593 types match too. See <xref linkend="rule-spec"/> below.
7599 GHC keeps trying to apply the rules as it optimises the program.
7600 For example, consider:
7609 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7610 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7611 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7612 not be substituted, and the rule would not fire.
7619 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7620 results. Consider this (artificial) example
7623 {-# RULES "f" f True = False #-}
7629 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7634 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7636 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7637 would have been a better chance that <literal>f</literal>'s RULE might fire.
7640 The way to get predictable behaviour is to use a NOINLINE
7641 pragma on <literal>f</literal>, to ensure
7642 that it is not inlined until its RULEs have had a chance to fire.
7652 <title>List fusion</title>
7655 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7656 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7657 intermediate list should be eliminated entirely.
7661 The following are good producers:
7673 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7679 Explicit lists (e.g. <literal>[True, False]</literal>)
7685 The cons constructor (e.g <literal>3:4:[]</literal>)
7691 <function>++</function>
7697 <function>map</function>
7703 <function>take</function>, <function>filter</function>
7709 <function>iterate</function>, <function>repeat</function>
7715 <function>zip</function>, <function>zipWith</function>
7724 The following are good consumers:
7736 <function>array</function> (on its second argument)
7742 <function>++</function> (on its first argument)
7748 <function>foldr</function>
7754 <function>map</function>
7760 <function>take</function>, <function>filter</function>
7766 <function>concat</function>
7772 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7778 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7779 will fuse with one but not the other)
7785 <function>partition</function>
7791 <function>head</function>
7797 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7803 <function>sequence_</function>
7809 <function>msum</function>
7815 <function>sortBy</function>
7824 So, for example, the following should generate no intermediate lists:
7827 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7833 This list could readily be extended; if there are Prelude functions that you use
7834 a lot which are not included, please tell us.
7838 If you want to write your own good consumers or producers, look at the
7839 Prelude definitions of the above functions to see how to do so.
7844 <sect2 id="rule-spec">
7845 <title>Specialisation
7849 Rewrite rules can be used to get the same effect as a feature
7850 present in earlier versions of GHC.
7851 For example, suppose that:
7854 genericLookup :: Ord a => Table a b -> a -> b
7855 intLookup :: Table Int b -> Int -> b
7858 where <function>intLookup</function> is an implementation of
7859 <function>genericLookup</function> that works very fast for
7860 keys of type <literal>Int</literal>. You might wish
7861 to tell GHC to use <function>intLookup</function> instead of
7862 <function>genericLookup</function> whenever the latter was called with
7863 type <literal>Table Int b -> Int -> b</literal>.
7864 It used to be possible to write
7867 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7870 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7873 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7876 This slightly odd-looking rule instructs GHC to replace
7877 <function>genericLookup</function> by <function>intLookup</function>
7878 <emphasis>whenever the types match</emphasis>.
7879 What is more, this rule does not need to be in the same
7880 file as <function>genericLookup</function>, unlike the
7881 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7882 have an original definition available to specialise).
7885 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7886 <function>intLookup</function> really behaves as a specialised version
7887 of <function>genericLookup</function>!!!</para>
7889 <para>An example in which using <literal>RULES</literal> for
7890 specialisation will Win Big:
7893 toDouble :: Real a => a -> Double
7894 toDouble = fromRational . toRational
7896 {-# RULES "toDouble/Int" toDouble = i2d #-}
7897 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7900 The <function>i2d</function> function is virtually one machine
7901 instruction; the default conversion—via an intermediate
7902 <literal>Rational</literal>—is obscenely expensive by
7909 <title>Controlling what's going on</title>
7917 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7923 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7924 If you add <option>-dppr-debug</option> you get a more detailed listing.
7930 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7933 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7934 {-# INLINE build #-}
7938 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7939 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7940 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7941 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7948 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7949 see how to write rules that will do fusion and yet give an efficient
7950 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7960 <sect2 id="core-pragma">
7961 <title>CORE pragma</title>
7963 <indexterm><primary>CORE pragma</primary></indexterm>
7964 <indexterm><primary>pragma, CORE</primary></indexterm>
7965 <indexterm><primary>core, annotation</primary></indexterm>
7968 The external core format supports <quote>Note</quote> annotations;
7969 the <literal>CORE</literal> pragma gives a way to specify what these
7970 should be in your Haskell source code. Syntactically, core
7971 annotations are attached to expressions and take a Haskell string
7972 literal as an argument. The following function definition shows an
7976 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7979 Semantically, this is equivalent to:
7987 However, when external core is generated (via
7988 <option>-fext-core</option>), there will be Notes attached to the
7989 expressions <function>show</function> and <varname>x</varname>.
7990 The core function declaration for <function>f</function> is:
7994 f :: %forall a . GHCziShow.ZCTShow a ->
7995 a -> GHCziBase.ZMZN GHCziBase.Char =
7996 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7998 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8000 (tpl1::GHCziBase.Int ->
8002 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8004 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8005 (tpl3::GHCziBase.ZMZN a ->
8006 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8014 Here, we can see that the function <function>show</function> (which
8015 has been expanded out to a case expression over the Show dictionary)
8016 has a <literal>%note</literal> attached to it, as does the
8017 expression <varname>eta</varname> (which used to be called
8018 <varname>x</varname>).
8025 <sect1 id="special-ids">
8026 <title>Special built-in functions</title>
8027 <para>GHC has a few built-in functions with special behaviour. These
8028 are now described in the module <ulink
8029 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8030 in the library documentation.</para>
8034 <sect1 id="generic-classes">
8035 <title>Generic classes</title>
8038 The ideas behind this extension are described in detail in "Derivable type classes",
8039 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8040 An example will give the idea:
8048 fromBin :: [Int] -> (a, [Int])
8050 toBin {| Unit |} Unit = []
8051 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8052 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8053 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8055 fromBin {| Unit |} bs = (Unit, bs)
8056 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8057 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8058 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8059 (y,bs'') = fromBin bs'
8062 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8063 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8064 which are defined thus in the library module <literal>Generics</literal>:
8068 data a :+: b = Inl a | Inr b
8069 data a :*: b = a :*: b
8072 Now you can make a data type into an instance of Bin like this:
8074 instance (Bin a, Bin b) => Bin (a,b)
8075 instance Bin a => Bin [a]
8077 That is, just leave off the "where" clause. Of course, you can put in the
8078 where clause and over-ride whichever methods you please.
8082 <title> Using generics </title>
8083 <para>To use generics you need to</para>
8086 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8087 <option>-XGenerics</option> (to generate extra per-data-type code),
8088 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8092 <para>Import the module <literal>Generics</literal> from the
8093 <literal>lang</literal> package. This import brings into
8094 scope the data types <literal>Unit</literal>,
8095 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8096 don't need this import if you don't mention these types
8097 explicitly; for example, if you are simply giving instance
8098 declarations.)</para>
8103 <sect2> <title> Changes wrt the paper </title>
8105 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8106 can be written infix (indeed, you can now use
8107 any operator starting in a colon as an infix type constructor). Also note that
8108 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8109 Finally, note that the syntax of the type patterns in the class declaration
8110 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8111 alone would ambiguous when they appear on right hand sides (an extension we
8112 anticipate wanting).
8116 <sect2> <title>Terminology and restrictions</title>
8118 Terminology. A "generic default method" in a class declaration
8119 is one that is defined using type patterns as above.
8120 A "polymorphic default method" is a default method defined as in Haskell 98.
8121 A "generic class declaration" is a class declaration with at least one
8122 generic default method.
8130 Alas, we do not yet implement the stuff about constructor names and
8137 A generic class can have only one parameter; you can't have a generic
8138 multi-parameter class.
8144 A default method must be defined entirely using type patterns, or entirely
8145 without. So this is illegal:
8148 op :: a -> (a, Bool)
8149 op {| Unit |} Unit = (Unit, True)
8152 However it is perfectly OK for some methods of a generic class to have
8153 generic default methods and others to have polymorphic default methods.
8159 The type variable(s) in the type pattern for a generic method declaration
8160 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:
8164 op {| p :*: q |} (x :*: y) = op (x :: p)
8172 The type patterns in a generic default method must take one of the forms:
8178 where "a" and "b" are type variables. Furthermore, all the type patterns for
8179 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8180 must use the same type variables. So this is illegal:
8184 op {| a :+: b |} (Inl x) = True
8185 op {| p :+: q |} (Inr y) = False
8187 The type patterns must be identical, even in equations for different methods of the class.
8188 So this too is illegal:
8192 op1 {| a :*: b |} (x :*: y) = True
8195 op2 {| p :*: q |} (x :*: y) = False
8197 (The reason for this restriction is that we gather all the equations for a particular type constructor
8198 into a single generic instance declaration.)
8204 A generic method declaration must give a case for each of the three type constructors.
8210 The type for a generic method can be built only from:
8212 <listitem> <para> Function arrows </para> </listitem>
8213 <listitem> <para> Type variables </para> </listitem>
8214 <listitem> <para> Tuples </para> </listitem>
8215 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8217 Here are some example type signatures for generic methods:
8220 op2 :: Bool -> (a,Bool)
8221 op3 :: [Int] -> a -> a
8224 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8228 This restriction is an implementation restriction: we just haven't got around to
8229 implementing the necessary bidirectional maps over arbitrary type constructors.
8230 It would be relatively easy to add specific type constructors, such as Maybe and list,
8231 to the ones that are allowed.</para>
8236 In an instance declaration for a generic class, the idea is that the compiler
8237 will fill in the methods for you, based on the generic templates. However it can only
8242 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8247 No constructor of the instance type has unboxed fields.
8251 (Of course, these things can only arise if you are already using GHC extensions.)
8252 However, you can still give an instance declarations for types which break these rules,
8253 provided you give explicit code to override any generic default methods.
8261 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8262 what the compiler does with generic declarations.
8267 <sect2> <title> Another example </title>
8269 Just to finish with, here's another example I rather like:
8273 nCons {| Unit |} _ = 1
8274 nCons {| a :*: b |} _ = 1
8275 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8278 tag {| Unit |} _ = 1
8279 tag {| a :*: b |} _ = 1
8280 tag {| a :+: b |} (Inl x) = tag x
8281 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8287 <sect1 id="monomorphism">
8288 <title>Control over monomorphism</title>
8290 <para>GHC supports two flags that control the way in which generalisation is
8291 carried out at let and where bindings.
8295 <title>Switching off the dreaded Monomorphism Restriction</title>
8296 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8298 <para>Haskell's monomorphism restriction (see
8299 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8301 of the Haskell Report)
8302 can be completely switched off by
8303 <option>-XNoMonomorphismRestriction</option>.
8308 <title>Monomorphic pattern bindings</title>
8309 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8310 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8312 <para> As an experimental change, we are exploring the possibility of
8313 making pattern bindings monomorphic; that is, not generalised at all.
8314 A pattern binding is a binding whose LHS has no function arguments,
8315 and is not a simple variable. For example:
8317 f x = x -- Not a pattern binding
8318 f = \x -> x -- Not a pattern binding
8319 f :: Int -> Int = \x -> x -- Not a pattern binding
8321 (g,h) = e -- A pattern binding
8322 (f) = e -- A pattern binding
8323 [x] = e -- A pattern binding
8325 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8326 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8335 ;;; Local Variables: ***
8337 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8338 ;;; ispell-local-dictionary: "british" ***
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