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 flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Language options can be controlled in two ways:
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
54 </itemizedlist></para>
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 <option>-XPrintExplicitForalls</option>,
60 <option>-XForeignFunctionInterface</option>,
61 <option>-XUnliftedFFITypes</option>,
62 <option>-XGADTs</option>,
63 <option>-XImplicitParams</option>,
64 <option>-XScopedTypeVariables</option>,
65 <option>-XUnboxedTuples</option>,
66 <option>-XTypeSynonymInstances</option>,
67 <option>-XStandaloneDeriving</option>,
68 <option>-XDeriveDataTypeable</option>,
69 <option>-XFlexibleContexts</option>,
70 <option>-XFlexibleInstances</option>,
71 <option>-XConstrainedClassMethods</option>,
72 <option>-XMultiParamTypeClasses</option>,
73 <option>-XFunctionalDependencies</option>,
74 <option>-XMagicHash</option>,
75 <option>-XPolymorphicComponents</option>,
76 <option>-XExistentialQuantification</option>,
77 <option>-XUnicodeSyntax</option>,
78 <option>-XPostfixOperators</option>,
79 <option>-XPatternGuards</option>,
80 <option>-XLiberalTypeSynonyms</option>,
81 <option>-XRankNTypes</option>,
82 <option>-XImpredicativeTypes</option>,
83 <option>-XTypeOperators</option>,
84 <option>-XRecursiveDo</option>,
85 <option>-XParallelListComp</option>,
86 <option>-XEmptyDataDecls</option>,
87 <option>-XKindSignatures</option>,
88 <option>-XGeneralizedNewtypeDeriving</option>,
89 <option>-XTypeFamilies</option>.
90 Enabling these options is the <emphasis>only</emphasis>
91 effect of <option>-fglasgow-exts</option>.
92 We are trying to move away from this portmanteau flag,
93 and towards enabling features individually.</para>
97 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
98 <sect1 id="primitives">
99 <title>Unboxed types and primitive operations</title>
101 <para>GHC is built on a raft of primitive data types and operations;
102 "primitive" in the sense that they cannot be defined in Haskell itself.
103 While you really can use this stuff to write fast code,
104 we generally find it a lot less painful, and more satisfying in the
105 long run, to use higher-level language features and libraries. With
106 any luck, the code you write will be optimised to the efficient
107 unboxed version in any case. And if it isn't, we'd like to know
110 <para>All these primitive data types and operations are exported by the
111 library <literal>GHC.Prim</literal>, for which there is
112 <ulink url="../libraries/base/GHC.Prim.html">detailed online documentation</ulink>.
113 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
116 If you want to mention any of the primitive data types or operations in your
117 program, you must first import <literal>GHC.Prim</literal> to bring them
118 into scope. Many of them have names ending in "#", and to mention such
119 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
122 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
123 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
124 we briefly summarise here. </para>
126 <sect2 id="glasgow-unboxed">
131 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
134 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
135 that values of that type are represented by a pointer to a heap
136 object. The representation of a Haskell <literal>Int</literal>, for
137 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
138 type, however, is represented by the value itself, no pointers or heap
139 allocation are involved.
143 Unboxed types correspond to the “raw machine” types you
144 would use in C: <literal>Int#</literal> (long int),
145 <literal>Double#</literal> (double), <literal>Addr#</literal>
146 (void *), etc. The <emphasis>primitive operations</emphasis>
147 (PrimOps) on these types are what you might expect; e.g.,
148 <literal>(+#)</literal> is addition on
149 <literal>Int#</literal>s, and is the machine-addition that we all
150 know and love—usually one instruction.
154 Primitive (unboxed) types cannot be defined in Haskell, and are
155 therefore built into the language and compiler. Primitive types are
156 always unlifted; that is, a value of a primitive type cannot be
157 bottom. We use the convention (but it is only a convention)
158 that primitive types, values, and
159 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
160 For some primitive types we have special syntax for literals, also
161 described in the <link linkend="magic-hash">same section</link>.
165 Primitive values are often represented by a simple bit-pattern, such
166 as <literal>Int#</literal>, <literal>Float#</literal>,
167 <literal>Double#</literal>. But this is not necessarily the case:
168 a primitive value might be represented by a pointer to a
169 heap-allocated object. Examples include
170 <literal>Array#</literal>, the type of primitive arrays. A
171 primitive array is heap-allocated because it is too big a value to fit
172 in a register, and would be too expensive to copy around; in a sense,
173 it is accidental that it is represented by a pointer. If a pointer
174 represents a primitive value, then it really does point to that value:
175 no unevaluated thunks, no indirections…nothing can be at the
176 other end of the pointer than the primitive value.
177 A numerically-intensive program using unboxed types can
178 go a <emphasis>lot</emphasis> faster than its “standard”
179 counterpart—we saw a threefold speedup on one example.
183 There are some restrictions on the use of primitive types:
185 <listitem><para>The main restriction
186 is that you can't pass a primitive value to a polymorphic
187 function or store one in a polymorphic data type. This rules out
188 things like <literal>[Int#]</literal> (i.e. lists of primitive
189 integers). The reason for this restriction is that polymorphic
190 arguments and constructor fields are assumed to be pointers: if an
191 unboxed integer is stored in one of these, the garbage collector would
192 attempt to follow it, leading to unpredictable space leaks. Or a
193 <function>seq</function> operation on the polymorphic component may
194 attempt to dereference the pointer, with disastrous results. Even
195 worse, the unboxed value might be larger than a pointer
196 (<literal>Double#</literal> for instance).
199 <listitem><para> You cannot define a newtype whose representation type
200 (the argument type of the data constructor) is an unboxed type. Thus,
206 <listitem><para> You cannot bind a variable with an unboxed type
207 in a <emphasis>top-level</emphasis> binding.
209 <listitem><para> You cannot bind a variable with an unboxed type
210 in a <emphasis>recursive</emphasis> binding.
212 <listitem><para> You may bind unboxed variables in a (non-recursive,
213 non-top-level) pattern binding, but any such variable causes the entire
215 to become strict. For example:
217 data Foo = Foo Int Int#
219 f x = let (Foo a b, w) = ..rhs.. in ..body..
221 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
223 is strict, and the program behaves as if you had written
225 data Foo = Foo Int Int#
227 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
236 <sect2 id="unboxed-tuples">
237 <title>Unboxed Tuples
241 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
242 they're available by default with <option>-fglasgow-exts</option>. An
243 unboxed tuple looks like this:
255 where <literal>e_1..e_n</literal> are expressions of any
256 type (primitive or non-primitive). The type of an unboxed tuple looks
261 Unboxed tuples are used for functions that need to return multiple
262 values, but they avoid the heap allocation normally associated with
263 using fully-fledged tuples. When an unboxed tuple is returned, the
264 components are put directly into registers or on the stack; the
265 unboxed tuple itself does not have a composite representation. Many
266 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
268 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
269 tuples to avoid unnecessary allocation during sequences of operations.
273 There are some pretty stringent restrictions on the use of unboxed tuples:
278 Values of unboxed tuple types are subject to the same restrictions as
279 other unboxed types; i.e. they may not be stored in polymorphic data
280 structures or passed to polymorphic functions.
287 No variable can have an unboxed tuple type, nor may a constructor or function
288 argument have an unboxed tuple type. The following are all illegal:
292 data Foo = Foo (# Int, Int #)
294 f :: (# Int, Int #) -> (# Int, Int #)
297 g :: (# Int, Int #) -> Int
300 h x = let y = (# x,x #) in ...
307 The typical use of unboxed tuples is simply to return multiple values,
308 binding those multiple results with a <literal>case</literal> expression, thus:
310 f x y = (# x+1, y-1 #)
311 g x = case f x x of { (# a, b #) -> a + b }
313 You can have an unboxed tuple in a pattern binding, thus
315 f x = let (# p,q #) = h x in ..body..
317 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
318 the resulting binding is lazy like any other Haskell pattern binding. The
319 above example desugars like this:
321 f x = let t = case h x o f{ (# p,q #) -> (p,q)
326 Indeed, the bindings can even be recursive.
333 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
335 <sect1 id="syntax-extns">
336 <title>Syntactic extensions</title>
338 <sect2 id="magic-hash">
339 <title>The magic hash</title>
340 <para>The language extension <option>-XMagicHash</option> allows "#" as a
341 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
342 a valid type constructor or data constructor.</para>
344 <para>The hash sign does not change sematics at all. We tend to use variable
345 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
346 but there is no requirement to do so; they are just plain ordinary variables.
347 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
348 For example, to bring <literal>Int#</literal> into scope you must
349 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
350 the <option>-XMagicHash</option> extension
351 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
352 that is now in scope.</para>
353 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
355 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
356 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
357 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
358 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
359 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
360 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
361 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
362 is a <literal>Word#</literal>. </para> </listitem>
363 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
364 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
369 <sect2 id="new-qualified-operators">
370 <title>New qualified operator syntax</title>
372 <para>A new syntax for referencing qualified operators is
373 planned to be introduced by Haskell', and is enabled in GHC
375 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
376 option. In the new syntax, the prefix form of a qualified
378 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
379 (in Haskell 98 this would
380 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
381 and the infix form is
382 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
383 (in Haskell 98 this would
384 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
387 add x y = Prelude.(+) x y
388 subtract y = (`Prelude.(-)` y)
390 The new form of qualified operators is intended to regularise
391 the syntax by eliminating odd cases
392 like <literal>Prelude..</literal>. For example,
393 when <literal>NewQualifiedOperators</literal> is on, it is possible to
394 write the enerated sequence <literal>[Monday..]</literal>
395 without spaces, whereas in Haskell 98 this would be a
396 reference to the operator ‘<literal>.</literal>‘
397 from module <literal>Monday</literal>.</para>
399 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
400 98 syntax for qualified operators is not accepted, so this
401 option may cause existing Haskell 98 code to break.</para>
406 <!-- ====================== HIERARCHICAL MODULES ======================= -->
409 <sect2 id="hierarchical-modules">
410 <title>Hierarchical Modules</title>
412 <para>GHC supports a small extension to the syntax of module
413 names: a module name is allowed to contain a dot
414 <literal>‘.’</literal>. This is also known as the
415 “hierarchical module namespace” extension, because
416 it extends the normally flat Haskell module namespace into a
417 more flexible hierarchy of modules.</para>
419 <para>This extension has very little impact on the language
420 itself; modules names are <emphasis>always</emphasis> fully
421 qualified, so you can just think of the fully qualified module
422 name as <quote>the module name</quote>. In particular, this
423 means that the full module name must be given after the
424 <literal>module</literal> keyword at the beginning of the
425 module; for example, the module <literal>A.B.C</literal> must
428 <programlisting>module A.B.C</programlisting>
431 <para>It is a common strategy to use the <literal>as</literal>
432 keyword to save some typing when using qualified names with
433 hierarchical modules. For example:</para>
436 import qualified Control.Monad.ST.Strict as ST
439 <para>For details on how GHC searches for source and interface
440 files in the presence of hierarchical modules, see <xref
441 linkend="search-path"/>.</para>
443 <para>GHC comes with a large collection of libraries arranged
444 hierarchically; see the accompanying <ulink
445 url="../libraries/index.html">library
446 documentation</ulink>. More libraries to install are available
448 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
451 <!-- ====================== PATTERN GUARDS ======================= -->
453 <sect2 id="pattern-guards">
454 <title>Pattern guards</title>
457 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
458 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.)
462 Suppose we have an abstract data type of finite maps, with a
466 lookup :: FiniteMap -> Int -> Maybe Int
469 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
470 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
474 clunky env var1 var2 | ok1 && ok2 = val1 + val2
475 | otherwise = var1 + var2
486 The auxiliary functions are
490 maybeToBool :: Maybe a -> Bool
491 maybeToBool (Just x) = True
492 maybeToBool Nothing = False
494 expectJust :: Maybe a -> a
495 expectJust (Just x) = x
496 expectJust Nothing = error "Unexpected Nothing"
500 What is <function>clunky</function> doing? The guard <literal>ok1 &&
501 ok2</literal> checks that both lookups succeed, using
502 <function>maybeToBool</function> to convert the <function>Maybe</function>
503 types to booleans. The (lazily evaluated) <function>expectJust</function>
504 calls extract the values from the results of the lookups, and binds the
505 returned values to <varname>val1</varname> and <varname>val2</varname>
506 respectively. If either lookup fails, then clunky takes the
507 <literal>otherwise</literal> case and returns the sum of its arguments.
511 This is certainly legal Haskell, but it is a tremendously verbose and
512 un-obvious way to achieve the desired effect. Arguably, a more direct way
513 to write clunky would be to use case expressions:
517 clunky env var1 var2 = case lookup env var1 of
519 Just val1 -> case lookup env var2 of
521 Just val2 -> val1 + val2
527 This is a bit shorter, but hardly better. Of course, we can rewrite any set
528 of pattern-matching, guarded equations as case expressions; that is
529 precisely what the compiler does when compiling equations! The reason that
530 Haskell provides guarded equations is because they allow us to write down
531 the cases we want to consider, one at a time, independently of each other.
532 This structure is hidden in the case version. Two of the right-hand sides
533 are really the same (<function>fail</function>), and the whole expression
534 tends to become more and more indented.
538 Here is how I would write clunky:
543 | Just val1 <- lookup env var1
544 , Just val2 <- lookup env var2
546 ...other equations for clunky...
550 The semantics should be clear enough. The qualifiers are matched in order.
551 For a <literal><-</literal> qualifier, which I call a pattern guard, the
552 right hand side is evaluated and matched against the pattern on the left.
553 If the match fails then the whole guard fails and the next equation is
554 tried. If it succeeds, then the appropriate binding takes place, and the
555 next qualifier is matched, in the augmented environment. Unlike list
556 comprehensions, however, the type of the expression to the right of the
557 <literal><-</literal> is the same as the type of the pattern to its
558 left. The bindings introduced by pattern guards scope over all the
559 remaining guard qualifiers, and over the right hand side of the equation.
563 Just as with list comprehensions, boolean expressions can be freely mixed
564 with among the pattern guards. For example:
575 Haskell's current guards therefore emerge as a special case, in which the
576 qualifier list has just one element, a boolean expression.
580 <!-- ===================== View patterns =================== -->
582 <sect2 id="view-patterns">
587 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
588 More information and examples of view patterns can be found on the
589 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
594 View patterns are somewhat like pattern guards that can be nested inside
595 of other patterns. They are a convenient way of pattern-matching
596 against values of abstract types. For example, in a programming language
597 implementation, we might represent the syntax of the types of the
606 view :: Type -> TypeView
608 -- additional operations for constructing Typ's ...
611 The representation of Typ is held abstract, permitting implementations
612 to use a fancy representation (e.g., hash-consing to manage sharing).
614 Without view patterns, using this signature a little inconvenient:
616 size :: Typ -> Integer
617 size t = case view t of
619 Arrow t1 t2 -> size t1 + size t2
622 It is necessary to iterate the case, rather than using an equational
623 function definition. And the situation is even worse when the matching
624 against <literal>t</literal> is buried deep inside another pattern.
628 View patterns permit calling the view function inside the pattern and
629 matching against the result:
631 size (view -> Unit) = 1
632 size (view -> Arrow t1 t2) = size t1 + size t2
635 That is, we add a new form of pattern, written
636 <replaceable>expression</replaceable> <literal>-></literal>
637 <replaceable>pattern</replaceable> that means "apply the expression to
638 whatever we're trying to match against, and then match the result of
639 that application against the pattern". The expression can be any Haskell
640 expression of function type, and view patterns can be used wherever
645 The semantics of a pattern <literal>(</literal>
646 <replaceable>exp</replaceable> <literal>-></literal>
647 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
653 <para>The variables bound by the view pattern are the variables bound by
654 <replaceable>pat</replaceable>.
658 Any variables in <replaceable>exp</replaceable> are bound occurrences,
659 but variables bound "to the left" in a pattern are in scope. This
660 feature permits, for example, one argument to a function to be used in
661 the view of another argument. For example, the function
662 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
663 written using view patterns as follows:
666 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
667 ...other equations for clunky...
672 More precisely, the scoping rules are:
676 In a single pattern, variables bound by patterns to the left of a view
677 pattern expression are in scope. For example:
679 example :: Maybe ((String -> Integer,Integer), String) -> Bool
680 example Just ((f,_), f -> 4) = True
683 Additionally, in function definitions, variables bound by matching earlier curried
684 arguments may be used in view pattern expressions in later arguments:
686 example :: (String -> Integer) -> String -> Bool
687 example f (f -> 4) = True
689 That is, the scoping is the same as it would be if the curried arguments
690 were collected into a tuple.
696 In mutually recursive bindings, such as <literal>let</literal>,
697 <literal>where</literal>, or the top level, view patterns in one
698 declaration may not mention variables bound by other declarations. That
699 is, each declaration must be self-contained. For example, the following
700 program is not allowed:
707 restriction in the future; the only cost is that type checking patterns
708 would get a little more complicated.)
718 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
719 <replaceable>T1</replaceable> <literal>-></literal>
720 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
721 a <replaceable>T2</replaceable>, then the whole view pattern matches a
722 <replaceable>T1</replaceable>.
725 <listitem><para> Matching: To the equations in Section 3.17.3 of the
726 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
727 Report</ulink>, add the following:
729 case v of { (e -> p) -> e1 ; _ -> e2 }
731 case (e v) of { p -> e1 ; _ -> e2 }
733 That is, to match a variable <replaceable>v</replaceable> against a pattern
734 <literal>(</literal> <replaceable>exp</replaceable>
735 <literal>-></literal> <replaceable>pat</replaceable>
736 <literal>)</literal>, evaluate <literal>(</literal>
737 <replaceable>exp</replaceable> <replaceable> v</replaceable>
738 <literal>)</literal> and match the result against
739 <replaceable>pat</replaceable>.
742 <listitem><para> Efficiency: When the same view function is applied in
743 multiple branches of a function definition or a case expression (e.g.,
744 in <literal>size</literal> above), GHC makes an attempt to collect these
745 applications into a single nested case expression, so that the view
746 function is only applied once. Pattern compilation in GHC follows the
747 matrix algorithm described in Chapter 4 of <ulink
748 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
749 Implementation of Functional Programming Languages</ulink>. When the
750 top rows of the first column of a matrix are all view patterns with the
751 "same" expression, these patterns are transformed into a single nested
752 case. This includes, for example, adjacent view patterns that line up
755 f ((view -> A, p1), p2) = e1
756 f ((view -> B, p3), p4) = e2
760 <para> The current notion of when two view pattern expressions are "the
761 same" is very restricted: it is not even full syntactic equality.
762 However, it does include variables, literals, applications, and tuples;
763 e.g., two instances of <literal>view ("hi", "there")</literal> will be
764 collected. However, the current implementation does not compare up to
765 alpha-equivalence, so two instances of <literal>(x, view x ->
766 y)</literal> will not be coalesced.
776 <!-- ===================== Recursive do-notation =================== -->
778 <sect2 id="mdo-notation">
779 <title>The recursive do-notation
782 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
783 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
784 by Levent Erkok, John Launchbury,
785 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
786 This paper is essential reading for anyone making non-trivial use of mdo-notation,
787 and we do not repeat it here.
790 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
791 that is, the variables bound in a do-expression are visible only in the textually following
792 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
793 group. It turns out that several applications can benefit from recursive bindings in
794 the do-notation, and this extension provides the necessary syntactic support.
797 Here is a simple (yet contrived) example:
800 import Control.Monad.Fix
802 justOnes = mdo xs <- Just (1:xs)
806 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
810 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
813 class Monad m => MonadFix m where
814 mfix :: (a -> m a) -> m a
817 The function <literal>mfix</literal>
818 dictates how the required recursion operation should be performed. For example,
819 <literal>justOnes</literal> desugars as follows:
821 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
823 For full details of the way in which mdo is typechecked and desugared, see
824 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
825 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
828 If recursive bindings are required for a monad,
829 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
830 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
831 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
832 for Haskell's internal state monad (strict and lazy, respectively).
835 Here are some important points in using the recursive-do notation:
838 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
839 than <literal>do</literal>).
843 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
844 <literal>-fglasgow-exts</literal>.
848 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
849 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
850 be distinct (Section 3.3 of the paper).
854 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
855 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
856 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
857 and improve termination (Section 3.2 of the paper).
863 Historical note: The old implementation of the mdo-notation (and most
864 of the existing documents) used the name
865 <literal>MonadRec</literal> for the class and the corresponding library.
866 This name is not supported by GHC.
872 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
874 <sect2 id="parallel-list-comprehensions">
875 <title>Parallel List Comprehensions</title>
876 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
878 <indexterm><primary>parallel list comprehensions</primary>
881 <para>Parallel list comprehensions are a natural extension to list
882 comprehensions. List comprehensions can be thought of as a nice
883 syntax for writing maps and filters. Parallel comprehensions
884 extend this to include the zipWith family.</para>
886 <para>A parallel list comprehension has multiple independent
887 branches of qualifier lists, each separated by a `|' symbol. For
888 example, the following zips together two lists:</para>
891 [ (x, y) | x <- xs | y <- ys ]
894 <para>The behavior of parallel list comprehensions follows that of
895 zip, in that the resulting list will have the same length as the
896 shortest branch.</para>
898 <para>We can define parallel list comprehensions by translation to
899 regular comprehensions. Here's the basic idea:</para>
901 <para>Given a parallel comprehension of the form: </para>
904 [ e | p1 <- e11, p2 <- e12, ...
905 | q1 <- e21, q2 <- e22, ...
910 <para>This will be translated to: </para>
913 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
914 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
919 <para>where `zipN' is the appropriate zip for the given number of
924 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
926 <sect2 id="generalised-list-comprehensions">
927 <title>Generalised (SQL-Like) List Comprehensions</title>
928 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
930 <indexterm><primary>extended list comprehensions</primary>
932 <indexterm><primary>group</primary></indexterm>
933 <indexterm><primary>sql</primary></indexterm>
936 <para>Generalised list comprehensions are a further enhancement to the
937 list comprehension syntatic sugar to allow operations such as sorting
938 and grouping which are familiar from SQL. They are fully described in the
939 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
940 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
941 except that the syntax we use differs slightly from the paper.</para>
942 <para>Here is an example:
944 employees = [ ("Simon", "MS", 80)
945 , ("Erik", "MS", 100)
947 , ("Gordon", "Ed", 45)
948 , ("Paul", "Yale", 60)]
950 output = [ (the dept, sum salary)
951 | (name, dept, salary) <- employees
953 , then sortWith by (sum salary)
956 In this example, the list <literal>output</literal> would take on
960 [("Yale", 60), ("Ed", 85), ("MS", 180)]
963 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
964 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
965 function that is exported by <literal>GHC.Exts</literal>.)</para>
967 <para>There are five new forms of comprehension qualifier,
968 all introduced by the (existing) keyword <literal>then</literal>:
976 This statement requires that <literal>f</literal> have the type <literal>
977 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
978 motivating example, as this form is used to apply <literal>take 5</literal>.
989 This form is similar to the previous one, but allows you to create a function
990 which will be passed as the first argument to f. As a consequence f must have
991 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
992 from the type, this function lets f "project out" some information
993 from the elements of the list it is transforming.</para>
995 <para>An example is shown in the opening example, where <literal>sortWith</literal>
996 is supplied with a function that lets it find out the <literal>sum salary</literal>
997 for any item in the list comprehension it transforms.</para>
1005 then group by e using f
1008 <para>This is the most general of the grouping-type statements. In this form,
1009 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1010 As with the <literal>then f by e</literal> case above, the first argument
1011 is a function supplied to f by the compiler which lets it compute e on every
1012 element of the list being transformed. However, unlike the non-grouping case,
1013 f additionally partitions the list into a number of sublists: this means that
1014 at every point after this statement, binders occurring before it in the comprehension
1015 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1016 this, let's look at an example:</para>
1019 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1020 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1021 groupRuns f = groupBy (\x y -> f x == f y)
1023 output = [ (the x, y)
1024 | x <- ([1..3] ++ [1..2])
1026 , then group by x using groupRuns ]
1029 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1032 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1035 <para>Note that we have used the <literal>the</literal> function to change the type
1036 of x from a list to its original numeric type. The variable y, in contrast, is left
1037 unchanged from the list form introduced by the grouping.</para>
1047 <para>This form of grouping is essentially the same as the one described above. However,
1048 since no function to use for the grouping has been supplied it will fall back on the
1049 <literal>groupWith</literal> function defined in
1050 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1051 is the form of the group statement that we made use of in the opening example.</para>
1062 <para>With this form of the group statement, f is required to simply have the type
1063 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1064 comprehension so far directly. An example of this form is as follows:</para>
1070 , then group using inits]
1073 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1076 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1084 <!-- ===================== REBINDABLE SYNTAX =================== -->
1086 <sect2 id="rebindable-syntax">
1087 <title>Rebindable syntax and the implicit Prelude import</title>
1089 <para><indexterm><primary>-XNoImplicitPrelude
1090 option</primary></indexterm> GHC normally imports
1091 <filename>Prelude.hi</filename> files for you. If you'd
1092 rather it didn't, then give it a
1093 <option>-XNoImplicitPrelude</option> option. The idea is
1094 that you can then import a Prelude of your own. (But don't
1095 call it <literal>Prelude</literal>; the Haskell module
1096 namespace is flat, and you must not conflict with any
1097 Prelude module.)</para>
1099 <para>Suppose you are importing a Prelude of your own
1100 in order to define your own numeric class
1101 hierarchy. It completely defeats that purpose if the
1102 literal "1" means "<literal>Prelude.fromInteger
1103 1</literal>", which is what the Haskell Report specifies.
1104 So the <option>-XNoImplicitPrelude</option>
1105 flag <emphasis>also</emphasis> causes
1106 the following pieces of built-in syntax to refer to
1107 <emphasis>whatever is in scope</emphasis>, not the Prelude
1111 <para>An integer literal <literal>368</literal> means
1112 "<literal>fromInteger (368::Integer)</literal>", rather than
1113 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1116 <listitem><para>Fractional literals are handed in just the same way,
1117 except that the translation is
1118 <literal>fromRational (3.68::Rational)</literal>.
1121 <listitem><para>The equality test in an overloaded numeric pattern
1122 uses whatever <literal>(==)</literal> is in scope.
1125 <listitem><para>The subtraction operation, and the
1126 greater-than-or-equal test, in <literal>n+k</literal> patterns
1127 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1131 <para>Negation (e.g. "<literal>- (f x)</literal>")
1132 means "<literal>negate (f x)</literal>", both in numeric
1133 patterns, and expressions.
1137 <para>"Do" notation is translated using whatever
1138 functions <literal>(>>=)</literal>,
1139 <literal>(>>)</literal>, and <literal>fail</literal>,
1140 are in scope (not the Prelude
1141 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1142 comprehensions, are unaffected. </para></listitem>
1146 notation (see <xref linkend="arrow-notation"/>)
1147 uses whatever <literal>arr</literal>,
1148 <literal>(>>>)</literal>, <literal>first</literal>,
1149 <literal>app</literal>, <literal>(|||)</literal> and
1150 <literal>loop</literal> functions are in scope. But unlike the
1151 other constructs, the types of these functions must match the
1152 Prelude types very closely. Details are in flux; if you want
1156 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1157 even if that is a little unexpected. For example, the
1158 static semantics of the literal <literal>368</literal>
1159 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1160 <literal>fromInteger</literal> to have any of the types:
1162 fromInteger :: Integer -> Integer
1163 fromInteger :: forall a. Foo a => Integer -> a
1164 fromInteger :: Num a => a -> Integer
1165 fromInteger :: Integer -> Bool -> Bool
1169 <para>Be warned: this is an experimental facility, with
1170 fewer checks than usual. Use <literal>-dcore-lint</literal>
1171 to typecheck the desugared program. If Core Lint is happy
1172 you should be all right.</para>
1176 <sect2 id="postfix-operators">
1177 <title>Postfix operators</title>
1180 The <option>-XPostfixOperators</option> flag enables a small
1181 extension to the syntax of left operator sections, which allows you to
1182 define postfix operators. The extension is this: the left section
1186 is equivalent (from the point of view of both type checking and execution) to the expression
1190 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1191 The strict Haskell 98 interpretation is that the section is equivalent to
1195 That is, the operator must be a function of two arguments. GHC allows it to
1196 take only one argument, and that in turn allows you to write the function
1199 <para>The extension does not extend to the left-hand side of function
1200 definitions; you must define such a function in prefix form.</para>
1204 <sect2 id="disambiguate-fields">
1205 <title>Record field disambiguation</title>
1207 In record construction and record pattern matching
1208 it is entirely unambiguous which field is referred to, even if there are two different
1209 data types in scope with a common field name. For example:
1212 data S = MkS { x :: Int, y :: Bool }
1217 data T = MkT { x :: Int }
1219 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1221 ok2 n = MkT { x = n+1 } -- Unambiguous
1223 bad1 k = k { x = 3 } -- Ambiguous
1224 bad2 k = x k -- Ambiguous
1226 Even though there are two <literal>x</literal>'s in scope,
1227 it is clear that the <literal>x</literal> in the pattern in the
1228 definition of <literal>ok1</literal> can only mean the field
1229 <literal>x</literal> from type <literal>S</literal>. Similarly for
1230 the function <literal>ok2</literal>. However, in the record update
1231 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1232 it is not clear which of the two types is intended.
1235 Haskell 98 regards all four as ambiguous, but with the
1236 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1237 the former two. The rules are precisely the same as those for instance
1238 declarations in Haskell 98, where the method names on the left-hand side
1239 of the method bindings in an instance declaration refer unambiguously
1240 to the method of that class (provided they are in scope at all), even
1241 if there are other variables in scope with the same name.
1242 This reduces the clutter of qualified names when you import two
1243 records from different modules that use the same field name.
1247 <!-- ===================== Record puns =================== -->
1249 <sect2 id="record-puns">
1254 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1258 When using records, it is common to write a pattern that binds a
1259 variable with the same name as a record field, such as:
1262 data C = C {a :: Int}
1268 Record punning permits the variable name to be elided, so one can simply
1275 to mean the same pattern as above. That is, in a record pattern, the
1276 pattern <literal>a</literal> expands into the pattern <literal>a =
1277 a</literal> for the same name <literal>a</literal>.
1281 Note that puns and other patterns can be mixed in the same record:
1283 data C = C {a :: Int, b :: Int}
1284 f (C {a, b = 4}) = a
1286 and that puns can be used wherever record patterns occur (e.g. in
1287 <literal>let</literal> bindings or at the top-level).
1291 Record punning can also be used in an expression, writing, for example,
1297 let a = 1 in C {a = a}
1300 Note that this expansion is purely syntactic, so the record pun
1301 expression refers to the nearest enclosing variable that is spelled the
1302 same as the field name.
1307 <!-- ===================== Record wildcards =================== -->
1309 <sect2 id="record-wildcards">
1310 <title>Record wildcards
1314 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1318 For records with many fields, it can be tiresome to write out each field
1319 individually in a record pattern, as in
1321 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1322 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1327 Record wildcard syntax permits a (<literal>..</literal>) in a record
1328 pattern, where each elided field <literal>f</literal> is replaced by the
1329 pattern <literal>f = f</literal>. For example, the above pattern can be
1332 f (C {a = 1, ..}) = b + c + d
1337 Note that wildcards can be mixed with other patterns, including puns
1338 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1339 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1340 wherever record patterns occur, including in <literal>let</literal>
1341 bindings and at the top-level. For example, the top-level binding
1345 defines <literal>b</literal>, <literal>c</literal>, and
1346 <literal>d</literal>.
1350 Record wildcards can also be used in expressions, writing, for example,
1353 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1359 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1362 Note that this expansion is purely syntactic, so the record wildcard
1363 expression refers to the nearest enclosing variables that are spelled
1364 the same as the omitted field names.
1369 <!-- ===================== Local fixity declarations =================== -->
1371 <sect2 id="local-fixity-declarations">
1372 <title>Local Fixity Declarations
1375 <para>A careful reading of the Haskell 98 Report reveals that fixity
1376 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1377 <literal>infixr</literal>) are permitted to appear inside local bindings
1378 such those introduced by <literal>let</literal> and
1379 <literal>where</literal>. However, the Haskell Report does not specify
1380 the semantics of such bindings very precisely.
1383 <para>In GHC, a fixity declaration may accompany a local binding:
1390 and the fixity declaration applies wherever the binding is in scope.
1391 For example, in a <literal>let</literal>, it applies in the right-hand
1392 sides of other <literal>let</literal>-bindings and the body of the
1393 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1394 expressions (<xref linkend="mdo-notation"/>), the local fixity
1395 declarations of a <literal>let</literal> statement scope over other
1396 statements in the group, just as the bound name does.
1400 Moreover, a local fixity declaration *must* accompany a local binding of
1401 that name: it is not possible to revise the fixity of name bound
1404 let infixr 9 $ in ...
1407 Because local fixity declarations are technically Haskell 98, no flag is
1408 necessary to enable them.
1412 <sect2 id="package-imports">
1413 <title>Package-qualified imports</title>
1415 <para>With the <option>-XPackageImports</option> flag, GHC allows
1416 import declarations to be qualified by the package name that the
1417 module is intended to be imported from. For example:</para>
1420 import "network" Network.Socket
1423 <para>would import the module <literal>Network.Socket</literal> from
1424 the package <literal>network</literal> (any version). This may
1425 be used to disambiguate an import when the same module is
1426 available from multiple packages, or is present in both the
1427 current package being built and an external package.</para>
1429 <para>Note: you probably don't need to use this feature, it was
1430 added mainly so that we can build backwards-compatible versions of
1431 packages when APIs change. It can lead to fragile dependencies in
1432 the common case: modules occasionally move from one package to
1433 another, rendering any package-qualified imports broken.</para>
1436 <sect2 id="syntax-stolen">
1437 <title>Summary of stolen syntax</title>
1439 <para>Turning on an option that enables special syntax
1440 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1441 to compile, perhaps because it uses a variable name which has
1442 become a reserved word. This section lists the syntax that is
1443 "stolen" by language extensions.
1445 notation and nonterminal names from the Haskell 98 lexical syntax
1446 (see the Haskell 98 Report).
1447 We only list syntax changes here that might affect
1448 existing working programs (i.e. "stolen" syntax). Many of these
1449 extensions will also enable new context-free syntax, but in all
1450 cases programs written to use the new syntax would not be
1451 compilable without the option enabled.</para>
1453 <para>There are two classes of special
1458 <para>New reserved words and symbols: character sequences
1459 which are no longer available for use as identifiers in the
1463 <para>Other special syntax: sequences of characters that have
1464 a different meaning when this particular option is turned
1469 The following syntax is stolen:
1474 <literal>forall</literal>
1475 <indexterm><primary><literal>forall</literal></primary></indexterm>
1478 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1479 <option>-XLiberalTypeSynonyms</option>,
1480 <option>-XRank2Types</option>,
1481 <option>-XRankNTypes</option>,
1482 <option>-XPolymorphicComponents</option>,
1483 <option>-XExistentialQuantification</option>
1489 <literal>mdo</literal>
1490 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1493 Stolen by: <option>-XRecursiveDo</option>,
1499 <literal>foreign</literal>
1500 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1503 Stolen by: <option>-XForeignFunctionInterface</option>,
1509 <literal>rec</literal>,
1510 <literal>proc</literal>, <literal>-<</literal>,
1511 <literal>>-</literal>, <literal>-<<</literal>,
1512 <literal>>>-</literal>, and <literal>(|</literal>,
1513 <literal>|)</literal> brackets
1514 <indexterm><primary><literal>proc</literal></primary></indexterm>
1517 Stolen by: <option>-XArrows</option>,
1523 <literal>?<replaceable>varid</replaceable></literal>,
1524 <literal>%<replaceable>varid</replaceable></literal>
1525 <indexterm><primary>implicit parameters</primary></indexterm>
1528 Stolen by: <option>-XImplicitParams</option>,
1534 <literal>[|</literal>,
1535 <literal>[e|</literal>, <literal>[p|</literal>,
1536 <literal>[d|</literal>, <literal>[t|</literal>,
1537 <literal>$(</literal>,
1538 <literal>$<replaceable>varid</replaceable></literal>
1539 <indexterm><primary>Template Haskell</primary></indexterm>
1542 Stolen by: <option>-XTemplateHaskell</option>,
1548 <literal>[:<replaceable>varid</replaceable>|</literal>
1549 <indexterm><primary>quasi-quotation</primary></indexterm>
1552 Stolen by: <option>-XQuasiQuotes</option>,
1558 <replaceable>varid</replaceable>{<literal>#</literal>},
1559 <replaceable>char</replaceable><literal>#</literal>,
1560 <replaceable>string</replaceable><literal>#</literal>,
1561 <replaceable>integer</replaceable><literal>#</literal>,
1562 <replaceable>float</replaceable><literal>#</literal>,
1563 <replaceable>float</replaceable><literal>##</literal>,
1564 <literal>(#</literal>, <literal>#)</literal>,
1567 Stolen by: <option>-XMagicHash</option>,
1576 <!-- TYPE SYSTEM EXTENSIONS -->
1577 <sect1 id="data-type-extensions">
1578 <title>Extensions to data types and type synonyms</title>
1580 <sect2 id="nullary-types">
1581 <title>Data types with no constructors</title>
1583 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1584 a data type with no constructors. For example:</para>
1588 data T a -- T :: * -> *
1591 <para>Syntactically, the declaration lacks the "= constrs" part. The
1592 type can be parameterised over types of any kind, but if the kind is
1593 not <literal>*</literal> then an explicit kind annotation must be used
1594 (see <xref linkend="kinding"/>).</para>
1596 <para>Such data types have only one value, namely bottom.
1597 Nevertheless, they can be useful when defining "phantom types".</para>
1600 <sect2 id="infix-tycons">
1601 <title>Infix type constructors, classes, and type variables</title>
1604 GHC allows type constructors, classes, and type variables to be operators, and
1605 to be written infix, very much like expressions. More specifically:
1608 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1609 The lexical syntax is the same as that for data constructors.
1612 Data type and type-synonym declarations can be written infix, parenthesised
1613 if you want further arguments. E.g.
1615 data a :*: b = Foo a b
1616 type a :+: b = Either a b
1617 class a :=: b where ...
1619 data (a :**: b) x = Baz a b x
1620 type (a :++: b) y = Either (a,b) y
1624 Types, and class constraints, can be written infix. For example
1627 f :: (a :=: b) => a -> b
1631 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1632 The lexical syntax is the same as that for variable operators, excluding "(.)",
1633 "(!)", and "(*)". In a binding position, the operator must be
1634 parenthesised. For example:
1636 type T (+) = Int + Int
1640 liftA2 :: Arrow (~>)
1641 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1647 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1648 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1651 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1652 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1653 sets the fixity for a data constructor and the corresponding type constructor. For example:
1657 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1658 and similarly for <literal>:*:</literal>.
1659 <literal>Int `a` Bool</literal>.
1662 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1669 <sect2 id="type-synonyms">
1670 <title>Liberalised type synonyms</title>
1673 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1674 on individual synonym declarations.
1675 With the <option>-XLiberalTypeSynonyms</option> extension,
1676 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1677 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1680 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1681 in a type synonym, thus:
1683 type Discard a = forall b. Show b => a -> b -> (a, String)
1688 g :: Discard Int -> (Int,String) -- A rank-2 type
1695 If you also use <option>-XUnboxedTuples</option>,
1696 you can write an unboxed tuple in a type synonym:
1698 type Pr = (# Int, Int #)
1706 You can apply a type synonym to a forall type:
1708 type Foo a = a -> a -> Bool
1710 f :: Foo (forall b. b->b)
1712 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1714 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1719 You can apply a type synonym to a partially applied type synonym:
1721 type Generic i o = forall x. i x -> o x
1724 foo :: Generic Id []
1726 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1728 foo :: forall x. x -> [x]
1736 GHC currently does kind checking before expanding synonyms (though even that
1740 After expanding type synonyms, GHC does validity checking on types, looking for
1741 the following mal-formedness which isn't detected simply by kind checking:
1744 Type constructor applied to a type involving for-alls.
1747 Unboxed tuple on left of an arrow.
1750 Partially-applied type synonym.
1754 this will be rejected:
1756 type Pr = (# Int, Int #)
1761 because GHC does not allow unboxed tuples on the left of a function arrow.
1766 <sect2 id="existential-quantification">
1767 <title>Existentially quantified data constructors
1771 The idea of using existential quantification in data type declarations
1772 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1773 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1774 London, 1991). It was later formalised by Laufer and Odersky
1775 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1776 TOPLAS, 16(5), pp1411-1430, 1994).
1777 It's been in Lennart
1778 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1779 proved very useful. Here's the idea. Consider the declaration:
1785 data Foo = forall a. MkFoo a (a -> Bool)
1792 The data type <literal>Foo</literal> has two constructors with types:
1798 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1805 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1806 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1807 For example, the following expression is fine:
1813 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1819 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1820 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1821 isUpper</function> packages a character with a compatible function. These
1822 two things are each of type <literal>Foo</literal> and can be put in a list.
1826 What can we do with a value of type <literal>Foo</literal>?. In particular,
1827 what happens when we pattern-match on <function>MkFoo</function>?
1833 f (MkFoo val fn) = ???
1839 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1840 are compatible, the only (useful) thing we can do with them is to
1841 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1848 f (MkFoo val fn) = fn val
1854 What this allows us to do is to package heterogeneous values
1855 together with a bunch of functions that manipulate them, and then treat
1856 that collection of packages in a uniform manner. You can express
1857 quite a bit of object-oriented-like programming this way.
1860 <sect3 id="existential">
1861 <title>Why existential?
1865 What has this to do with <emphasis>existential</emphasis> quantification?
1866 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1872 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1878 But Haskell programmers can safely think of the ordinary
1879 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1880 adding a new existential quantification construct.
1885 <sect3 id="existential-with-context">
1886 <title>Existentials and type classes</title>
1889 An easy extension is to allow
1890 arbitrary contexts before the constructor. For example:
1896 data Baz = forall a. Eq a => Baz1 a a
1897 | forall b. Show b => Baz2 b (b -> b)
1903 The two constructors have the types you'd expect:
1909 Baz1 :: forall a. Eq a => a -> a -> Baz
1910 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1916 But when pattern matching on <function>Baz1</function> the matched values can be compared
1917 for equality, and when pattern matching on <function>Baz2</function> the first matched
1918 value can be converted to a string (as well as applying the function to it).
1919 So this program is legal:
1926 f (Baz1 p q) | p == q = "Yes"
1928 f (Baz2 v fn) = show (fn v)
1934 Operationally, in a dictionary-passing implementation, the
1935 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1936 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1937 extract it on pattern matching.
1942 <sect3 id="existential-records">
1943 <title>Record Constructors</title>
1946 GHC allows existentials to be used with records syntax as well. For example:
1949 data Counter a = forall self. NewCounter
1951 , _inc :: self -> self
1952 , _display :: self -> IO ()
1956 Here <literal>tag</literal> is a public field, with a well-typed selector
1957 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1958 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1959 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1960 compile-time error. In other words, <emphasis>GHC defines a record selector function
1961 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1962 (This example used an underscore in the fields for which record selectors
1963 will not be defined, but that is only programming style; GHC ignores them.)
1967 To make use of these hidden fields, we need to create some helper functions:
1970 inc :: Counter a -> Counter a
1971 inc (NewCounter x i d t) = NewCounter
1972 { _this = i x, _inc = i, _display = d, tag = t }
1974 display :: Counter a -> IO ()
1975 display NewCounter{ _this = x, _display = d } = d x
1978 Now we can define counters with different underlying implementations:
1981 counterA :: Counter String
1982 counterA = NewCounter
1983 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1985 counterB :: Counter String
1986 counterB = NewCounter
1987 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1990 display (inc counterA) -- prints "1"
1991 display (inc (inc counterB)) -- prints "##"
1994 Record update syntax is supported for existentials (and GADTs):
1996 setTag :: Counter a -> a -> Counter a
1997 setTag obj t = obj{ tag = t }
1999 The rule for record update is this: <emphasis>
2000 the types of the updated fields may
2001 mention only the universally-quantified type variables
2002 of the data constructor. For GADTs, the field may mention only types
2003 that appear as a simple type-variable argument in the constructor's result
2004 type</emphasis>. For example:
2006 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2007 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2008 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2009 -- existentially quantified)
2011 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2012 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2013 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2014 -- type-variable argument in G1's result type)
2022 <title>Restrictions</title>
2025 There are several restrictions on the ways in which existentially-quantified
2026 constructors can be use.
2035 When pattern matching, each pattern match introduces a new,
2036 distinct, type for each existential type variable. These types cannot
2037 be unified with any other type, nor can they escape from the scope of
2038 the pattern match. For example, these fragments are incorrect:
2046 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2047 is the result of <function>f1</function>. One way to see why this is wrong is to
2048 ask what type <function>f1</function> has:
2052 f1 :: Foo -> a -- Weird!
2056 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2061 f1 :: forall a. Foo -> a -- Wrong!
2065 The original program is just plain wrong. Here's another sort of error
2069 f2 (Baz1 a b) (Baz1 p q) = a==q
2073 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2074 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2075 from the two <function>Baz1</function> constructors.
2083 You can't pattern-match on an existentially quantified
2084 constructor in a <literal>let</literal> or <literal>where</literal> group of
2085 bindings. So this is illegal:
2089 f3 x = a==b where { Baz1 a b = x }
2092 Instead, use a <literal>case</literal> expression:
2095 f3 x = case x of Baz1 a b -> a==b
2098 In general, you can only pattern-match
2099 on an existentially-quantified constructor in a <literal>case</literal> expression or
2100 in the patterns of a function definition.
2102 The reason for this restriction is really an implementation one.
2103 Type-checking binding groups is already a nightmare without
2104 existentials complicating the picture. Also an existential pattern
2105 binding at the top level of a module doesn't make sense, because it's
2106 not clear how to prevent the existentially-quantified type "escaping".
2107 So for now, there's a simple-to-state restriction. We'll see how
2115 You can't use existential quantification for <literal>newtype</literal>
2116 declarations. So this is illegal:
2120 newtype T = forall a. Ord a => MkT a
2124 Reason: a value of type <literal>T</literal> must be represented as a
2125 pair of a dictionary for <literal>Ord t</literal> and a value of type
2126 <literal>t</literal>. That contradicts the idea that
2127 <literal>newtype</literal> should have no concrete representation.
2128 You can get just the same efficiency and effect by using
2129 <literal>data</literal> instead of <literal>newtype</literal>. If
2130 there is no overloading involved, then there is more of a case for
2131 allowing an existentially-quantified <literal>newtype</literal>,
2132 because the <literal>data</literal> version does carry an
2133 implementation cost, but single-field existentially quantified
2134 constructors aren't much use. So the simple restriction (no
2135 existential stuff on <literal>newtype</literal>) stands, unless there
2136 are convincing reasons to change it.
2144 You can't use <literal>deriving</literal> to define instances of a
2145 data type with existentially quantified data constructors.
2147 Reason: in most cases it would not make sense. For example:;
2150 data T = forall a. MkT [a] deriving( Eq )
2153 To derive <literal>Eq</literal> in the standard way we would need to have equality
2154 between the single component of two <function>MkT</function> constructors:
2158 (MkT a) == (MkT b) = ???
2161 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2162 It's just about possible to imagine examples in which the derived instance
2163 would make sense, but it seems altogether simpler simply to prohibit such
2164 declarations. Define your own instances!
2175 <!-- ====================== Generalised algebraic data types ======================= -->
2177 <sect2 id="gadt-style">
2178 <title>Declaring data types with explicit constructor signatures</title>
2180 <para>GHC allows you to declare an algebraic data type by
2181 giving the type signatures of constructors explicitly. For example:
2185 Just :: a -> Maybe a
2187 The form is called a "GADT-style declaration"
2188 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2189 can only be declared using this form.</para>
2190 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2191 For example, these two declarations are equivalent:
2193 data Foo = forall a. MkFoo a (a -> Bool)
2194 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2197 <para>Any data type that can be declared in standard Haskell-98 syntax
2198 can also be declared using GADT-style syntax.
2199 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2200 they treat class constraints on the data constructors differently.
2201 Specifically, if the constructor is given a type-class context, that
2202 context is made available by pattern matching. For example:
2205 MkSet :: Eq a => [a] -> Set a
2207 makeSet :: Eq a => [a] -> Set a
2208 makeSet xs = MkSet (nub xs)
2210 insert :: a -> Set a -> Set a
2211 insert a (MkSet as) | a `elem` as = MkSet as
2212 | otherwise = MkSet (a:as)
2214 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2215 gives rise to a <literal>(Eq a)</literal>
2216 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2217 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2218 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2219 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2220 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2221 In the example, the equality dictionary is used to satisfy the equality constraint
2222 generated by the call to <literal>elem</literal>, so that the type of
2223 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2226 For example, one possible application is to reify dictionaries:
2228 data NumInst a where
2229 MkNumInst :: Num a => NumInst a
2231 intInst :: NumInst Int
2234 plus :: NumInst a -> a -> a -> a
2235 plus MkNumInst p q = p + q
2237 Here, a value of type <literal>NumInst a</literal> is equivalent
2238 to an explicit <literal>(Num a)</literal> dictionary.
2241 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2242 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2246 = Num a => MkNumInst (NumInst a)
2248 Notice that, unlike the situation when declaring an existential, there is
2249 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2250 data type's universally quantified type variable <literal>a</literal>.
2251 A constructor may have both universal and existential type variables: for example,
2252 the following two declarations are equivalent:
2255 = forall b. (Num a, Eq b) => MkT1 a b
2257 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2260 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2261 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2262 In Haskell 98 the definition
2264 data Eq a => Set' a = MkSet' [a]
2266 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2267 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2268 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2269 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2270 GHC's behaviour is much more useful, as well as much more intuitive.
2274 The rest of this section gives further details about GADT-style data
2279 The result type of each data constructor must begin with the type constructor being defined.
2280 If the result type of all constructors
2281 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2282 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2283 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2287 The type signature of
2288 each constructor is independent, and is implicitly universally quantified as usual.
2289 Different constructors may have different universally-quantified type variables
2290 and different type-class constraints.
2291 For example, this is fine:
2294 T1 :: Eq b => b -> T b
2295 T2 :: (Show c, Ix c) => c -> [c] -> T c
2300 Unlike a Haskell-98-style
2301 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2302 have no scope. Indeed, one can write a kind signature instead:
2304 data Set :: * -> * where ...
2306 or even a mixture of the two:
2308 data Foo a :: (* -> *) -> * where ...
2310 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2313 data Foo a (b :: * -> *) where ...
2319 You can use strictness annotations, in the obvious places
2320 in the constructor type:
2323 Lit :: !Int -> Term Int
2324 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2325 Pair :: Term a -> Term b -> Term (a,b)
2330 You can use a <literal>deriving</literal> clause on a GADT-style data type
2331 declaration. For example, these two declarations are equivalent
2333 data Maybe1 a where {
2334 Nothing1 :: Maybe1 a ;
2335 Just1 :: a -> Maybe1 a
2336 } deriving( Eq, Ord )
2338 data Maybe2 a = Nothing2 | Just2 a
2344 You can use record syntax on a GADT-style data type declaration:
2348 Adult { name :: String, children :: [Person] } :: Person
2349 Child { name :: String } :: Person
2351 As usual, for every constructor that has a field <literal>f</literal>, the type of
2352 field <literal>f</literal> must be the same (modulo alpha conversion).
2355 At the moment, record updates are not yet possible with GADT-style declarations,
2356 so support is limited to record construction, selection and pattern matching.
2359 aPerson = Adult { name = "Fred", children = [] }
2361 shortName :: Person -> Bool
2362 hasChildren (Adult { children = kids }) = not (null kids)
2363 hasChildren (Child {}) = False
2368 As in the case of existentials declared using the Haskell-98-like record syntax
2369 (<xref linkend="existential-records"/>),
2370 record-selector functions are generated only for those fields that have well-typed
2372 Here is the example of that section, in GADT-style syntax:
2374 data Counter a where
2375 NewCounter { _this :: self
2376 , _inc :: self -> self
2377 , _display :: self -> IO ()
2382 As before, only one selector function is generated here, that for <literal>tag</literal>.
2383 Nevertheless, you can still use all the field names in pattern matching and record construction.
2385 </itemizedlist></para>
2389 <title>Generalised Algebraic Data Types (GADTs)</title>
2391 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2392 by allowing constructors to have richer return types. Here is an example:
2395 Lit :: Int -> Term Int
2396 Succ :: Term Int -> Term Int
2397 IsZero :: Term Int -> Term Bool
2398 If :: Term Bool -> Term a -> Term a -> Term a
2399 Pair :: Term a -> Term b -> Term (a,b)
2401 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2402 case with ordinary data types. This generality allows us to
2403 write a well-typed <literal>eval</literal> function
2404 for these <literal>Terms</literal>:
2408 eval (Succ t) = 1 + eval t
2409 eval (IsZero t) = eval t == 0
2410 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2411 eval (Pair e1 e2) = (eval e1, eval e2)
2413 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2414 For example, in the right hand side of the equation
2419 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2420 A precise specification of the type rules is beyond what this user manual aspires to,
2421 but the design closely follows that described in
2423 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2424 unification-based type inference for GADTs</ulink>,
2426 The general principle is this: <emphasis>type refinement is only carried out
2427 based on user-supplied type annotations</emphasis>.
2428 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2429 and lots of obscure error messages will
2430 occur. However, the refinement is quite general. For example, if we had:
2432 eval :: Term a -> a -> a
2433 eval (Lit i) j = i+j
2435 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2436 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2437 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2440 These and many other examples are given in papers by Hongwei Xi, and
2441 Tim Sheard. There is a longer introduction
2442 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2444 <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
2445 may use different notation to that implemented in GHC.
2448 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2449 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2452 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2453 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2454 The result type of each constructor must begin with the type constructor being defined,
2455 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2456 For example, in the <literal>Term</literal> data
2457 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2458 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2463 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2464 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2465 whose result type is not just <literal>T a b</literal>.
2469 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2470 an ordinary data type.
2474 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2478 Lit { val :: Int } :: Term Int
2479 Succ { num :: Term Int } :: Term Int
2480 Pred { num :: Term Int } :: Term Int
2481 IsZero { arg :: Term Int } :: Term Bool
2482 Pair { arg1 :: Term a
2485 If { cnd :: Term Bool
2490 However, for GADTs there is the following additional constraint:
2491 every constructor that has a field <literal>f</literal> must have
2492 the same result type (modulo alpha conversion)
2493 Hence, in the above example, we cannot merge the <literal>num</literal>
2494 and <literal>arg</literal> fields above into a
2495 single name. Although their field types are both <literal>Term Int</literal>,
2496 their selector functions actually have different types:
2499 num :: Term Int -> Term Int
2500 arg :: Term Bool -> Term Int
2505 When pattern-matching against data constructors drawn from a GADT,
2506 for example in a <literal>case</literal> expression, the following rules apply:
2508 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2509 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2510 <listitem><para>The type of any free variable mentioned in any of
2511 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2513 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2514 way to ensure that a variable a rigid type is to give it a type signature.
2515 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2516 Simple unification-based type inference for GADTs
2517 </ulink>. The criteria implemented by GHC are given in the Appendix.
2527 <!-- ====================== End of Generalised algebraic data types ======================= -->
2529 <sect1 id="deriving">
2530 <title>Extensions to the "deriving" mechanism</title>
2532 <sect2 id="deriving-inferred">
2533 <title>Inferred context for deriving clauses</title>
2536 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2539 data T0 f a = MkT0 a deriving( Eq )
2540 data T1 f a = MkT1 (f a) deriving( Eq )
2541 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2543 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2545 instance Eq a => Eq (T0 f a) where ...
2546 instance Eq (f a) => Eq (T1 f a) where ...
2547 instance Eq (f (f a)) => Eq (T2 f a) where ...
2549 The first of these is obviously fine. The second is still fine, although less obviously.
2550 The third is not Haskell 98, and risks losing termination of instances.
2553 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2554 each constraint in the inferred instance context must consist only of type variables,
2555 with no repetitions.
2558 This rule is applied regardless of flags. If you want a more exotic context, you can write
2559 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2563 <sect2 id="stand-alone-deriving">
2564 <title>Stand-alone deriving declarations</title>
2567 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2569 data Foo a = Bar a | Baz String
2571 deriving instance Eq a => Eq (Foo a)
2573 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2574 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2575 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2576 exactly as you would in an ordinary instance declaration.
2577 (In contrast the context is inferred in a <literal>deriving</literal> clause
2578 attached to a data type declaration.)
2580 A <literal>deriving instance</literal> declaration
2581 must obey the same rules concerning form and termination as ordinary instance declarations,
2582 controlled by the same flags; see <xref linkend="instance-decls"/>.
2585 Unlike a <literal>deriving</literal>
2586 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2587 than the data type (assuming you also use
2588 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2591 data Foo a = Bar a | Baz String
2593 deriving instance Eq a => Eq (Foo [a])
2594 deriving instance Eq a => Eq (Foo (Maybe a))
2596 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2597 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2600 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2601 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2604 newtype Foo a = MkFoo (State Int a)
2606 deriving instance MonadState Int Foo
2608 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2609 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2615 <sect2 id="deriving-typeable">
2616 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2619 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2620 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2621 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2622 classes <literal>Eq</literal>, <literal>Ord</literal>,
2623 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2626 GHC extends this list with two more classes that may be automatically derived
2627 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2628 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2629 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2630 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2632 <para>An instance of <literal>Typeable</literal> can only be derived if the
2633 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2634 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2636 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2637 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2639 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2640 are used, and only <literal>Typeable1</literal> up to
2641 <literal>Typeable7</literal> are provided in the library.)
2642 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2643 class, whose kind suits that of the data type constructor, and
2644 then writing the data type instance by hand.
2648 <sect2 id="newtype-deriving">
2649 <title>Generalised derived instances for newtypes</title>
2652 When you define an abstract type using <literal>newtype</literal>, you may want
2653 the new type to inherit some instances from its representation. In
2654 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2655 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2656 other classes you have to write an explicit instance declaration. For
2657 example, if you define
2660 newtype Dollars = Dollars Int
2663 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2664 explicitly define an instance of <literal>Num</literal>:
2667 instance Num Dollars where
2668 Dollars a + Dollars b = Dollars (a+b)
2671 All the instance does is apply and remove the <literal>newtype</literal>
2672 constructor. It is particularly galling that, since the constructor
2673 doesn't appear at run-time, this instance declaration defines a
2674 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2675 dictionary, only slower!
2679 <sect3> <title> Generalising the deriving clause </title>
2681 GHC now permits such instances to be derived instead,
2682 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2685 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2688 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2689 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2690 derives an instance declaration of the form
2693 instance Num Int => Num Dollars
2696 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2700 We can also derive instances of constructor classes in a similar
2701 way. For example, suppose we have implemented state and failure monad
2702 transformers, such that
2705 instance Monad m => Monad (State s m)
2706 instance Monad m => Monad (Failure m)
2708 In Haskell 98, we can define a parsing monad by
2710 type Parser tok m a = State [tok] (Failure m) a
2713 which is automatically a monad thanks to the instance declarations
2714 above. With the extension, we can make the parser type abstract,
2715 without needing to write an instance of class <literal>Monad</literal>, via
2718 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2721 In this case the derived instance declaration is of the form
2723 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2726 Notice that, since <literal>Monad</literal> is a constructor class, the
2727 instance is a <emphasis>partial application</emphasis> of the new type, not the
2728 entire left hand side. We can imagine that the type declaration is
2729 "eta-converted" to generate the context of the instance
2734 We can even derive instances of multi-parameter classes, provided the
2735 newtype is the last class parameter. In this case, a ``partial
2736 application'' of the class appears in the <literal>deriving</literal>
2737 clause. For example, given the class
2740 class StateMonad s m | m -> s where ...
2741 instance Monad m => StateMonad s (State s m) where ...
2743 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2745 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2746 deriving (Monad, StateMonad [tok])
2749 The derived instance is obtained by completing the application of the
2750 class to the new type:
2753 instance StateMonad [tok] (State [tok] (Failure m)) =>
2754 StateMonad [tok] (Parser tok m)
2759 As a result of this extension, all derived instances in newtype
2760 declarations are treated uniformly (and implemented just by reusing
2761 the dictionary for the representation type), <emphasis>except</emphasis>
2762 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2763 the newtype and its representation.
2767 <sect3> <title> A more precise specification </title>
2769 Derived instance declarations are constructed as follows. Consider the
2770 declaration (after expansion of any type synonyms)
2773 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2779 The <literal>ci</literal> are partial applications of
2780 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2781 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2784 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2787 The type <literal>t</literal> is an arbitrary type.
2790 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2791 nor in the <literal>ci</literal>, and
2794 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2795 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2796 should not "look through" the type or its constructor. You can still
2797 derive these classes for a newtype, but it happens in the usual way, not
2798 via this new mechanism.
2801 Then, for each <literal>ci</literal>, the derived instance
2804 instance ci t => ci (T v1...vk)
2806 As an example which does <emphasis>not</emphasis> work, consider
2808 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2810 Here we cannot derive the instance
2812 instance Monad (State s m) => Monad (NonMonad m)
2815 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2816 and so cannot be "eta-converted" away. It is a good thing that this
2817 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2818 not, in fact, a monad --- for the same reason. Try defining
2819 <literal>>>=</literal> with the correct type: you won't be able to.
2823 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2824 important, since we can only derive instances for the last one. If the
2825 <literal>StateMonad</literal> class above were instead defined as
2828 class StateMonad m s | m -> s where ...
2831 then we would not have been able to derive an instance for the
2832 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2833 classes usually have one "main" parameter for which deriving new
2834 instances is most interesting.
2836 <para>Lastly, all of this applies only for classes other than
2837 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2838 and <literal>Data</literal>, for which the built-in derivation applies (section
2839 4.3.3. of the Haskell Report).
2840 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2841 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2842 the standard method is used or the one described here.)
2849 <!-- TYPE SYSTEM EXTENSIONS -->
2850 <sect1 id="type-class-extensions">
2851 <title>Class and instances declarations</title>
2853 <sect2 id="multi-param-type-classes">
2854 <title>Class declarations</title>
2857 This section, and the next one, documents GHC's type-class extensions.
2858 There's lots of background in the paper <ulink
2859 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2860 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2861 Jones, Erik Meijer).
2864 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2868 <title>Multi-parameter type classes</title>
2870 Multi-parameter type classes are permitted. For example:
2874 class Collection c a where
2875 union :: c a -> c a -> c a
2883 <title>The superclasses of a class declaration</title>
2886 There are no restrictions on the context in a class declaration
2887 (which introduces superclasses), except that the class hierarchy must
2888 be acyclic. So these class declarations are OK:
2892 class Functor (m k) => FiniteMap m k where
2895 class (Monad m, Monad (t m)) => Transform t m where
2896 lift :: m a -> (t m) a
2902 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2903 of "acyclic" involves only the superclass relationships. For example,
2909 op :: D b => a -> b -> b
2912 class C a => D a where { ... }
2916 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2917 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2918 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2925 <sect3 id="class-method-types">
2926 <title>Class method types</title>
2929 Haskell 98 prohibits class method types to mention constraints on the
2930 class type variable, thus:
2933 fromList :: [a] -> s a
2934 elem :: Eq a => a -> s a -> Bool
2936 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2937 contains the constraint <literal>Eq a</literal>, constrains only the
2938 class type variable (in this case <literal>a</literal>).
2939 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2946 <sect2 id="functional-dependencies">
2947 <title>Functional dependencies
2950 <para> Functional dependencies are implemented as described by Mark Jones
2951 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2952 In Proceedings of the 9th European Symposium on Programming,
2953 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2957 Functional dependencies are introduced by a vertical bar in the syntax of a
2958 class declaration; e.g.
2960 class (Monad m) => MonadState s m | m -> s where ...
2962 class Foo a b c | a b -> c where ...
2964 There should be more documentation, but there isn't (yet). Yell if you need it.
2967 <sect3><title>Rules for functional dependencies </title>
2969 In a class declaration, all of the class type variables must be reachable (in the sense
2970 mentioned in <xref linkend="type-restrictions"/>)
2971 from the free variables of each method type.
2975 class Coll s a where
2977 insert :: s -> a -> s
2980 is not OK, because the type of <literal>empty</literal> doesn't mention
2981 <literal>a</literal>. Functional dependencies can make the type variable
2984 class Coll s a | s -> a where
2986 insert :: s -> a -> s
2989 Alternatively <literal>Coll</literal> might be rewritten
2992 class Coll s a where
2994 insert :: s a -> a -> s a
2998 which makes the connection between the type of a collection of
2999 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3000 Occasionally this really doesn't work, in which case you can split the
3008 class CollE s => Coll s a where
3009 insert :: s -> a -> s
3016 <title>Background on functional dependencies</title>
3018 <para>The following description of the motivation and use of functional dependencies is taken
3019 from the Hugs user manual, reproduced here (with minor changes) by kind
3020 permission of Mark Jones.
3023 Consider the following class, intended as part of a
3024 library for collection types:
3026 class Collects e ce where
3028 insert :: e -> ce -> ce
3029 member :: e -> ce -> Bool
3031 The type variable e used here represents the element type, while ce is the type
3032 of the container itself. Within this framework, we might want to define
3033 instances of this class for lists or characteristic functions (both of which
3034 can be used to represent collections of any equality type), bit sets (which can
3035 be used to represent collections of characters), or hash tables (which can be
3036 used to represent any collection whose elements have a hash function). Omitting
3037 standard implementation details, this would lead to the following declarations:
3039 instance Eq e => Collects e [e] where ...
3040 instance Eq e => Collects e (e -> Bool) where ...
3041 instance Collects Char BitSet where ...
3042 instance (Hashable e, Collects a ce)
3043 => Collects e (Array Int ce) where ...
3045 All this looks quite promising; we have a class and a range of interesting
3046 implementations. Unfortunately, there are some serious problems with the class
3047 declaration. First, the empty function has an ambiguous type:
3049 empty :: Collects e ce => ce
3051 By "ambiguous" we mean that there is a type variable e that appears on the left
3052 of the <literal>=></literal> symbol, but not on the right. The problem with
3053 this is that, according to the theoretical foundations of Haskell overloading,
3054 we cannot guarantee a well-defined semantics for any term with an ambiguous
3058 We can sidestep this specific problem by removing the empty member from the
3059 class declaration. However, although the remaining members, insert and member,
3060 do not have ambiguous types, we still run into problems when we try to use
3061 them. For example, consider the following two functions:
3063 f x y = insert x . insert y
3066 for which GHC infers the following types:
3068 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3069 g :: (Collects Bool c, Collects Char c) => c -> c
3071 Notice that the type for f allows the two parameters x and y to be assigned
3072 different types, even though it attempts to insert each of the two values, one
3073 after the other, into the same collection. If we're trying to model collections
3074 that contain only one type of value, then this is clearly an inaccurate
3075 type. Worse still, the definition for g is accepted, without causing a type
3076 error. As a result, the error in this code will not be flagged at the point
3077 where it appears. Instead, it will show up only when we try to use g, which
3078 might even be in a different module.
3081 <sect4><title>An attempt to use constructor classes</title>
3084 Faced with the problems described above, some Haskell programmers might be
3085 tempted to use something like the following version of the class declaration:
3087 class Collects e c where
3089 insert :: e -> c e -> c e
3090 member :: e -> c e -> Bool
3092 The key difference here is that we abstract over the type constructor c that is
3093 used to form the collection type c e, and not over that collection type itself,
3094 represented by ce in the original class declaration. This avoids the immediate
3095 problems that we mentioned above: empty has type <literal>Collects e c => c
3096 e</literal>, which is not ambiguous.
3099 The function f from the previous section has a more accurate type:
3101 f :: (Collects e c) => e -> e -> c e -> c e
3103 The function g from the previous section is now rejected with a type error as
3104 we would hope because the type of f does not allow the two arguments to have
3106 This, then, is an example of a multiple parameter class that does actually work
3107 quite well in practice, without ambiguity problems.
3108 There is, however, a catch. This version of the Collects class is nowhere near
3109 as general as the original class seemed to be: only one of the four instances
3110 for <literal>Collects</literal>
3111 given above can be used with this version of Collects because only one of
3112 them---the instance for lists---has a collection type that can be written in
3113 the form c e, for some type constructor c, and element type e.
3117 <sect4><title>Adding functional dependencies</title>
3120 To get a more useful version of the Collects class, Hugs provides a mechanism
3121 that allows programmers to specify dependencies between the parameters of a
3122 multiple parameter class (For readers with an interest in theoretical
3123 foundations and previous work: The use of dependency information can be seen
3124 both as a generalization of the proposal for `parametric type classes' that was
3125 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3126 later framework for "improvement" of qualified types. The
3127 underlying ideas are also discussed in a more theoretical and abstract setting
3128 in a manuscript [implparam], where they are identified as one point in a
3129 general design space for systems of implicit parameterization.).
3131 To start with an abstract example, consider a declaration such as:
3133 class C a b where ...
3135 which tells us simply that C can be thought of as a binary relation on types
3136 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3137 included in the definition of classes to add information about dependencies
3138 between parameters, as in the following examples:
3140 class D a b | a -> b where ...
3141 class E a b | a -> b, b -> a where ...
3143 The notation <literal>a -> b</literal> used here between the | and where
3144 symbols --- not to be
3145 confused with a function type --- indicates that the a parameter uniquely
3146 determines the b parameter, and might be read as "a determines b." Thus D is
3147 not just a relation, but actually a (partial) function. Similarly, from the two
3148 dependencies that are included in the definition of E, we can see that E
3149 represents a (partial) one-one mapping between types.
3152 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3153 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3154 m>=0, meaning that the y parameters are uniquely determined by the x
3155 parameters. Spaces can be used as separators if more than one variable appears
3156 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3157 annotated with multiple dependencies using commas as separators, as in the
3158 definition of E above. Some dependencies that we can write in this notation are
3159 redundant, and will be rejected because they don't serve any useful
3160 purpose, and may instead indicate an error in the program. Examples of
3161 dependencies like this include <literal>a -> a </literal>,
3162 <literal>a -> a a </literal>,
3163 <literal>a -> </literal>, etc. There can also be
3164 some redundancy if multiple dependencies are given, as in
3165 <literal>a->b</literal>,
3166 <literal>b->c </literal>, <literal>a->c </literal>, and
3167 in which some subset implies the remaining dependencies. Examples like this are
3168 not treated as errors. Note that dependencies appear only in class
3169 declarations, and not in any other part of the language. In particular, the
3170 syntax for instance declarations, class constraints, and types is completely
3174 By including dependencies in a class declaration, we provide a mechanism for
3175 the programmer to specify each multiple parameter class more precisely. The
3176 compiler, on the other hand, is responsible for ensuring that the set of
3177 instances that are in scope at any given point in the program is consistent
3178 with any declared dependencies. For example, the following pair of instance
3179 declarations cannot appear together in the same scope because they violate the
3180 dependency for D, even though either one on its own would be acceptable:
3182 instance D Bool Int where ...
3183 instance D Bool Char where ...
3185 Note also that the following declaration is not allowed, even by itself:
3187 instance D [a] b where ...
3189 The problem here is that this instance would allow one particular choice of [a]
3190 to be associated with more than one choice for b, which contradicts the
3191 dependency specified in the definition of D. More generally, this means that,
3192 in any instance of the form:
3194 instance D t s where ...
3196 for some particular types t and s, the only variables that can appear in s are
3197 the ones that appear in t, and hence, if the type t is known, then s will be
3198 uniquely determined.
3201 The benefit of including dependency information is that it allows us to define
3202 more general multiple parameter classes, without ambiguity problems, and with
3203 the benefit of more accurate types. To illustrate this, we return to the
3204 collection class example, and annotate the original definition of <literal>Collects</literal>
3205 with a simple dependency:
3207 class Collects e ce | ce -> e where
3209 insert :: e -> ce -> ce
3210 member :: e -> ce -> Bool
3212 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3213 determined by the type of the collection ce. Note that both parameters of
3214 Collects are of kind *; there are no constructor classes here. Note too that
3215 all of the instances of Collects that we gave earlier can be used
3216 together with this new definition.
3219 What about the ambiguity problems that we encountered with the original
3220 definition? The empty function still has type Collects e ce => ce, but it is no
3221 longer necessary to regard that as an ambiguous type: Although the variable e
3222 does not appear on the right of the => symbol, the dependency for class
3223 Collects tells us that it is uniquely determined by ce, which does appear on
3224 the right of the => symbol. Hence the context in which empty is used can still
3225 give enough information to determine types for both ce and e, without
3226 ambiguity. More generally, we need only regard a type as ambiguous if it
3227 contains a variable on the left of the => that is not uniquely determined
3228 (either directly or indirectly) by the variables on the right.
3231 Dependencies also help to produce more accurate types for user defined
3232 functions, and hence to provide earlier detection of errors, and less cluttered
3233 types for programmers to work with. Recall the previous definition for a
3236 f x y = insert x y = insert x . insert y
3238 for which we originally obtained a type:
3240 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3242 Given the dependency information that we have for Collects, however, we can
3243 deduce that a and b must be equal because they both appear as the second
3244 parameter in a Collects constraint with the same first parameter c. Hence we
3245 can infer a shorter and more accurate type for f:
3247 f :: (Collects a c) => a -> a -> c -> c
3249 In a similar way, the earlier definition of g will now be flagged as a type error.
3252 Although we have given only a few examples here, it should be clear that the
3253 addition of dependency information can help to make multiple parameter classes
3254 more useful in practice, avoiding ambiguity problems, and allowing more general
3255 sets of instance declarations.
3261 <sect2 id="instance-decls">
3262 <title>Instance declarations</title>
3264 <para>An instance declaration has the form
3266 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 ...
3268 The part before the "<literal>=></literal>" is the
3269 <emphasis>context</emphasis>, while the part after the
3270 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3273 <sect3 id="flexible-instance-head">
3274 <title>Relaxed rules for the instance head</title>
3277 In Haskell 98 the head of an instance declaration
3278 must be of the form <literal>C (T a1 ... an)</literal>, where
3279 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3280 and the <literal>a1 ... an</literal> are distinct type variables.
3281 GHC relaxes these rules in two ways.
3285 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3286 declaration to mention arbitrary nested types.
3287 For example, this becomes a legal instance declaration
3289 instance C (Maybe Int) where ...
3291 See also the <link linkend="instance-overlap">rules on overlap</link>.
3294 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3295 synonyms. As always, using a type synonym is just shorthand for
3296 writing the RHS of the type synonym definition. For example:
3300 type Point = (Int,Int)
3301 instance C Point where ...
3302 instance C [Point] where ...
3306 is legal. However, if you added
3310 instance C (Int,Int) where ...
3314 as well, then the compiler will complain about the overlapping
3315 (actually, identical) instance declarations. As always, type synonyms
3316 must be fully applied. You cannot, for example, write:
3320 instance Monad P where ...
3328 <sect3 id="instance-rules">
3329 <title>Relaxed rules for instance contexts</title>
3331 <para>In Haskell 98, the assertions in the context of the instance declaration
3332 must be of the form <literal>C a</literal> where <literal>a</literal>
3333 is a type variable that occurs in the head.
3337 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3338 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3339 With this flag the context of the instance declaration can each consist of arbitrary
3340 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3344 The Paterson Conditions: for each assertion in the context
3346 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3347 <listitem><para>The assertion has fewer constructors and variables (taken together
3348 and counting repetitions) than the head</para></listitem>
3352 <listitem><para>The Coverage Condition. For each functional dependency,
3353 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3354 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3355 every type variable in
3356 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3357 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3358 substitution mapping each type variable in the class declaration to the
3359 corresponding type in the instance declaration.
3362 These restrictions ensure that context reduction terminates: each reduction
3363 step makes the problem smaller by at least one
3364 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3365 if you give the <option>-XUndecidableInstances</option>
3366 flag (<xref linkend="undecidable-instances"/>).
3367 You can find lots of background material about the reason for these
3368 restrictions in the paper <ulink
3369 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3370 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3373 For example, these are OK:
3375 instance C Int [a] -- Multiple parameters
3376 instance Eq (S [a]) -- Structured type in head
3378 -- Repeated type variable in head
3379 instance C4 a a => C4 [a] [a]
3380 instance Stateful (ST s) (MutVar s)
3382 -- Head can consist of type variables only
3384 instance (Eq a, Show b) => C2 a b
3386 -- Non-type variables in context
3387 instance Show (s a) => Show (Sized s a)
3388 instance C2 Int a => C3 Bool [a]
3389 instance C2 Int a => C3 [a] b
3393 -- Context assertion no smaller than head
3394 instance C a => C a where ...
3395 -- (C b b) has more more occurrences of b than the head
3396 instance C b b => Foo [b] where ...
3401 The same restrictions apply to instances generated by
3402 <literal>deriving</literal> clauses. Thus the following is accepted:
3404 data MinHeap h a = H a (h a)
3407 because the derived instance
3409 instance (Show a, Show (h a)) => Show (MinHeap h a)
3411 conforms to the above rules.
3415 A useful idiom permitted by the above rules is as follows.
3416 If one allows overlapping instance declarations then it's quite
3417 convenient to have a "default instance" declaration that applies if
3418 something more specific does not:
3426 <sect3 id="undecidable-instances">
3427 <title>Undecidable instances</title>
3430 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3431 For example, sometimes you might want to use the following to get the
3432 effect of a "class synonym":
3434 class (C1 a, C2 a, C3 a) => C a where { }
3436 instance (C1 a, C2 a, C3 a) => C a where { }
3438 This allows you to write shorter signatures:
3444 f :: (C1 a, C2 a, C3 a) => ...
3446 The restrictions on functional dependencies (<xref
3447 linkend="functional-dependencies"/>) are particularly troublesome.
3448 It is tempting to introduce type variables in the context that do not appear in
3449 the head, something that is excluded by the normal rules. For example:
3451 class HasConverter a b | a -> b where
3454 data Foo a = MkFoo a
3456 instance (HasConverter a b,Show b) => Show (Foo a) where
3457 show (MkFoo value) = show (convert value)
3459 This is dangerous territory, however. Here, for example, is a program that would make the
3464 instance F [a] [[a]]
3465 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3467 Similarly, it can be tempting to lift the coverage condition:
3469 class Mul a b c | a b -> c where
3470 (.*.) :: a -> b -> c
3472 instance Mul Int Int Int where (.*.) = (*)
3473 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3474 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3476 The third instance declaration does not obey the coverage condition;
3477 and indeed the (somewhat strange) definition:
3479 f = \ b x y -> if b then x .*. [y] else y
3481 makes instance inference go into a loop, because it requires the constraint
3482 <literal>(Mul a [b] b)</literal>.
3485 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3486 the experimental flag <option>-XUndecidableInstances</option>
3487 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3488 both the Paterson Conditions and the Coverage Condition
3489 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3490 fixed-depth recursion stack. If you exceed the stack depth you get a
3491 sort of backtrace, and the opportunity to increase the stack depth
3492 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3498 <sect3 id="instance-overlap">
3499 <title>Overlapping instances</title>
3501 In general, <emphasis>GHC requires that that it be unambiguous which instance
3503 should be used to resolve a type-class constraint</emphasis>. This behaviour
3504 can be modified by two flags: <option>-XOverlappingInstances</option>
3505 <indexterm><primary>-XOverlappingInstances
3506 </primary></indexterm>
3507 and <option>-XIncoherentInstances</option>
3508 <indexterm><primary>-XIncoherentInstances
3509 </primary></indexterm>, as this section discusses. Both these
3510 flags are dynamic flags, and can be set on a per-module basis, using
3511 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3513 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3514 it tries to match every instance declaration against the
3516 by instantiating the head of the instance declaration. For example, consider
3519 instance context1 => C Int a where ... -- (A)
3520 instance context2 => C a Bool where ... -- (B)
3521 instance context3 => C Int [a] where ... -- (C)
3522 instance context4 => C Int [Int] where ... -- (D)
3524 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3525 but (C) and (D) do not. When matching, GHC takes
3526 no account of the context of the instance declaration
3527 (<literal>context1</literal> etc).
3528 GHC's default behaviour is that <emphasis>exactly one instance must match the
3529 constraint it is trying to resolve</emphasis>.
3530 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3531 including both declarations (A) and (B), say); an error is only reported if a
3532 particular constraint matches more than one.
3536 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3537 more than one instance to match, provided there is a most specific one. For
3538 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3539 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3540 most-specific match, the program is rejected.
3543 However, GHC is conservative about committing to an overlapping instance. For example:
3548 Suppose that from the RHS of <literal>f</literal> we get the constraint
3549 <literal>C Int [b]</literal>. But
3550 GHC does not commit to instance (C), because in a particular
3551 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3552 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3553 So GHC rejects the program.
3554 (If you add the flag <option>-XIncoherentInstances</option>,
3555 GHC will instead pick (C), without complaining about
3556 the problem of subsequent instantiations.)
3559 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3560 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3561 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3562 it instead. In this case, GHC will refrain from
3563 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3564 as before) but, rather than rejecting the program, it will infer the type
3566 f :: C Int [b] => [b] -> [b]
3568 That postpones the question of which instance to pick to the
3569 call site for <literal>f</literal>
3570 by which time more is known about the type <literal>b</literal>.
3571 You can write this type signature yourself if you use the
3572 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3576 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3580 instance Foo [b] where
3583 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3584 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3585 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3586 declaration. The solution is to postpone the choice by adding the constraint to the context
3587 of the instance declaration, thus:
3589 instance C Int [b] => Foo [b] where
3592 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3595 The willingness to be overlapped or incoherent is a property of
3596 the <emphasis>instance declaration</emphasis> itself, controlled by the
3597 presence or otherwise of the <option>-XOverlappingInstances</option>
3598 and <option>-XIncoherentInstances</option> flags when that module is
3599 being defined. Neither flag is required in a module that imports and uses the
3600 instance declaration. Specifically, during the lookup process:
3603 An instance declaration is ignored during the lookup process if (a) a more specific
3604 match is found, and (b) the instance declaration was compiled with
3605 <option>-XOverlappingInstances</option>. The flag setting for the
3606 more-specific instance does not matter.
3609 Suppose an instance declaration does not match the constraint being looked up, but
3610 does unify with it, so that it might match when the constraint is further
3611 instantiated. Usually GHC will regard this as a reason for not committing to
3612 some other constraint. But if the instance declaration was compiled with
3613 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3614 check for that declaration.
3617 These rules make it possible for a library author to design a library that relies on
3618 overlapping instances without the library client having to know.
3621 If an instance declaration is compiled without
3622 <option>-XOverlappingInstances</option>,
3623 then that instance can never be overlapped. This could perhaps be
3624 inconvenient. Perhaps the rule should instead say that the
3625 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3626 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3627 at a usage site should be permitted regardless of how the instance declarations
3628 are compiled, if the <option>-XOverlappingInstances</option> flag is
3629 used at the usage site. (Mind you, the exact usage site can occasionally be
3630 hard to pin down.) We are interested to receive feedback on these points.
3632 <para>The <option>-XIncoherentInstances</option> flag implies the
3633 <option>-XOverlappingInstances</option> flag, but not vice versa.
3641 <sect2 id="overloaded-strings">
3642 <title>Overloaded string literals
3646 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3647 string literal has type <literal>String</literal>, but with overloaded string
3648 literals enabled (with <literal>-XOverloadedStrings</literal>)
3649 a string literal has type <literal>(IsString a) => a</literal>.
3652 This means that the usual string syntax can be used, e.g., for packed strings
3653 and other variations of string like types. String literals behave very much
3654 like integer literals, i.e., they can be used in both expressions and patterns.
3655 If used in a pattern the literal with be replaced by an equality test, in the same
3656 way as an integer literal is.
3659 The class <literal>IsString</literal> is defined as:
3661 class IsString a where
3662 fromString :: String -> a
3664 The only predefined instance is the obvious one to make strings work as usual:
3666 instance IsString [Char] where
3669 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3670 it explicitly (for example, to give an instance declaration for it), you can import it
3671 from module <literal>GHC.Exts</literal>.
3674 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3678 Each type in a default declaration must be an
3679 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3683 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3684 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3685 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3686 <emphasis>or</emphasis> <literal>IsString</literal>.
3695 import GHC.Exts( IsString(..) )
3697 newtype MyString = MyString String deriving (Eq, Show)
3698 instance IsString MyString where
3699 fromString = MyString
3701 greet :: MyString -> MyString
3702 greet "hello" = "world"
3706 print $ greet "hello"
3707 print $ greet "fool"
3711 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3712 to work since it gets translated into an equality comparison.
3718 <sect1 id="type-families">
3719 <title>Type families</title>
3722 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3723 facilitate type-level
3724 programming. Type families are a generalisation of <firstterm>associated
3725 data types</firstterm>
3726 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3727 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3728 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3729 Symposium on Principles of Programming Languages (POPL'05)”, pages
3730 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3731 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3732 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3734 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3735 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3736 themselves are described in the paper “<ulink
3737 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3738 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3740 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3741 13th ACM SIGPLAN International Conference on Functional
3742 Programming”, ACM Press, pages 51-62, 2008. Type families
3743 essentially provide type-indexed data types and named functions on types,
3744 which are useful for generic programming and highly parameterised library
3745 interfaces as well as interfaces with enhanced static information, much like
3746 dependent types. They might also be regarded as an alternative to functional
3747 dependencies, but provide a more functional style of type-level programming
3748 than the relational style of functional dependencies.
3751 Indexed type families, or type families for short, are type constructors that
3752 represent sets of types. Set members are denoted by supplying the type family
3753 constructor with type parameters, which are called <firstterm>type
3754 indices</firstterm>. The
3755 difference between vanilla parametrised type constructors and family
3756 constructors is much like between parametrically polymorphic functions and
3757 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3758 behave the same at all type instances, whereas class methods can change their
3759 behaviour in dependence on the class type parameters. Similarly, vanilla type
3760 constructors imply the same data representation for all type instances, but
3761 family constructors can have varying representation types for varying type
3765 Indexed type families come in two flavours: <firstterm>data
3766 families</firstterm> and <firstterm>type synonym
3767 families</firstterm>. They are the indexed family variants of algebraic
3768 data types and type synonyms, respectively. The instances of data families
3769 can be data types and newtypes.
3772 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3773 Additional information on the use of type families in GHC is available on
3774 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3775 Haskell wiki page on type families</ulink>.
3778 <sect2 id="data-families">
3779 <title>Data families</title>
3782 Data families appear in two flavours: (1) they can be defined on the
3784 or (2) they can appear inside type classes (in which case they are known as
3785 associated types). The former is the more general variant, as it lacks the
3786 requirement for the type-indexes to coincide with the class
3787 parameters. However, the latter can lead to more clearly structured code and
3788 compiler warnings if some type instances were - possibly accidentally -
3789 omitted. In the following, we always discuss the general toplevel form first
3790 and then cover the additional constraints placed on associated types.
3793 <sect3 id="data-family-declarations">
3794 <title>Data family declarations</title>
3797 Indexed data families are introduced by a signature, such as
3799 data family GMap k :: * -> *
3801 The special <literal>family</literal> distinguishes family from standard
3802 data declarations. The result kind annotation is optional and, as
3803 usual, defaults to <literal>*</literal> if omitted. An example is
3807 Named arguments can also be given explicit kind signatures if needed.
3809 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3810 declarations] named arguments are entirely optional, so that we can
3811 declare <literal>Array</literal> alternatively with
3813 data family Array :: * -> *
3817 <sect4 id="assoc-data-family-decl">
3818 <title>Associated data family declarations</title>
3820 When a data family is declared as part of a type class, we drop
3821 the <literal>family</literal> special. The <literal>GMap</literal>
3822 declaration takes the following form
3824 class GMapKey k where
3825 data GMap k :: * -> *
3828 In contrast to toplevel declarations, named arguments must be used for
3829 all type parameters that are to be used as type-indexes. Moreover,
3830 the argument names must be class parameters. Each class parameter may
3831 only be used at most once per associated type, but some may be omitted
3832 and they may be in an order other than in the class head. Hence, the
3833 following contrived example is admissible:
3842 <sect3 id="data-instance-declarations">
3843 <title>Data instance declarations</title>
3846 Instance declarations of data and newtype families are very similar to
3847 standard data and newtype declarations. The only two differences are
3848 that the keyword <literal>data</literal> or <literal>newtype</literal>
3849 is followed by <literal>instance</literal> and that some or all of the
3850 type arguments can be non-variable types, but may not contain forall
3851 types or type synonym families. However, data families are generally
3852 allowed in type parameters, and type synonyms are allowed as long as
3853 they are fully applied and expand to a type that is itself admissible -
3854 exactly as this is required for occurrences of type synonyms in class
3855 instance parameters. For example, the <literal>Either</literal>
3856 instance for <literal>GMap</literal> is
3858 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3860 In this example, the declaration has only one variant. In general, it
3864 Data and newtype instance declarations are only permitted when an
3865 appropriate family declaration is in scope - just as a class instance declaratoin
3866 requires the class declaration to be visible. Moreover, each instance
3867 declaration has to conform to the kind determined by its family
3868 declaration. This implies that the number of parameters of an instance
3869 declaration matches the arity determined by the kind of the family.
3872 A data family instance declaration can use the full exprssiveness of
3873 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
3875 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
3876 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
3877 use either <literal>data</literal> or <literal>newtype</literal>. For example:
3880 data instance T Int = T1 Int | T2 Bool
3881 newtype instance T Char = TC Bool
3884 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
3885 and indeed can define a GADT. For example:
3888 data instance G [a] b where
3889 G1 :: c -> G [Int] b
3893 <listitem><para> You can use a <literal>deriving</literal> clause on a
3894 <literal>data instance</literal> or <literal>newtype instance</literal>
3901 Even if type families are defined as toplevel declarations, functions
3902 that perform different computations for different family instances may still
3903 need to be defined as methods of type classes. In particular, the
3904 following is not possible:
3907 data instance T Int = A
3908 data instance T Char = B
3910 foo A = 1 -- WRONG: These two equations together...
3911 foo B = 2 -- ...will produce a type error.
3913 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
3917 instance Foo Int where
3919 instance Foo Char where
3922 (Given the functionality provided by GADTs (Generalised Algebraic Data
3923 Types), it might seem as if a definition, such as the above, should be
3924 feasible. However, type families are - in contrast to GADTs - are
3925 <emphasis>open;</emphasis> i.e., new instances can always be added,
3927 modules. Supporting pattern matching across different data instances
3928 would require a form of extensible case construct.)
3931 <sect4 id="assoc-data-inst">
3932 <title>Associated data instances</title>
3934 When an associated data family instance is declared within a type
3935 class instance, we drop the <literal>instance</literal> keyword in the
3936 family instance. So, the <literal>Either</literal> instance
3937 for <literal>GMap</literal> becomes:
3939 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
3940 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3943 The most important point about associated family instances is that the
3944 type indexes corresponding to class parameters must be identical to
3945 the type given in the instance head; here this is the first argument
3946 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
3947 which coincides with the only class parameter. Any parameters to the
3948 family constructor that do not correspond to class parameters, need to
3949 be variables in every instance; here this is the
3950 variable <literal>v</literal>.
3953 Instances for an associated family can only appear as part of
3954 instances declarations of the class in which the family was declared -
3955 just as with the equations of the methods of a class. Also in
3956 correspondence to how methods are handled, declarations of associated
3957 types can be omitted in class instances. If an associated family
3958 instance is omitted, the corresponding instance type is not inhabited;
3959 i.e., only diverging expressions, such
3960 as <literal>undefined</literal>, can assume the type.
3964 <sect4 id="scoping-class-params">
3965 <title>Scoping of class parameters</title>
3967 In the case of multi-parameter type classes, the visibility of class
3968 parameters in the right-hand side of associated family instances
3969 depends <emphasis>solely</emphasis> on the parameters of the data
3970 family. As an example, consider the simple class declaration
3975 Only one of the two class parameters is a parameter to the data
3976 family. Hence, the following instance declaration is invalid:
3978 instance C [c] d where
3979 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
3981 Here, the right-hand side of the data instance mentions the type
3982 variable <literal>d</literal> that does not occur in its left-hand
3983 side. We cannot admit such data instances as they would compromise
3988 <sect4 id="family-class-inst">
3989 <title>Type class instances of family instances</title>
3991 Type class instances of instances of data families can be defined as
3992 usual, and in particular data instance declarations can
3993 have <literal>deriving</literal> clauses. For example, we can write
3995 data GMap () v = GMapUnit (Maybe v)
3998 which implicitly defines an instance of the form
4000 instance Show v => Show (GMap () v) where ...
4004 Note that class instances are always for
4005 particular <emphasis>instances</emphasis> of a data family and never
4006 for an entire family as a whole. This is for essentially the same
4007 reasons that we cannot define a toplevel function that performs
4008 pattern matching on the data constructors
4009 of <emphasis>different</emphasis> instances of a single type family.
4010 It would require a form of extensible case construct.
4014 <sect4 id="data-family-overlap">
4015 <title>Overlap of data instances</title>
4017 The instance declarations of a data family used in a single program
4018 may not overlap at all, independent of whether they are associated or
4019 not. In contrast to type class instances, this is not only a matter
4020 of consistency, but one of type safety.
4026 <sect3 id="data-family-import-export">
4027 <title>Import and export</title>
4030 The association of data constructors with type families is more dynamic
4031 than that is the case with standard data and newtype declarations. In
4032 the standard case, the notation <literal>T(..)</literal> in an import or
4033 export list denotes the type constructor and all the data constructors
4034 introduced in its declaration. However, a family declaration never
4035 introduces any data constructors; instead, data constructors are
4036 introduced by family instances. As a result, which data constructors
4037 are associated with a type family depends on the currently visible
4038 instance declarations for that family. Consequently, an import or
4039 export item of the form <literal>T(..)</literal> denotes the family
4040 constructor and all currently visible data constructors - in the case of
4041 an export item, these may be either imported or defined in the current
4042 module. The treatment of import and export items that explicitly list
4043 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4047 <sect4 id="data-family-impexp-assoc">
4048 <title>Associated families</title>
4050 As expected, an import or export item of the
4051 form <literal>C(..)</literal> denotes all of the class' methods and
4052 associated types. However, when associated types are explicitly
4053 listed as subitems of a class, we need some new syntax, as uppercase
4054 identifiers as subitems are usually data constructors, not type
4055 constructors. To clarify that we denote types here, each associated
4056 type name needs to be prefixed by the keyword <literal>type</literal>.
4057 So for example, when explicitly listing the components of
4058 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4059 GMap, empty, lookup, insert)</literal>.
4063 <sect4 id="data-family-impexp-examples">
4064 <title>Examples</title>
4066 Assuming our running <literal>GMapKey</literal> class example, let us
4067 look at some export lists and their meaning:
4070 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4071 just the class name.</para>
4074 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4075 Exports the class, the associated type <literal>GMap</literal>
4077 functions <literal>empty</literal>, <literal>lookup</literal>,
4078 and <literal>insert</literal>. None of the data constructors is
4082 <para><literal>module GMap (GMapKey(..), GMap(..))
4083 where...</literal>: As before, but also exports all the data
4084 constructors <literal>GMapInt</literal>,
4085 <literal>GMapChar</literal>,
4086 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4087 and <literal>GMapUnit</literal>.</para>
4090 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4091 GMap(..)) where...</literal>: As before.</para>
4094 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4095 where...</literal>: As before.</para>
4100 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4101 both the class <literal>GMapKey</literal> as well as its associated
4102 type <literal>GMap</literal>. However, you cannot
4103 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4104 sub-component specifications cannot be nested. To
4105 specify <literal>GMap</literal>'s data constructors, you have to list
4110 <sect4 id="data-family-impexp-instances">
4111 <title>Instances</title>
4113 Family instances are implicitly exported, just like class instances.
4114 However, this applies only to the heads of instances, not to the data
4115 constructors an instance defines.
4123 <sect2 id="synonym-families">
4124 <title>Synonym families</title>
4127 Type families appear in two flavours: (1) they can be defined on the
4128 toplevel or (2) they can appear inside type classes (in which case they
4129 are known as associated type synonyms). The former is the more general
4130 variant, as it lacks the requirement for the type-indexes to coincide with
4131 the class parameters. However, the latter can lead to more clearly
4132 structured code and compiler warnings if some type instances were -
4133 possibly accidentally - omitted. In the following, we always discuss the
4134 general toplevel form first and then cover the additional constraints
4135 placed on associated types.
4138 <sect3 id="type-family-declarations">
4139 <title>Type family declarations</title>
4142 Indexed type families are introduced by a signature, such as
4144 type family Elem c :: *
4146 The special <literal>family</literal> distinguishes family from standard
4147 type declarations. The result kind annotation is optional and, as
4148 usual, defaults to <literal>*</literal> if omitted. An example is
4152 Parameters can also be given explicit kind signatures if needed. We
4153 call the number of parameters in a type family declaration, the family's
4154 arity, and all applications of a type family must be fully saturated
4155 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4156 and it implies that the kind of a type family is not sufficient to
4157 determine a family's arity, and hence in general, also insufficient to
4158 determine whether a type family application is well formed. As an
4159 example, consider the following declaration:
4161 type family F a b :: * -> * -- F's arity is 2,
4162 -- although it's overall kind is * -> * -> * -> *
4164 Given this declaration the following are examples of well-formed and
4167 F Char [Int] -- OK! Kind: * -> *
4168 F Char [Int] Bool -- OK! Kind: *
4169 F IO Bool -- WRONG: kind mismatch in the first argument
4170 F Bool -- WRONG: unsaturated application
4174 <sect4 id="assoc-type-family-decl">
4175 <title>Associated type family declarations</title>
4177 When a type family is declared as part of a type class, we drop
4178 the <literal>family</literal> special. The <literal>Elem</literal>
4179 declaration takes the following form
4181 class Collects ce where
4185 The argument names of the type family must be class parameters. Each
4186 class parameter may only be used at most once per associated type, but
4187 some may be omitted and they may be in an order other than in the
4188 class head. Hence, the following contrived example is admissible:
4193 These rules are exactly as for associated data families.
4198 <sect3 id="type-instance-declarations">
4199 <title>Type instance declarations</title>
4201 Instance declarations of type families are very similar to standard type
4202 synonym declarations. The only two differences are that the
4203 keyword <literal>type</literal> is followed
4204 by <literal>instance</literal> and that some or all of the type
4205 arguments can be non-variable types, but may not contain forall types or
4206 type synonym families. However, data families are generally allowed, and
4207 type synonyms are allowed as long as they are fully applied and expand
4208 to a type that is admissible - these are the exact same requirements as
4209 for data instances. For example, the <literal>[e]</literal> instance
4210 for <literal>Elem</literal> is
4212 type instance Elem [e] = e
4216 Type family instance declarations are only legitimate when an
4217 appropriate family declaration is in scope - just like class instances
4218 require the class declaration to be visible. Moreover, each instance
4219 declaration has to conform to the kind determined by its family
4220 declaration, and the number of type parameters in an instance
4221 declaration must match the number of type parameters in the family
4222 declaration. Finally, the right-hand side of a type instance must be a
4223 monotype (i.e., it may not include foralls) and after the expansion of
4224 all saturated vanilla type synonyms, no synonyms, except family synonyms
4225 may remain. Here are some examples of admissible and illegal type
4228 type family F a :: *
4229 type instance F [Int] = Int -- OK!
4230 type instance F String = Char -- OK!
4231 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4232 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4233 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4235 type family G a b :: * -> *
4236 type instance G Int = (,) -- WRONG: must be two type parameters
4237 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4241 <sect4 id="assoc-type-instance">
4242 <title>Associated type instance declarations</title>
4244 When an associated family instance is declared within a type class
4245 instance, we drop the <literal>instance</literal> keyword in the family
4246 instance. So, the <literal>[e]</literal> instance
4247 for <literal>Elem</literal> becomes:
4249 instance (Eq (Elem [e])) => Collects ([e]) where
4253 The most important point about associated family instances is that the
4254 type indexes corresponding to class parameters must be identical to the
4255 type given in the instance head; here this is <literal>[e]</literal>,
4256 which coincides with the only class parameter.
4259 Instances for an associated family can only appear as part of instances
4260 declarations of the class in which the family was declared - just as
4261 with the equations of the methods of a class. Also in correspondence to
4262 how methods are handled, declarations of associated types can be omitted
4263 in class instances. If an associated family instance is omitted, the
4264 corresponding instance type is not inhabited; i.e., only diverging
4265 expressions, such as <literal>undefined</literal>, can assume the type.
4269 <sect4 id="type-family-overlap">
4270 <title>Overlap of type synonym instances</title>
4272 The instance declarations of a type family used in a single program
4273 may only overlap if the right-hand sides of the overlapping instances
4274 coincide for the overlapping types. More formally, two instance
4275 declarations overlap if there is a substitution that makes the
4276 left-hand sides of the instances syntactically the same. Whenever
4277 that is the case, the right-hand sides of the instances must also be
4278 syntactically equal under the same substitution. This condition is
4279 independent of whether the type family is associated or not, and it is
4280 not only a matter of consistency, but one of type safety.
4283 Here are two example to illustrate the condition under which overlap
4286 type instance F (a, Int) = [a]
4287 type instance F (Int, b) = [b] -- overlap permitted
4289 type instance G (a, Int) = [a]
4290 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4295 <sect4 id="type-family-decidability">
4296 <title>Decidability of type synonym instances</title>
4298 In order to guarantee that type inference in the presence of type
4299 families decidable, we need to place a number of additional
4300 restrictions on the formation of type instance declarations (c.f.,
4301 Definition 5 (Relaxed Conditions) of “<ulink
4302 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4303 Checking with Open Type Functions</ulink>”). Instance
4304 declarations have the general form
4306 type instance F t1 .. tn = t
4308 where we require that for every type family application <literal>(G s1
4309 .. sm)</literal> in <literal>t</literal>,
4312 <para><literal>s1 .. sm</literal> do not contain any type family
4313 constructors,</para>
4316 <para>the total number of symbols (data type constructors and type
4317 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4318 in <literal>t1 .. tn</literal>, and</para>
4321 <para>for every type
4322 variable <literal>a</literal>, <literal>a</literal> occurs
4323 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4324 .. tn</literal>.</para>
4327 These restrictions are easily verified and ensure termination of type
4328 inference. However, they are not sufficient to guarantee completeness
4329 of type inference in the presence of, so called, ''loopy equalities'',
4330 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4331 a type variable is underneath a family application and data
4332 constructor application - see the above mentioned paper for details.
4335 If the option <option>-XUndecidableInstances</option> is passed to the
4336 compiler, the above restrictions are not enforced and it is on the
4337 programmer to ensure termination of the normalisation of type families
4338 during type inference.
4343 <sect3 id-="equality-constraints">
4344 <title>Equality constraints</title>
4346 Type context can include equality constraints of the form <literal>t1 ~
4347 t2</literal>, which denote that the types <literal>t1</literal>
4348 and <literal>t2</literal> need to be the same. In the presence of type
4349 families, whether two types are equal cannot generally be decided
4350 locally. Hence, the contexts of function signatures may include
4351 equality constraints, as in the following example:
4353 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4355 where we require that the element type of <literal>c1</literal>
4356 and <literal>c2</literal> are the same. In general, the
4357 types <literal>t1</literal> and <literal>t2</literal> of an equality
4358 constraint may be arbitrary monotypes; i.e., they may not contain any
4359 quantifiers, independent of whether higher-rank types are otherwise
4363 Equality constraints can also appear in class and instance contexts.
4364 The former enable a simple translation of programs using functional
4365 dependencies into programs using family synonyms instead. The general
4366 idea is to rewrite a class declaration of the form
4368 class C a b | a -> b
4372 class (F a ~ b) => C a b where
4375 That is, we represent every functional dependency (FD) <literal>a1 .. an
4376 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4377 superclass context equality <literal>F a1 .. an ~ b</literal>,
4378 essentially giving a name to the functional dependency. In class
4379 instances, we define the type instances of FD families in accordance
4380 with the class head. Method signatures are not affected by that
4384 NB: Equalities in superclass contexts are not fully implemented in
4389 <sect3 id-="ty-fams-in-instances">
4390 <title>Type families and instance declarations</title>
4391 <para>Type families require us to extend the rules for
4392 the form of instance heads, which are given
4393 in <xref linkend="flexible-instance-head"/>.
4396 <listitem><para>Data type families may appear in an instance head</para></listitem>
4397 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4399 The reason for the latter restriction is that there is no way to check for. Consider
4402 type instance F Bool = Int
4409 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4410 The situation is especially bad because the type instance for <literal>F Bool</literal>
4411 might be in another module, or even in a module that is not yet written.
4418 <sect1 id="other-type-extensions">
4419 <title>Other type system extensions</title>
4421 <sect2 id="type-restrictions">
4422 <title>Type signatures</title>
4424 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4426 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4427 that the type-class constraints in a type signature must have the
4428 form <emphasis>(class type-variable)</emphasis> or
4429 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4430 With <option>-XFlexibleContexts</option>
4431 these type signatures are perfectly OK
4434 g :: Ord (T a ()) => ...
4438 GHC imposes the following restrictions on the constraints in a type signature.
4442 forall tv1..tvn (c1, ...,cn) => type
4445 (Here, we write the "foralls" explicitly, although the Haskell source
4446 language omits them; in Haskell 98, all the free type variables of an
4447 explicit source-language type signature are universally quantified,
4448 except for the class type variables in a class declaration. However,
4449 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4458 <emphasis>Each universally quantified type variable
4459 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4461 A type variable <literal>a</literal> is "reachable" if it appears
4462 in the same constraint as either a type variable free in
4463 <literal>type</literal>, or another reachable type variable.
4464 A value with a type that does not obey
4465 this reachability restriction cannot be used without introducing
4466 ambiguity; that is why the type is rejected.
4467 Here, for example, is an illegal type:
4471 forall a. Eq a => Int
4475 When a value with this type was used, the constraint <literal>Eq tv</literal>
4476 would be introduced where <literal>tv</literal> is a fresh type variable, and
4477 (in the dictionary-translation implementation) the value would be
4478 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4479 can never know which instance of <literal>Eq</literal> to use because we never
4480 get any more information about <literal>tv</literal>.
4484 that the reachability condition is weaker than saying that <literal>a</literal> is
4485 functionally dependent on a type variable free in
4486 <literal>type</literal> (see <xref
4487 linkend="functional-dependencies"/>). The reason for this is there
4488 might be a "hidden" dependency, in a superclass perhaps. So
4489 "reachable" is a conservative approximation to "functionally dependent".
4490 For example, consider:
4492 class C a b | a -> b where ...
4493 class C a b => D a b where ...
4494 f :: forall a b. D a b => a -> a
4496 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4497 but that is not immediately apparent from <literal>f</literal>'s type.
4503 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4504 universally quantified type variables <literal>tvi</literal></emphasis>.
4506 For example, this type is OK because <literal>C a b</literal> mentions the
4507 universally quantified type variable <literal>b</literal>:
4511 forall a. C a b => burble
4515 The next type is illegal because the constraint <literal>Eq b</literal> does not
4516 mention <literal>a</literal>:
4520 forall a. Eq b => burble
4524 The reason for this restriction is milder than the other one. The
4525 excluded types are never useful or necessary (because the offending
4526 context doesn't need to be witnessed at this point; it can be floated
4527 out). Furthermore, floating them out increases sharing. Lastly,
4528 excluding them is a conservative choice; it leaves a patch of
4529 territory free in case we need it later.
4543 <sect2 id="implicit-parameters">
4544 <title>Implicit parameters</title>
4546 <para> Implicit parameters are implemented as described in
4547 "Implicit parameters: dynamic scoping with static types",
4548 J Lewis, MB Shields, E Meijer, J Launchbury,
4549 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4553 <para>(Most of the following, still rather incomplete, documentation is
4554 due to Jeff Lewis.)</para>
4556 <para>Implicit parameter support is enabled with the option
4557 <option>-XImplicitParams</option>.</para>
4560 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4561 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4562 context. In Haskell, all variables are statically bound. Dynamic
4563 binding of variables is a notion that goes back to Lisp, but was later
4564 discarded in more modern incarnations, such as Scheme. Dynamic binding
4565 can be very confusing in an untyped language, and unfortunately, typed
4566 languages, in particular Hindley-Milner typed languages like Haskell,
4567 only support static scoping of variables.
4570 However, by a simple extension to the type class system of Haskell, we
4571 can support dynamic binding. Basically, we express the use of a
4572 dynamically bound variable as a constraint on the type. These
4573 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4574 function uses a dynamically-bound variable <literal>?x</literal>
4575 of type <literal>t'</literal>". For
4576 example, the following expresses the type of a sort function,
4577 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4579 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4581 The dynamic binding constraints are just a new form of predicate in the type class system.
4584 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4585 where <literal>x</literal> is
4586 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4587 Use of this construct also introduces a new
4588 dynamic-binding constraint in the type of the expression.
4589 For example, the following definition
4590 shows how we can define an implicitly parameterized sort function in
4591 terms of an explicitly parameterized <literal>sortBy</literal> function:
4593 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4595 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4601 <title>Implicit-parameter type constraints</title>
4603 Dynamic binding constraints behave just like other type class
4604 constraints in that they are automatically propagated. Thus, when a
4605 function is used, its implicit parameters are inherited by the
4606 function that called it. For example, our <literal>sort</literal> function might be used
4607 to pick out the least value in a list:
4609 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4610 least xs = head (sort xs)
4612 Without lifting a finger, the <literal>?cmp</literal> parameter is
4613 propagated to become a parameter of <literal>least</literal> as well. With explicit
4614 parameters, the default is that parameters must always be explicit
4615 propagated. With implicit parameters, the default is to always
4619 An implicit-parameter type constraint differs from other type class constraints in the
4620 following way: All uses of a particular implicit parameter must have
4621 the same type. This means that the type of <literal>(?x, ?x)</literal>
4622 is <literal>(?x::a) => (a,a)</literal>, and not
4623 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4627 <para> You can't have an implicit parameter in the context of a class or instance
4628 declaration. For example, both these declarations are illegal:
4630 class (?x::Int) => C a where ...
4631 instance (?x::a) => Foo [a] where ...
4633 Reason: exactly which implicit parameter you pick up depends on exactly where
4634 you invoke a function. But the ``invocation'' of instance declarations is done
4635 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4636 Easiest thing is to outlaw the offending types.</para>
4638 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4640 f :: (?x :: [a]) => Int -> Int
4643 g :: (Read a, Show a) => String -> String
4646 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4647 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4648 quite unambiguous, and fixes the type <literal>a</literal>.
4653 <title>Implicit-parameter bindings</title>
4656 An implicit parameter is <emphasis>bound</emphasis> using the standard
4657 <literal>let</literal> or <literal>where</literal> binding forms.
4658 For example, we define the <literal>min</literal> function by binding
4659 <literal>cmp</literal>.
4662 min = let ?cmp = (<=) in least
4666 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4667 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4668 (including in a list comprehension, or do-notation, or pattern guards),
4669 or a <literal>where</literal> clause.
4670 Note the following points:
4673 An implicit-parameter binding group must be a
4674 collection of simple bindings to implicit-style variables (no
4675 function-style bindings, and no type signatures); these bindings are
4676 neither polymorphic or recursive.
4679 You may not mix implicit-parameter bindings with ordinary bindings in a
4680 single <literal>let</literal>
4681 expression; use two nested <literal>let</literal>s instead.
4682 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4686 You may put multiple implicit-parameter bindings in a
4687 single binding group; but they are <emphasis>not</emphasis> treated
4688 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4689 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4690 parameter. The bindings are not nested, and may be re-ordered without changing
4691 the meaning of the program.
4692 For example, consider:
4694 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4696 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4697 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4699 f :: (?x::Int) => Int -> Int
4707 <sect3><title>Implicit parameters and polymorphic recursion</title>
4710 Consider these two definitions:
4713 len1 xs = let ?acc = 0 in len_acc1 xs
4716 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4721 len2 xs = let ?acc = 0 in len_acc2 xs
4723 len_acc2 :: (?acc :: Int) => [a] -> Int
4725 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4727 The only difference between the two groups is that in the second group
4728 <literal>len_acc</literal> is given a type signature.
4729 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4730 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4731 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4732 has a type signature, the recursive call is made to the
4733 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4734 as an implicit parameter. So we get the following results in GHCi:
4741 Adding a type signature dramatically changes the result! This is a rather
4742 counter-intuitive phenomenon, worth watching out for.
4746 <sect3><title>Implicit parameters and monomorphism</title>
4748 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4749 Haskell Report) to implicit parameters. For example, consider:
4757 Since the binding for <literal>y</literal> falls under the Monomorphism
4758 Restriction it is not generalised, so the type of <literal>y</literal> is
4759 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4760 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4761 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4762 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4763 <literal>y</literal> in the body of the <literal>let</literal> will see the
4764 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4765 <literal>14</literal>.
4770 <!-- ======================= COMMENTED OUT ========================
4772 We intend to remove linear implicit parameters, so I'm at least removing
4773 them from the 6.6 user manual
4775 <sect2 id="linear-implicit-parameters">
4776 <title>Linear implicit parameters</title>
4778 Linear implicit parameters are an idea developed by Koen Claessen,
4779 Mark Shields, and Simon PJ. They address the long-standing
4780 problem that monads seem over-kill for certain sorts of problem, notably:
4783 <listitem> <para> distributing a supply of unique names </para> </listitem>
4784 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4785 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4789 Linear implicit parameters are just like ordinary implicit parameters,
4790 except that they are "linear"; that is, they cannot be copied, and
4791 must be explicitly "split" instead. Linear implicit parameters are
4792 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4793 (The '/' in the '%' suggests the split!)
4798 import GHC.Exts( Splittable )
4800 data NameSupply = ...
4802 splitNS :: NameSupply -> (NameSupply, NameSupply)
4803 newName :: NameSupply -> Name
4805 instance Splittable NameSupply where
4809 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4810 f env (Lam x e) = Lam x' (f env e)
4813 env' = extend env x x'
4814 ...more equations for f...
4816 Notice that the implicit parameter %ns is consumed
4818 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4819 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4823 So the translation done by the type checker makes
4824 the parameter explicit:
4826 f :: NameSupply -> Env -> Expr -> Expr
4827 f ns env (Lam x e) = Lam x' (f ns1 env e)
4829 (ns1,ns2) = splitNS ns
4831 env = extend env x x'
4833 Notice the call to 'split' introduced by the type checker.
4834 How did it know to use 'splitNS'? Because what it really did
4835 was to introduce a call to the overloaded function 'split',
4836 defined by the class <literal>Splittable</literal>:
4838 class Splittable a where
4841 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4842 split for name supplies. But we can simply write
4848 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4850 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4851 <literal>GHC.Exts</literal>.
4856 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4857 are entirely distinct implicit parameters: you
4858 can use them together and they won't interfere with each other. </para>
4861 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4863 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4864 in the context of a class or instance declaration. </para></listitem>
4868 <sect3><title>Warnings</title>
4871 The monomorphism restriction is even more important than usual.
4872 Consider the example above:
4874 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4875 f env (Lam x e) = Lam x' (f env e)
4878 env' = extend env x x'
4880 If we replaced the two occurrences of x' by (newName %ns), which is
4881 usually a harmless thing to do, we get:
4883 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4884 f env (Lam x e) = Lam (newName %ns) (f env e)
4886 env' = extend env x (newName %ns)
4888 But now the name supply is consumed in <emphasis>three</emphasis> places
4889 (the two calls to newName,and the recursive call to f), so
4890 the result is utterly different. Urk! We don't even have
4894 Well, this is an experimental change. With implicit
4895 parameters we have already lost beta reduction anyway, and
4896 (as John Launchbury puts it) we can't sensibly reason about
4897 Haskell programs without knowing their typing.
4902 <sect3><title>Recursive functions</title>
4903 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4906 foo :: %x::T => Int -> [Int]
4908 foo n = %x : foo (n-1)
4910 where T is some type in class Splittable.</para>
4912 Do you get a list of all the same T's or all different T's
4913 (assuming that split gives two distinct T's back)?
4915 If you supply the type signature, taking advantage of polymorphic
4916 recursion, you get what you'd probably expect. Here's the
4917 translated term, where the implicit param is made explicit:
4920 foo x n = let (x1,x2) = split x
4921 in x1 : foo x2 (n-1)
4923 But if you don't supply a type signature, GHC uses the Hindley
4924 Milner trick of using a single monomorphic instance of the function
4925 for the recursive calls. That is what makes Hindley Milner type inference
4926 work. So the translation becomes
4930 foom n = x : foom (n-1)
4934 Result: 'x' is not split, and you get a list of identical T's. So the
4935 semantics of the program depends on whether or not foo has a type signature.
4938 You may say that this is a good reason to dislike linear implicit parameters
4939 and you'd be right. That is why they are an experimental feature.
4945 ================ END OF Linear Implicit Parameters commented out -->
4947 <sect2 id="kinding">
4948 <title>Explicitly-kinded quantification</title>
4951 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4952 to give the kind explicitly as (machine-checked) documentation,
4953 just as it is nice to give a type signature for a function. On some occasions,
4954 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4955 John Hughes had to define the data type:
4957 data Set cxt a = Set [a]
4958 | Unused (cxt a -> ())
4960 The only use for the <literal>Unused</literal> constructor was to force the correct
4961 kind for the type variable <literal>cxt</literal>.
4964 GHC now instead allows you to specify the kind of a type variable directly, wherever
4965 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4968 This flag enables kind signatures in the following places:
4970 <listitem><para><literal>data</literal> declarations:
4972 data Set (cxt :: * -> *) a = Set [a]
4973 </screen></para></listitem>
4974 <listitem><para><literal>type</literal> declarations:
4976 type T (f :: * -> *) = f Int
4977 </screen></para></listitem>
4978 <listitem><para><literal>class</literal> declarations:
4980 class (Eq a) => C (f :: * -> *) a where ...
4981 </screen></para></listitem>
4982 <listitem><para><literal>forall</literal>'s in type signatures:
4984 f :: forall (cxt :: * -> *). Set cxt Int
4985 </screen></para></listitem>
4990 The parentheses are required. Some of the spaces are required too, to
4991 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4992 will get a parse error, because "<literal>::*->*</literal>" is a
4993 single lexeme in Haskell.
4997 As part of the same extension, you can put kind annotations in types
5000 f :: (Int :: *) -> Int
5001 g :: forall a. a -> (a :: *)
5005 atype ::= '(' ctype '::' kind ')
5007 The parentheses are required.
5012 <sect2 id="universal-quantification">
5013 <title>Arbitrary-rank polymorphism
5017 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5018 allows us to say exactly what this means. For example:
5026 g :: forall b. (b -> b)
5028 The two are treated identically.
5032 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5033 explicit universal quantification in
5035 For example, all the following types are legal:
5037 f1 :: forall a b. a -> b -> a
5038 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5040 f2 :: (forall a. a->a) -> Int -> Int
5041 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5043 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5045 f4 :: Int -> (forall a. a -> a)
5047 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5048 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5049 The <literal>forall</literal> makes explicit the universal quantification that
5050 is implicitly added by Haskell.
5053 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5054 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5055 shows, the polymorphic type on the left of the function arrow can be overloaded.
5058 The function <literal>f3</literal> has a rank-3 type;
5059 it has rank-2 types on the left of a function arrow.
5062 GHC has three flags to control higher-rank types:
5065 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5068 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5071 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5072 That is, you can nest <literal>forall</literal>s
5073 arbitrarily deep in function arrows.
5074 In particular, a forall-type (also called a "type scheme"),
5075 including an operational type class context, is legal:
5077 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5078 of a function arrow </para> </listitem>
5079 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5080 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5081 field type signatures.</para> </listitem>
5082 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5083 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5087 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5088 a type variable any more!
5097 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5098 the types of the constructor arguments. Here are several examples:
5104 data T a = T1 (forall b. b -> b -> b) a
5106 data MonadT m = MkMonad { return :: forall a. a -> m a,
5107 bind :: forall a b. m a -> (a -> m b) -> m b
5110 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5116 The constructors have rank-2 types:
5122 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5123 MkMonad :: forall m. (forall a. a -> m a)
5124 -> (forall a b. m a -> (a -> m b) -> m b)
5126 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5132 Notice that you don't need to use a <literal>forall</literal> if there's an
5133 explicit context. For example in the first argument of the
5134 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5135 prefixed to the argument type. The implicit <literal>forall</literal>
5136 quantifies all type variables that are not already in scope, and are
5137 mentioned in the type quantified over.
5141 As for type signatures, implicit quantification happens for non-overloaded
5142 types too. So if you write this:
5145 data T a = MkT (Either a b) (b -> b)
5148 it's just as if you had written this:
5151 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5154 That is, since the type variable <literal>b</literal> isn't in scope, it's
5155 implicitly universally quantified. (Arguably, it would be better
5156 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5157 where that is what is wanted. Feedback welcomed.)
5161 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5162 the constructor to suitable values, just as usual. For example,
5173 a3 = MkSwizzle reverse
5176 a4 = let r x = Just x
5183 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5184 mkTs f x y = [T1 f x, T1 f y]
5190 The type of the argument can, as usual, be more general than the type
5191 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5192 does not need the <literal>Ord</literal> constraint.)
5196 When you use pattern matching, the bound variables may now have
5197 polymorphic types. For example:
5203 f :: T a -> a -> (a, Char)
5204 f (T1 w k) x = (w k x, w 'c' 'd')
5206 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5207 g (MkSwizzle s) xs f = s (map f (s xs))
5209 h :: MonadT m -> [m a] -> m [a]
5210 h m [] = return m []
5211 h m (x:xs) = bind m x $ \y ->
5212 bind m (h m xs) $ \ys ->
5219 In the function <function>h</function> we use the record selectors <literal>return</literal>
5220 and <literal>bind</literal> to extract the polymorphic bind and return functions
5221 from the <literal>MonadT</literal> data structure, rather than using pattern
5227 <title>Type inference</title>
5230 In general, type inference for arbitrary-rank types is undecidable.
5231 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5232 to get a decidable algorithm by requiring some help from the programmer.
5233 We do not yet have a formal specification of "some help" but the rule is this:
5236 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5237 provides an explicit polymorphic type for x, or GHC's type inference will assume
5238 that x's type has no foralls in it</emphasis>.
5241 What does it mean to "provide" an explicit type for x? You can do that by
5242 giving a type signature for x directly, using a pattern type signature
5243 (<xref linkend="scoped-type-variables"/>), thus:
5245 \ f :: (forall a. a->a) -> (f True, f 'c')
5247 Alternatively, you can give a type signature to the enclosing
5248 context, which GHC can "push down" to find the type for the variable:
5250 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5252 Here the type signature on the expression can be pushed inwards
5253 to give a type signature for f. Similarly, and more commonly,
5254 one can give a type signature for the function itself:
5256 h :: (forall a. a->a) -> (Bool,Char)
5257 h f = (f True, f 'c')
5259 You don't need to give a type signature if the lambda bound variable
5260 is a constructor argument. Here is an example we saw earlier:
5262 f :: T a -> a -> (a, Char)
5263 f (T1 w k) x = (w k x, w 'c' 'd')
5265 Here we do not need to give a type signature to <literal>w</literal>, because
5266 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5273 <sect3 id="implicit-quant">
5274 <title>Implicit quantification</title>
5277 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5278 user-written types, if and only if there is no explicit <literal>forall</literal>,
5279 GHC finds all the type variables mentioned in the type that are not already
5280 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5284 f :: forall a. a -> a
5291 h :: forall b. a -> b -> b
5297 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5300 f :: (a -> a) -> Int
5302 f :: forall a. (a -> a) -> Int
5304 f :: (forall a. a -> a) -> Int
5307 g :: (Ord a => a -> a) -> Int
5308 -- MEANS the illegal type
5309 g :: forall a. (Ord a => a -> a) -> Int
5311 g :: (forall a. Ord a => a -> a) -> Int
5313 The latter produces an illegal type, which you might think is silly,
5314 but at least the rule is simple. If you want the latter type, you
5315 can write your for-alls explicitly. Indeed, doing so is strongly advised
5322 <sect2 id="impredicative-polymorphism">
5323 <title>Impredicative polymorphism
5325 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5326 enabled with <option>-XImpredicativeTypes</option>.
5328 that you can call a polymorphic function at a polymorphic type, and
5329 parameterise data structures over polymorphic types. For example:
5331 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5332 f (Just g) = Just (g [3], g "hello")
5335 Notice here that the <literal>Maybe</literal> type is parameterised by the
5336 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5339 <para>The technical details of this extension are described in the paper
5340 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5341 type inference for higher-rank types and impredicativity</ulink>,
5342 which appeared at ICFP 2006.
5346 <sect2 id="scoped-type-variables">
5347 <title>Lexically scoped type variables
5351 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5352 which some type signatures are simply impossible to write. For example:
5354 f :: forall a. [a] -> [a]
5360 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5361 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5362 The type variables bound by a <literal>forall</literal> scope over
5363 the entire definition of the accompanying value declaration.
5364 In this example, the type variable <literal>a</literal> scopes over the whole
5365 definition of <literal>f</literal>, including over
5366 the type signature for <varname>ys</varname>.
5367 In Haskell 98 it is not possible to declare
5368 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5369 it becomes possible to do so.
5371 <para>Lexically-scoped type variables are enabled by
5372 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5374 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5375 variables work, compared to earlier releases. Read this section
5379 <title>Overview</title>
5381 <para>The design follows the following principles
5383 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5384 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5385 design.)</para></listitem>
5386 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5387 type variables. This means that every programmer-written type signature
5388 (including one that contains free scoped type variables) denotes a
5389 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5390 checker, and no inference is involved.</para></listitem>
5391 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5392 changing the program.</para></listitem>
5396 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5398 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5399 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5400 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5401 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5405 In Haskell, a programmer-written type signature is implicitly quantified over
5406 its free type variables (<ulink
5407 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5409 of the Haskell Report).
5410 Lexically scoped type variables affect this implicit quantification rules
5411 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5412 quantified. For example, if type variable <literal>a</literal> is in scope,
5415 (e :: a -> a) means (e :: a -> a)
5416 (e :: b -> b) means (e :: forall b. b->b)
5417 (e :: a -> b) means (e :: forall b. a->b)
5425 <sect3 id="decl-type-sigs">
5426 <title>Declaration type signatures</title>
5427 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5428 quantification (using <literal>forall</literal>) brings into scope the
5429 explicitly-quantified
5430 type variables, in the definition of the named function. For example:
5432 f :: forall a. [a] -> [a]
5433 f (x:xs) = xs ++ [ x :: a ]
5435 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5436 the definition of "<literal>f</literal>".
5438 <para>This only happens if:
5440 <listitem><para> The quantification in <literal>f</literal>'s type
5441 signature is explicit. For example:
5444 g (x:xs) = xs ++ [ x :: a ]
5446 This program will be rejected, because "<literal>a</literal>" does not scope
5447 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5448 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5449 quantification rules.
5451 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5452 not a pattern binding.
5455 f1 :: forall a. [a] -> [a]
5456 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5458 f2 :: forall a. [a] -> [a]
5459 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5461 f3 :: forall a. [a] -> [a]
5462 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5464 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5465 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5466 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5467 the type signature brings <literal>a</literal> into scope.
5473 <sect3 id="exp-type-sigs">
5474 <title>Expression type signatures</title>
5476 <para>An expression type signature that has <emphasis>explicit</emphasis>
5477 quantification (using <literal>forall</literal>) brings into scope the
5478 explicitly-quantified
5479 type variables, in the annotated expression. For example:
5481 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5483 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5484 type variable <literal>s</literal> into scope, in the annotated expression
5485 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5490 <sect3 id="pattern-type-sigs">
5491 <title>Pattern type signatures</title>
5493 A type signature may occur in any pattern; this is a <emphasis>pattern type
5494 signature</emphasis>.
5497 -- f and g assume that 'a' is already in scope
5498 f = \(x::Int, y::a) -> x
5500 h ((x,y) :: (Int,Bool)) = (y,x)
5502 In the case where all the type variables in the pattern type signature are
5503 already in scope (i.e. bound by the enclosing context), matters are simple: the
5504 signature simply constrains the type of the pattern in the obvious way.
5507 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5508 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5509 that are already in scope. For example:
5511 f :: forall a. [a] -> (Int, [a])
5514 (ys::[a], n) = (reverse xs, length xs) -- OK
5515 zs::[a] = xs ++ ys -- OK
5517 Just (v::b) = ... -- Not OK; b is not in scope
5519 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5520 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5524 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5525 type signature may mention a type variable that is not in scope; in this case,
5526 <emphasis>the signature brings that type variable into scope</emphasis>.
5527 This is particularly important for existential data constructors. For example:
5529 data T = forall a. MkT [a]
5532 k (MkT [t::a]) = MkT t3
5536 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5537 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5538 because it is bound by the pattern match. GHC's rule is that in this situation
5539 (and only then), a pattern type signature can mention a type variable that is
5540 not already in scope; the effect is to bring it into scope, standing for the
5541 existentially-bound type variable.
5544 When a pattern type signature binds a type variable in this way, GHC insists that the
5545 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5546 This means that any user-written type signature always stands for a completely known type.
5549 If all this seems a little odd, we think so too. But we must have
5550 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5551 could not name existentially-bound type variables in subsequent type signatures.
5554 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5555 signature is allowed to mention a lexical variable that is not already in
5557 For example, both <literal>f</literal> and <literal>g</literal> would be
5558 illegal if <literal>a</literal> was not already in scope.
5564 <!-- ==================== Commented out part about result type signatures
5566 <sect3 id="result-type-sigs">
5567 <title>Result type signatures</title>
5570 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5573 {- f assumes that 'a' is already in scope -}
5574 f x y :: [a] = [x,y,x]
5576 g = \ x :: [Int] -> [3,4]
5578 h :: forall a. [a] -> a
5582 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5583 the result of the function. Similarly, the body of the lambda in the RHS of
5584 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5585 alternative in <literal>h</literal> is <literal>a</literal>.
5587 <para> A result type signature never brings new type variables into scope.</para>
5589 There are a couple of syntactic wrinkles. First, notice that all three
5590 examples would parse quite differently with parentheses:
5592 {- f assumes that 'a' is already in scope -}
5593 f x (y :: [a]) = [x,y,x]
5595 g = \ (x :: [Int]) -> [3,4]
5597 h :: forall a. [a] -> a
5601 Now the signature is on the <emphasis>pattern</emphasis>; and
5602 <literal>h</literal> would certainly be ill-typed (since the pattern
5603 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5605 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5606 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5607 token or a parenthesised type of some sort). To see why,
5608 consider how one would parse this:
5617 <sect3 id="cls-inst-scoped-tyvars">
5618 <title>Class and instance declarations</title>
5621 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5622 scope over the methods defined in the <literal>where</literal> part. For example:
5640 <sect2 id="typing-binds">
5641 <title>Generalised typing of mutually recursive bindings</title>
5644 The Haskell Report specifies that a group of bindings (at top level, or in a
5645 <literal>let</literal> or <literal>where</literal>) should be sorted into
5646 strongly-connected components, and then type-checked in dependency order
5647 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5648 Report, Section 4.5.1</ulink>).
5649 As each group is type-checked, any binders of the group that
5651 an explicit type signature are put in the type environment with the specified
5653 and all others are monomorphic until the group is generalised
5654 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5657 <para>Following a suggestion of Mark Jones, in his paper
5658 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5660 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5662 <emphasis>the dependency analysis ignores references to variables that have an explicit
5663 type signature</emphasis>.
5664 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5665 typecheck. For example, consider:
5667 f :: Eq a => a -> Bool
5668 f x = (x == x) || g True || g "Yes"
5670 g y = (y <= y) || f True
5672 This is rejected by Haskell 98, but under Jones's scheme the definition for
5673 <literal>g</literal> is typechecked first, separately from that for
5674 <literal>f</literal>,
5675 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5676 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5677 type is generalised, to get
5679 g :: Ord a => a -> Bool
5681 Now, the definition for <literal>f</literal> is typechecked, with this type for
5682 <literal>g</literal> in the type environment.
5686 The same refined dependency analysis also allows the type signatures of
5687 mutually-recursive functions to have different contexts, something that is illegal in
5688 Haskell 98 (Section 4.5.2, last sentence). With
5689 <option>-XRelaxedPolyRec</option>
5690 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5691 type signatures; in practice this means that only variables bound by the same
5692 pattern binding must have the same context. For example, this is fine:
5694 f :: Eq a => a -> Bool
5695 f x = (x == x) || g True
5697 g :: Ord a => a -> Bool
5698 g y = (y <= y) || f True
5704 <!-- ==================== End of type system extensions ================= -->
5706 <!-- ====================== TEMPLATE HASKELL ======================= -->
5708 <sect1 id="template-haskell">
5709 <title>Template Haskell</title>
5711 <para>Template Haskell allows you to do compile-time meta-programming in
5714 the main technical innovations is discussed in "<ulink
5715 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5716 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5719 There is a Wiki page about
5720 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5721 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5725 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5726 Haskell library reference material</ulink>
5727 (look for module <literal>Language.Haskell.TH</literal>).
5728 Many changes to the original design are described in
5729 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5730 Notes on Template Haskell version 2</ulink>.
5731 Not all of these changes are in GHC, however.
5734 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5735 as a worked example to help get you started.
5739 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5740 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5745 <title>Syntax</title>
5747 <para> Template Haskell has the following new syntactic
5748 constructions. You need to use the flag
5749 <option>-XTemplateHaskell</option>
5750 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5751 </indexterm>to switch these syntactic extensions on
5752 (<option>-XTemplateHaskell</option> is no longer implied by
5753 <option>-fglasgow-exts</option>).</para>
5757 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5758 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5759 There must be no space between the "$" and the identifier or parenthesis. This use
5760 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5761 of "." as an infix operator. If you want the infix operator, put spaces around it.
5763 <para> A splice can occur in place of
5765 <listitem><para> an expression; the spliced expression must
5766 have type <literal>Q Exp</literal></para></listitem>
5767 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5770 Inside a splice you can can only call functions defined in imported modules,
5771 not functions defined elsewhere in the same module.</listitem>
5775 A expression quotation is written in Oxford brackets, thus:
5777 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5778 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5779 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5780 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5781 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5782 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5783 </itemizedlist></para></listitem>
5786 A quasi-quotation can appear in either a pattern context or an
5787 expression context and is also written in Oxford brackets:
5789 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5790 where the "..." is an arbitrary string; a full description of the
5791 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5792 </itemizedlist></para></listitem>
5795 A name can be quoted with either one or two prefix single quotes:
5797 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5798 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5799 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5801 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5802 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5805 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5806 may also be given as an argument to the <literal>reify</literal> function.
5812 (Compared to the original paper, there are many differences of detail.
5813 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5814 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5815 Type splices are not implemented, and neither are pattern splices or quotations.
5819 <sect2> <title> Using Template Haskell </title>
5823 The data types and monadic constructor functions for Template Haskell are in the library
5824 <literal>Language.Haskell.THSyntax</literal>.
5828 You can only run a function at compile time if it is imported from another module. That is,
5829 you can't define a function in a module, and call it from within a splice in the same module.
5830 (It would make sense to do so, but it's hard to implement.)
5834 You can only run a function at compile time if it is imported
5835 from another module <emphasis>that is not part of a mutually-recursive group of modules
5836 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5837 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5838 splice is to be run.</para>
5840 For example, when compiling module A,
5841 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5842 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5846 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5849 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5850 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5851 compiles and runs a program, and then looks at the result. So it's important that
5852 the program it compiles produces results whose representations are identical to
5853 those of the compiler itself.
5857 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5858 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5863 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5864 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5865 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5872 -- Import our template "pr"
5873 import Printf ( pr )
5875 -- The splice operator $ takes the Haskell source code
5876 -- generated at compile time by "pr" and splices it into
5877 -- the argument of "putStrLn".
5878 main = putStrLn ( $(pr "Hello") )
5884 -- Skeletal printf from the paper.
5885 -- It needs to be in a separate module to the one where
5886 -- you intend to use it.
5888 -- Import some Template Haskell syntax
5889 import Language.Haskell.TH
5891 -- Describe a format string
5892 data Format = D | S | L String
5894 -- Parse a format string. This is left largely to you
5895 -- as we are here interested in building our first ever
5896 -- Template Haskell program and not in building printf.
5897 parse :: String -> [Format]
5900 -- Generate Haskell source code from a parsed representation
5901 -- of the format string. This code will be spliced into
5902 -- the module which calls "pr", at compile time.
5903 gen :: [Format] -> Q Exp
5904 gen [D] = [| \n -> show n |]
5905 gen [S] = [| \s -> s |]
5906 gen [L s] = stringE s
5908 -- Here we generate the Haskell code for the splice
5909 -- from an input format string.
5910 pr :: String -> Q Exp
5911 pr s = gen (parse s)
5914 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5917 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5920 <para>Run "main.exe" and here is your output:</para>
5930 <title>Using Template Haskell with Profiling</title>
5931 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5933 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5934 interpreter to run the splice expressions. The bytecode interpreter
5935 runs the compiled expression on top of the same runtime on which GHC
5936 itself is running; this means that the compiled code referred to by
5937 the interpreted expression must be compatible with this runtime, and
5938 in particular this means that object code that is compiled for
5939 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5940 expression, because profiled object code is only compatible with the
5941 profiling version of the runtime.</para>
5943 <para>This causes difficulties if you have a multi-module program
5944 containing Template Haskell code and you need to compile it for
5945 profiling, because GHC cannot load the profiled object code and use it
5946 when executing the splices. Fortunately GHC provides a workaround.
5947 The basic idea is to compile the program twice:</para>
5951 <para>Compile the program or library first the normal way, without
5952 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5955 <para>Then compile it again with <option>-prof</option>, and
5956 additionally use <option>-osuf
5957 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5958 to name the object files differently (you can choose any suffix
5959 that isn't the normal object suffix here). GHC will automatically
5960 load the object files built in the first step when executing splice
5961 expressions. If you omit the <option>-osuf</option> flag when
5962 building with <option>-prof</option> and Template Haskell is used,
5963 GHC will emit an error message. </para>
5968 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5969 <para>Quasi-quotation allows patterns and expressions to be written using
5970 programmer-defined concrete syntax; the motivation behind the extension and
5971 several examples are documented in
5972 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5973 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5974 2007). The example below shows how to write a quasiquoter for a simple
5975 expression language.</para>
5978 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5979 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5980 functions for quoting expressions and patterns, respectively. The first argument
5981 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5982 context of the quasi-quotation statement determines which of the two parsers is
5983 called: if the quasi-quotation occurs in an expression context, the expression
5984 parser is called, and if it occurs in a pattern context, the pattern parser is
5988 Note that in the example we make use of an antiquoted
5989 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5990 (this syntax for anti-quotation was defined by the parser's
5991 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5992 integer value argument of the constructor <literal>IntExpr</literal> when
5993 pattern matching. Please see the referenced paper for further details regarding
5994 anti-quotation as well as the description of a technique that uses SYB to
5995 leverage a single parser of type <literal>String -> a</literal> to generate both
5996 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5997 pattern parser that returns a value of type <literal>Q Pat</literal>.
6000 <para>In general, a quasi-quote has the form
6001 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6002 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6003 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6004 can be arbitrary, and may contain newlines.
6007 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6008 the example, <literal>expr</literal> cannot be defined
6009 in <literal>Main.hs</literal> where it is used, but must be imported.
6020 main = do { print $ eval [$expr|1 + 2|]
6022 { [$expr|'int:n|] -> print n
6031 import qualified Language.Haskell.TH as TH
6032 import Language.Haskell.TH.Quote
6034 data Expr = IntExpr Integer
6035 | AntiIntExpr String
6036 | BinopExpr BinOp Expr Expr
6038 deriving(Show, Typeable, Data)
6044 deriving(Show, Typeable, Data)
6046 eval :: Expr -> Integer
6047 eval (IntExpr n) = n
6048 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6055 expr = QuasiQuoter parseExprExp parseExprPat
6057 -- Parse an Expr, returning its representation as
6058 -- either a Q Exp or a Q Pat. See the referenced paper
6059 -- for how to use SYB to do this by writing a single
6060 -- parser of type String -> Expr instead of two
6061 -- separate parsers.
6063 parseExprExp :: String -> Q Exp
6066 parseExprPat :: String -> Q Pat
6070 <para>Now run the compiler:
6073 $ ghc --make -XQuasiQuotes Main.hs -o main
6076 <para>Run "main" and here is your output:</para>
6088 <!-- ===================== Arrow notation =================== -->
6090 <sect1 id="arrow-notation">
6091 <title>Arrow notation
6094 <para>Arrows are a generalization of monads introduced by John Hughes.
6095 For more details, see
6100 “Generalising Monads to Arrows”,
6101 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6102 pp67–111, May 2000.
6103 The paper that introduced arrows: a friendly introduction, motivated with
6104 programming examples.
6110 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6111 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6112 Introduced the notation described here.
6118 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6119 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6126 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6127 John Hughes, in <citetitle>5th International Summer School on
6128 Advanced Functional Programming</citetitle>,
6129 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6131 This paper includes another introduction to the notation,
6132 with practical examples.
6138 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6139 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6140 A terse enumeration of the formal rules used
6141 (extracted from comments in the source code).
6147 The arrows web page at
6148 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6153 With the <option>-XArrows</option> flag, GHC supports the arrow
6154 notation described in the second of these papers,
6155 translating it using combinators from the
6156 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6158 What follows is a brief introduction to the notation;
6159 it won't make much sense unless you've read Hughes's paper.
6162 <para>The extension adds a new kind of expression for defining arrows:
6164 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6165 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6167 where <literal>proc</literal> is a new keyword.
6168 The variables of the pattern are bound in the body of the
6169 <literal>proc</literal>-expression,
6170 which is a new sort of thing called a <firstterm>command</firstterm>.
6171 The syntax of commands is as follows:
6173 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6174 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6175 | <replaceable>cmd</replaceable><superscript>0</superscript>
6177 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6178 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6179 infix operators as for expressions, and
6181 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6182 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6183 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6184 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6185 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6186 | <replaceable>fcmd</replaceable>
6188 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6189 | ( <replaceable>cmd</replaceable> )
6190 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6192 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6193 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6194 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6195 | <replaceable>cmd</replaceable>
6197 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6198 except that the bodies are commands instead of expressions.
6202 Commands produce values, but (like monadic computations)
6203 may yield more than one value,
6204 or none, and may do other things as well.
6205 For the most part, familiarity with monadic notation is a good guide to
6207 However the values of expressions, even monadic ones,
6208 are determined by the values of the variables they contain;
6209 this is not necessarily the case for commands.
6213 A simple example of the new notation is the expression
6215 proc x -> f -< x+1
6217 We call this a <firstterm>procedure</firstterm> or
6218 <firstterm>arrow abstraction</firstterm>.
6219 As with a lambda expression, the variable <literal>x</literal>
6220 is a new variable bound within the <literal>proc</literal>-expression.
6221 It refers to the input to the arrow.
6222 In the above example, <literal>-<</literal> is not an identifier but an
6223 new reserved symbol used for building commands from an expression of arrow
6224 type and an expression to be fed as input to that arrow.
6225 (The weird look will make more sense later.)
6226 It may be read as analogue of application for arrows.
6227 The above example is equivalent to the Haskell expression
6229 arr (\ x -> x+1) >>> f
6231 That would make no sense if the expression to the left of
6232 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6233 More generally, the expression to the left of <literal>-<</literal>
6234 may not involve any <firstterm>local variable</firstterm>,
6235 i.e. a variable bound in the current arrow abstraction.
6236 For such a situation there is a variant <literal>-<<</literal>, as in
6238 proc x -> f x -<< x+1
6240 which is equivalent to
6242 arr (\ x -> (f x, x+1)) >>> app
6244 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6246 Such an arrow is equivalent to a monad, so if you're using this form
6247 you may find a monadic formulation more convenient.
6251 <title>do-notation for commands</title>
6254 Another form of command is a form of <literal>do</literal>-notation.
6255 For example, you can write
6264 You can read this much like ordinary <literal>do</literal>-notation,
6265 but with commands in place of monadic expressions.
6266 The first line sends the value of <literal>x+1</literal> as an input to
6267 the arrow <literal>f</literal>, and matches its output against
6268 <literal>y</literal>.
6269 In the next line, the output is discarded.
6270 The arrow <function>returnA</function> is defined in the
6271 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6272 module as <literal>arr id</literal>.
6273 The above example is treated as an abbreviation for
6275 arr (\ x -> (x, x)) >>>
6276 first (arr (\ x -> x+1) >>> f) >>>
6277 arr (\ (y, x) -> (y, (x, y))) >>>
6278 first (arr (\ y -> 2*y) >>> g) >>>
6280 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6281 first (arr (\ (x, z) -> x*z) >>> h) >>>
6282 arr (\ (t, z) -> t+z) >>>
6285 Note that variables not used later in the composition are projected out.
6286 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6288 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6289 module, this reduces to
6291 arr (\ x -> (x+1, x)) >>>
6293 arr (\ (y, x) -> (2*y, (x, y))) >>>
6295 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6297 arr (\ (t, z) -> t+z)
6299 which is what you might have written by hand.
6300 With arrow notation, GHC keeps track of all those tuples of variables for you.
6304 Note that although the above translation suggests that
6305 <literal>let</literal>-bound variables like <literal>z</literal> must be
6306 monomorphic, the actual translation produces Core,
6307 so polymorphic variables are allowed.
6311 It's also possible to have mutually recursive bindings,
6312 using the new <literal>rec</literal> keyword, as in the following example:
6314 counter :: ArrowCircuit a => a Bool Int
6315 counter = proc reset -> do
6316 rec output <- returnA -< if reset then 0 else next
6317 next <- delay 0 -< output+1
6318 returnA -< output
6320 The translation of such forms uses the <function>loop</function> combinator,
6321 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6327 <title>Conditional commands</title>
6330 In the previous example, we used a conditional expression to construct the
6332 Sometimes we want to conditionally execute different commands, as in
6339 which is translated to
6341 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6342 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6344 Since the translation uses <function>|||</function>,
6345 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6349 There are also <literal>case</literal> commands, like
6355 y <- h -< (x1, x2)
6359 The syntax is the same as for <literal>case</literal> expressions,
6360 except that the bodies of the alternatives are commands rather than expressions.
6361 The translation is similar to that of <literal>if</literal> commands.
6367 <title>Defining your own control structures</title>
6370 As we're seen, arrow notation provides constructs,
6371 modelled on those for expressions,
6372 for sequencing, value recursion and conditionals.
6373 But suitable combinators,
6374 which you can define in ordinary Haskell,
6375 may also be used to build new commands out of existing ones.
6376 The basic idea is that a command defines an arrow from environments to values.
6377 These environments assign values to the free local variables of the command.
6378 Thus combinators that produce arrows from arrows
6379 may also be used to build commands from commands.
6380 For example, the <literal>ArrowChoice</literal> class includes a combinator
6382 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6384 so we can use it to build commands:
6386 expr' = proc x -> do
6389 symbol Plus -< ()
6390 y <- term -< ()
6393 symbol Minus -< ()
6394 y <- term -< ()
6397 (The <literal>do</literal> on the first line is needed to prevent the first
6398 <literal><+> ...</literal> from being interpreted as part of the
6399 expression on the previous line.)
6400 This is equivalent to
6402 expr' = (proc x -> returnA -< x)
6403 <+> (proc x -> do
6404 symbol Plus -< ()
6405 y <- term -< ()
6407 <+> (proc x -> do
6408 symbol Minus -< ()
6409 y <- term -< ()
6412 It is essential that this operator be polymorphic in <literal>e</literal>
6413 (representing the environment input to the command
6414 and thence to its subcommands)
6415 and satisfy the corresponding naturality property
6417 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6419 at least for strict <literal>k</literal>.
6420 (This should be automatic if you're not using <function>seq</function>.)
6421 This ensures that environments seen by the subcommands are environments
6422 of the whole command,
6423 and also allows the translation to safely trim these environments.
6424 The operator must also not use any variable defined within the current
6429 We could define our own operator
6431 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6432 untilA body cond = proc x ->
6433 b <- cond -< x
6434 if b then returnA -< ()
6437 untilA body cond -< x
6439 and use it in the same way.
6440 Of course this infix syntax only makes sense for binary operators;
6441 there is also a more general syntax involving special brackets:
6445 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6452 <title>Primitive constructs</title>
6455 Some operators will need to pass additional inputs to their subcommands.
6456 For example, in an arrow type supporting exceptions,
6457 the operator that attaches an exception handler will wish to pass the
6458 exception that occurred to the handler.
6459 Such an operator might have a type
6461 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6463 where <literal>Ex</literal> is the type of exceptions handled.
6464 You could then use this with arrow notation by writing a command
6466 body `handleA` \ ex -> handler
6468 so that if an exception is raised in the command <literal>body</literal>,
6469 the variable <literal>ex</literal> is bound to the value of the exception
6470 and the command <literal>handler</literal>,
6471 which typically refers to <literal>ex</literal>, is entered.
6472 Though the syntax here looks like a functional lambda,
6473 we are talking about commands, and something different is going on.
6474 The input to the arrow represented by a command consists of values for
6475 the free local variables in the command, plus a stack of anonymous values.
6476 In all the prior examples, this stack was empty.
6477 In the second argument to <function>handleA</function>,
6478 this stack consists of one value, the value of the exception.
6479 The command form of lambda merely gives this value a name.
6484 the values on the stack are paired to the right of the environment.
6485 So operators like <function>handleA</function> that pass
6486 extra inputs to their subcommands can be designed for use with the notation
6487 by pairing the values with the environment in this way.
6488 More precisely, the type of each argument of the operator (and its result)
6489 should have the form
6491 a (...(e,t1), ... tn) t
6493 where <replaceable>e</replaceable> is a polymorphic variable
6494 (representing the environment)
6495 and <replaceable>ti</replaceable> are the types of the values on the stack,
6496 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6497 The polymorphic variable <replaceable>e</replaceable> must not occur in
6498 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6499 <replaceable>t</replaceable>.
6500 However the arrows involved need not be the same.
6501 Here are some more examples of suitable operators:
6503 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6504 runReader :: ... => a e c -> a' (e,State) c
6505 runState :: ... => a e c -> a' (e,State) (c,State)
6507 We can supply the extra input required by commands built with the last two
6508 by applying them to ordinary expressions, as in
6512 (|runReader (do { ... })|) s
6514 which adds <literal>s</literal> to the stack of inputs to the command
6515 built using <function>runReader</function>.
6519 The command versions of lambda abstraction and application are analogous to
6520 the expression versions.
6521 In particular, the beta and eta rules describe equivalences of commands.
6522 These three features (operators, lambda abstraction and application)
6523 are the core of the notation; everything else can be built using them,
6524 though the results would be somewhat clumsy.
6525 For example, we could simulate <literal>do</literal>-notation by defining
6527 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6528 u `bind` f = returnA &&& u >>> f
6530 bind_ :: Arrow a => a e b -> a e c -> a e c
6531 u `bind_` f = u `bind` (arr fst >>> f)
6533 We could simulate <literal>if</literal> by defining
6535 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6536 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6543 <title>Differences with the paper</title>
6548 <para>Instead of a single form of arrow application (arrow tail) with two
6549 translations, the implementation provides two forms
6550 <quote><literal>-<</literal></quote> (first-order)
6551 and <quote><literal>-<<</literal></quote> (higher-order).
6556 <para>User-defined operators are flagged with banana brackets instead of
6557 a new <literal>form</literal> keyword.
6566 <title>Portability</title>
6569 Although only GHC implements arrow notation directly,
6570 there is also a preprocessor
6572 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6573 that translates arrow notation into Haskell 98
6574 for use with other Haskell systems.
6575 You would still want to check arrow programs with GHC;
6576 tracing type errors in the preprocessor output is not easy.
6577 Modules intended for both GHC and the preprocessor must observe some
6578 additional restrictions:
6583 The module must import
6584 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6590 The preprocessor cannot cope with other Haskell extensions.
6591 These would have to go in separate modules.
6597 Because the preprocessor targets Haskell (rather than Core),
6598 <literal>let</literal>-bound variables are monomorphic.
6609 <!-- ==================== BANG PATTERNS ================= -->
6611 <sect1 id="bang-patterns">
6612 <title>Bang patterns
6613 <indexterm><primary>Bang patterns</primary></indexterm>
6615 <para>GHC supports an extension of pattern matching called <emphasis>bang
6616 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6617 Bang patterns are under consideration for Haskell Prime.
6619 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6620 prime feature description</ulink> contains more discussion and examples
6621 than the material below.
6624 The key change is the addition of a new rule to the
6625 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6626 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6627 against a value <replaceable>v</replaceable> behaves as follows:
6629 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6630 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6634 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6637 <sect2 id="bang-patterns-informal">
6638 <title>Informal description of bang patterns
6641 The main idea is to add a single new production to the syntax of patterns:
6645 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6646 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6651 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6652 whereas without the bang it would be lazy.
6653 Bang patterns can be nested of course:
6657 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6658 <literal>y</literal>.
6659 A bang only really has an effect if it precedes a variable or wild-card pattern:
6664 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6665 putting a bang before a pattern that
6666 forces evaluation anyway does nothing.
6669 There is one (apparent) exception to this general rule that a bang only
6670 makes a difference when it precedes a variable or wild-card: a bang at the
6671 top level of a <literal>let</literal> or <literal>where</literal>
6672 binding makes the binding strict, regardless of the pattern. For example:
6676 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6677 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6678 (We say "apparent" exception because the Right Way to think of it is that the bang
6679 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6680 is part of the syntax of the <emphasis>binding</emphasis>.)
6681 Nested bangs in a pattern binding behave uniformly with all other forms of
6682 pattern matching. For example
6684 let (!x,[y]) = e in b
6686 is equivalent to this:
6688 let { t = case e of (x,[y]) -> x `seq` (x,y)
6693 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6694 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6695 evaluation of <literal>x</literal>.
6698 Bang patterns work in <literal>case</literal> expressions too, of course:
6700 g5 x = let y = f x in body
6701 g6 x = case f x of { y -> body }
6702 g7 x = case f x of { !y -> body }
6704 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6705 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6706 result, and then evaluates <literal>body</literal>.
6711 <sect2 id="bang-patterns-sem">
6712 <title>Syntax and semantics
6716 We add a single new production to the syntax of patterns:
6720 There is one problem with syntactic ambiguity. Consider:
6724 Is this a definition of the infix function "<literal>(!)</literal>",
6725 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6726 ambiguity in favour of the latter. If you want to define
6727 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6732 The semantics of Haskell pattern matching is described in <ulink
6733 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6734 Section 3.17.2</ulink> of the Haskell Report. To this description add
6735 one extra item 10, saying:
6736 <itemizedlist><listitem><para>Matching
6737 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6738 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6739 <listitem><para>otherwise, <literal>pat</literal> is matched against
6740 <literal>v</literal></para></listitem>
6742 </para></listitem></itemizedlist>
6743 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6744 Section 3.17.3</ulink>, add a new case (t):
6746 case v of { !pat -> e; _ -> e' }
6747 = v `seq` case v of { pat -> e; _ -> e' }
6750 That leaves let expressions, whose translation is given in
6751 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6753 of the Haskell Report.
6754 In the translation box, first apply
6755 the following transformation: for each pattern <literal>pi</literal> that is of
6756 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6757 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6758 have a bang at the top, apply the rules in the existing box.
6760 <para>The effect of the let rule is to force complete matching of the pattern
6761 <literal>qi</literal> before evaluation of the body is begun. The bang is
6762 retained in the translated form in case <literal>qi</literal> is a variable,
6770 The let-binding can be recursive. However, it is much more common for
6771 the let-binding to be non-recursive, in which case the following law holds:
6772 <literal>(let !p = rhs in body)</literal>
6774 <literal>(case rhs of !p -> body)</literal>
6777 A pattern with a bang at the outermost level is not allowed at the top level of
6783 <!-- ==================== ASSERTIONS ================= -->
6785 <sect1 id="assertions">
6787 <indexterm><primary>Assertions</primary></indexterm>
6791 If you want to make use of assertions in your standard Haskell code, you
6792 could define a function like the following:
6798 assert :: Bool -> a -> a
6799 assert False x = error "assertion failed!"
6806 which works, but gives you back a less than useful error message --
6807 an assertion failed, but which and where?
6811 One way out is to define an extended <function>assert</function> function which also
6812 takes a descriptive string to include in the error message and
6813 perhaps combine this with the use of a pre-processor which inserts
6814 the source location where <function>assert</function> was used.
6818 Ghc offers a helping hand here, doing all of this for you. For every
6819 use of <function>assert</function> in the user's source:
6825 kelvinToC :: Double -> Double
6826 kelvinToC k = assert (k >= 0.0) (k+273.15)
6832 Ghc will rewrite this to also include the source location where the
6839 assert pred val ==> assertError "Main.hs|15" pred val
6845 The rewrite is only performed by the compiler when it spots
6846 applications of <function>Control.Exception.assert</function>, so you
6847 can still define and use your own versions of
6848 <function>assert</function>, should you so wish. If not, import
6849 <literal>Control.Exception</literal> to make use
6850 <function>assert</function> in your code.
6854 GHC ignores assertions when optimisation is turned on with the
6855 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6856 <literal>assert pred e</literal> will be rewritten to
6857 <literal>e</literal>. You can also disable assertions using the
6858 <option>-fignore-asserts</option>
6859 option<indexterm><primary><option>-fignore-asserts</option></primary>
6860 </indexterm>.</para>
6863 Assertion failures can be caught, see the documentation for the
6864 <literal>Control.Exception</literal> library for the details.
6870 <!-- =============================== PRAGMAS =========================== -->
6872 <sect1 id="pragmas">
6873 <title>Pragmas</title>
6875 <indexterm><primary>pragma</primary></indexterm>
6877 <para>GHC supports several pragmas, or instructions to the
6878 compiler placed in the source code. Pragmas don't normally affect
6879 the meaning of the program, but they might affect the efficiency
6880 of the generated code.</para>
6882 <para>Pragmas all take the form
6884 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6886 where <replaceable>word</replaceable> indicates the type of
6887 pragma, and is followed optionally by information specific to that
6888 type of pragma. Case is ignored in
6889 <replaceable>word</replaceable>. The various values for
6890 <replaceable>word</replaceable> that GHC understands are described
6891 in the following sections; any pragma encountered with an
6892 unrecognised <replaceable>word</replaceable> is (silently)
6893 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6894 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6896 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
6900 pragma must precede the <literal>module</literal> keyword in the file.
6903 There can be as many file-header pragmas as you please, and they can be
6904 preceded or followed by comments.
6907 File-header pragmas are read once only, before
6908 pre-processing the file (e.g. with cpp).
6911 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
6912 <literal>{-# OPTIONS_GHC #-}</literal>, and
6913 <literal>{-# INCLUDE #-}</literal>.
6918 <sect2 id="language-pragma">
6919 <title>LANGUAGE pragma</title>
6921 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6922 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6924 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6926 It is the intention that all Haskell compilers support the
6927 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6928 all extensions are supported by all compilers, of
6929 course. The <literal>LANGUAGE</literal> pragma should be used instead
6930 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6932 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6934 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6936 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6938 <para>Every language extension can also be turned into a command-line flag
6939 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6940 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6943 <para>A list of all supported language extensions can be obtained by invoking
6944 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6946 <para>Any extension from the <literal>Extension</literal> type defined in
6948 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6949 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6953 <sect2 id="options-pragma">
6954 <title>OPTIONS_GHC pragma</title>
6955 <indexterm><primary>OPTIONS_GHC</primary>
6957 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6960 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6961 additional options that are given to the compiler when compiling
6962 this source file. See <xref linkend="source-file-options"/> for
6965 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6966 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6969 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6971 <sect2 id="include-pragma">
6972 <title>INCLUDE pragma</title>
6974 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6975 of C header files that should be <literal>#include</literal>'d into
6976 the C source code generated by the compiler for the current module (if
6977 compiling via C). For example:</para>
6980 {-# INCLUDE "foo.h" #-}
6981 {-# INCLUDE <stdio.h> #-}</programlisting>
6983 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6985 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6986 to the <option>-#include</option> option (<xref
6987 linkend="options-C-compiler" />), because the
6988 <literal>INCLUDE</literal> pragma is understood by other
6989 compilers. Yet another alternative is to add the include file to each
6990 <literal>foreign import</literal> declaration in your code, but we
6991 don't recommend using this approach with GHC.</para>
6994 <sect2 id="warning-deprecated-pragma">
6995 <title>WARNING and DEPRECATED pragmas</title>
6996 <indexterm><primary>WARNING</primary></indexterm>
6997 <indexterm><primary>DEPRECATED</primary></indexterm>
6999 <para>The WARNING pragma allows you to attach an arbitrary warning
7000 to a particular function, class, or type.
7001 A DEPRECATED pragma lets you specify that
7002 a particular function, class, or type is deprecated.
7003 There are two ways of using these pragmas.
7007 <para>You can work on an entire module thus:</para>
7009 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7014 module Wibble {-# WARNING "This is an unstable interface." #-} where
7017 <para>When you compile any module that import
7018 <literal>Wibble</literal>, GHC will print the specified
7023 <para>You can attach a warning to a function, class, type, or data constructor, with the
7024 following top-level declarations:</para>
7026 {-# DEPRECATED f, C, T "Don't use these" #-}
7027 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7029 <para>When you compile any module that imports and uses any
7030 of the specified entities, GHC will print the specified
7032 <para> You can only attach to entities declared at top level in the module
7033 being compiled, and you can only use unqualified names in the list of
7034 entities. A capitalised name, such as <literal>T</literal>
7035 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7036 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7037 both are in scope. If both are in scope, there is currently no way to
7038 specify one without the other (c.f. fixities
7039 <xref linkend="infix-tycons"/>).</para>
7042 Warnings and deprecations are not reported for
7043 (a) uses within the defining module, and
7044 (b) uses in an export list.
7045 The latter reduces spurious complaints within a library
7046 in which one module gathers together and re-exports
7047 the exports of several others.
7049 <para>You can suppress the warnings with the flag
7050 <option>-fno-warn-warnings-deprecations</option>.</para>
7053 <sect2 id="inline-noinline-pragma">
7054 <title>INLINE and NOINLINE pragmas</title>
7056 <para>These pragmas control the inlining of function
7059 <sect3 id="inline-pragma">
7060 <title>INLINE pragma</title>
7061 <indexterm><primary>INLINE</primary></indexterm>
7063 <para>GHC (with <option>-O</option>, as always) tries to
7064 inline (or “unfold”) functions/values that are
7065 “small enough,” thus avoiding the call overhead
7066 and possibly exposing other more-wonderful optimisations.
7067 Normally, if GHC decides a function is “too
7068 expensive” to inline, it will not do so, nor will it
7069 export that unfolding for other modules to use.</para>
7071 <para>The sledgehammer you can bring to bear is the
7072 <literal>INLINE</literal><indexterm><primary>INLINE
7073 pragma</primary></indexterm> pragma, used thusly:</para>
7076 key_function :: Int -> String -> (Bool, Double)
7077 {-# INLINE key_function #-}
7080 <para>The major effect of an <literal>INLINE</literal> pragma
7081 is to declare a function's “cost” to be very low.
7082 The normal unfolding machinery will then be very keen to
7083 inline it. However, an <literal>INLINE</literal> pragma for a
7084 function "<literal>f</literal>" has a number of other effects:
7087 No functions are inlined into <literal>f</literal>. Otherwise
7088 GHC might inline a big function into <literal>f</literal>'s right hand side,
7089 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7092 The float-in, float-out, and common-sub-expression transformations are not
7093 applied to the body of <literal>f</literal>.
7096 An INLINE function is not worker/wrappered by strictness analysis.
7097 It's going to be inlined wholesale instead.
7100 All of these effects are aimed at ensuring that what gets inlined is
7101 exactly what you asked for, no more and no less.
7103 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7104 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7105 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7106 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7107 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7108 when there is no choice even an INLINE function can be selected, in which case
7109 the INLINE pragma is ignored.
7110 For example, for a self-recursive function, the loop breaker can only be the function
7111 itself, so an INLINE pragma is always ignored.</para>
7113 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7114 function can be put anywhere its type signature could be
7117 <para><literal>INLINE</literal> pragmas are a particularly
7119 <literal>then</literal>/<literal>return</literal> (or
7120 <literal>bind</literal>/<literal>unit</literal>) functions in
7121 a monad. For example, in GHC's own
7122 <literal>UniqueSupply</literal> monad code, we have:</para>
7125 {-# INLINE thenUs #-}
7126 {-# INLINE returnUs #-}
7129 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7130 linkend="noinline-pragma"/>).</para>
7132 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7133 so if you want your code to be HBC-compatible you'll have to surround
7134 the pragma with C pre-processor directives
7135 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7139 <sect3 id="noinline-pragma">
7140 <title>NOINLINE pragma</title>
7142 <indexterm><primary>NOINLINE</primary></indexterm>
7143 <indexterm><primary>NOTINLINE</primary></indexterm>
7145 <para>The <literal>NOINLINE</literal> pragma does exactly what
7146 you'd expect: it stops the named function from being inlined
7147 by the compiler. You shouldn't ever need to do this, unless
7148 you're very cautious about code size.</para>
7150 <para><literal>NOTINLINE</literal> is a synonym for
7151 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7152 specified by Haskell 98 as the standard way to disable
7153 inlining, so it should be used if you want your code to be
7157 <sect3 id="phase-control">
7158 <title>Phase control</title>
7160 <para> Sometimes you want to control exactly when in GHC's
7161 pipeline the INLINE pragma is switched on. Inlining happens
7162 only during runs of the <emphasis>simplifier</emphasis>. Each
7163 run of the simplifier has a different <emphasis>phase
7164 number</emphasis>; the phase number decreases towards zero.
7165 If you use <option>-dverbose-core2core</option> you'll see the
7166 sequence of phase numbers for successive runs of the
7167 simplifier. In an INLINE pragma you can optionally specify a
7171 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7172 <literal>f</literal>
7173 until phase <literal>k</literal>, but from phase
7174 <literal>k</literal> onwards be very keen to inline it.
7177 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7178 <literal>f</literal>
7179 until phase <literal>k</literal>, but from phase
7180 <literal>k</literal> onwards do not inline it.
7183 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7184 <literal>f</literal>
7185 until phase <literal>k</literal>, but from phase
7186 <literal>k</literal> onwards be willing to inline it (as if
7187 there was no pragma).
7190 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7191 <literal>f</literal>
7192 until phase <literal>k</literal>, but from phase
7193 <literal>k</literal> onwards do not inline it.
7196 The same information is summarised here:
7198 -- Before phase 2 Phase 2 and later
7199 {-# INLINE [2] f #-} -- No Yes
7200 {-# INLINE [~2] f #-} -- Yes No
7201 {-# NOINLINE [2] f #-} -- No Maybe
7202 {-# NOINLINE [~2] f #-} -- Maybe No
7204 {-# INLINE f #-} -- Yes Yes
7205 {-# NOINLINE f #-} -- No No
7207 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7208 function body is small, or it is applied to interesting-looking arguments etc).
7209 Another way to understand the semantics is this:
7211 <listitem><para>For both INLINE and NOINLINE, the phase number says
7212 when inlining is allowed at all.</para></listitem>
7213 <listitem><para>The INLINE pragma has the additional effect of making the
7214 function body look small, so that when inlining is allowed it is very likely to
7219 <para>The same phase-numbering control is available for RULES
7220 (<xref linkend="rewrite-rules"/>).</para>
7224 <sect2 id="annotation-pragmas">
7225 <title>ANN pragmas</title>
7227 <para>GHC offers the ability to annotate various code constructs with additional
7228 data by using three pragmas. This data can then be inspected at a later date by
7229 using GHC-as-a-library.</para>
7231 <sect3 id="ann-pragma">
7232 <title>Annotating values</title>
7234 <indexterm><primary>ANN</primary></indexterm>
7236 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7237 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7238 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7239 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7240 you would do this:</para>
7243 {-# ANN foo (Just "Hello") #-}
7248 A number of restrictions apply to use of annotations:
7250 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7251 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7252 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7253 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7254 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7256 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7257 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7260 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7261 please give the GHC team a shout</ulink>.
7264 <para>However, apart from these restrictions, many things are allowed, including expressions which not fully evaluated!
7265 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7268 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7273 <sect3 id="typeann-pragma">
7274 <title>Annotating types</title>
7276 <indexterm><primary>ANN type</primary></indexterm>
7277 <indexterm><primary>ANN</primary></indexterm>
7279 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7282 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7287 <sect3 id="modann-pragma">
7288 <title>Annotating modules</title>
7290 <indexterm><primary>ANN module</primary></indexterm>
7291 <indexterm><primary>ANN</primary></indexterm>
7293 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7296 {-# ANN module (Just "A `Maybe String' annotation") #-}
7301 <sect2 id="line-pragma">
7302 <title>LINE pragma</title>
7304 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7305 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7306 <para>This pragma is similar to C's <literal>#line</literal>
7307 pragma, and is mainly for use in automatically generated Haskell
7308 code. It lets you specify the line number and filename of the
7309 original code; for example</para>
7311 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7313 <para>if you'd generated the current file from something called
7314 <filename>Foo.vhs</filename> and this line corresponds to line
7315 42 in the original. GHC will adjust its error messages to refer
7316 to the line/file named in the <literal>LINE</literal>
7321 <title>RULES pragma</title>
7323 <para>The RULES pragma lets you specify rewrite rules. It is
7324 described in <xref linkend="rewrite-rules"/>.</para>
7327 <sect2 id="specialize-pragma">
7328 <title>SPECIALIZE pragma</title>
7330 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7331 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7332 <indexterm><primary>overloading, death to</primary></indexterm>
7334 <para>(UK spelling also accepted.) For key overloaded
7335 functions, you can create extra versions (NB: more code space)
7336 specialised to particular types. Thus, if you have an
7337 overloaded function:</para>
7340 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7343 <para>If it is heavily used on lists with
7344 <literal>Widget</literal> keys, you could specialise it as
7348 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7351 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7352 be put anywhere its type signature could be put.</para>
7354 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7355 (a) a specialised version of the function and (b) a rewrite rule
7356 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7357 un-specialised function into a call to the specialised one.</para>
7359 <para>The type in a SPECIALIZE pragma can be any type that is less
7360 polymorphic than the type of the original function. In concrete terms,
7361 if the original function is <literal>f</literal> then the pragma
7363 {-# SPECIALIZE f :: <type> #-}
7365 is valid if and only if the definition
7367 f_spec :: <type>
7370 is valid. Here are some examples (where we only give the type signature
7371 for the original function, not its code):
7373 f :: Eq a => a -> b -> b
7374 {-# SPECIALISE f :: Int -> b -> b #-}
7376 g :: (Eq a, Ix b) => a -> b -> b
7377 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7379 h :: Eq a => a -> a -> a
7380 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7382 The last of these examples will generate a
7383 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7384 well. If you use this kind of specialisation, let us know how well it works.
7387 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7388 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7389 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7390 The <literal>INLINE</literal> pragma affects the specialised version of the
7391 function (only), and applies even if the function is recursive. The motivating
7394 -- A GADT for arrays with type-indexed representation
7396 ArrInt :: !Int -> ByteArray# -> Arr Int
7397 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7399 (!:) :: Arr e -> Int -> e
7400 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7401 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7402 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7403 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7405 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7406 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7407 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7408 the specialised function will be inlined. It has two calls to
7409 <literal>(!:)</literal>,
7410 both at type <literal>Int</literal>. Both these calls fire the first
7411 specialisation, whose body is also inlined. The result is a type-based
7412 unrolling of the indexing function.</para>
7413 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7414 on an ordinarily-recursive function.</para>
7416 <para>Note: In earlier versions of GHC, it was possible to provide your own
7417 specialised function for a given type:
7420 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7423 This feature has been removed, as it is now subsumed by the
7424 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7428 <sect2 id="specialize-instance-pragma">
7429 <title>SPECIALIZE instance pragma
7433 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7434 <indexterm><primary>overloading, death to</primary></indexterm>
7435 Same idea, except for instance declarations. For example:
7438 instance (Eq a) => Eq (Foo a) where {
7439 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7443 The pragma must occur inside the <literal>where</literal> part
7444 of the instance declaration.
7447 Compatible with HBC, by the way, except perhaps in the placement
7453 <sect2 id="unpack-pragma">
7454 <title>UNPACK pragma</title>
7456 <indexterm><primary>UNPACK</primary></indexterm>
7458 <para>The <literal>UNPACK</literal> indicates to the compiler
7459 that it should unpack the contents of a constructor field into
7460 the constructor itself, removing a level of indirection. For
7464 data T = T {-# UNPACK #-} !Float
7465 {-# UNPACK #-} !Float
7468 <para>will create a constructor <literal>T</literal> containing
7469 two unboxed floats. This may not always be an optimisation: if
7470 the <function>T</function> constructor is scrutinised and the
7471 floats passed to a non-strict function for example, they will
7472 have to be reboxed (this is done automatically by the
7475 <para>Unpacking constructor fields should only be used in
7476 conjunction with <option>-O</option>, in order to expose
7477 unfoldings to the compiler so the reboxing can be removed as
7478 often as possible. For example:</para>
7482 f (T f1 f2) = f1 + f2
7485 <para>The compiler will avoid reboxing <function>f1</function>
7486 and <function>f2</function> by inlining <function>+</function>
7487 on floats, but only when <option>-O</option> is on.</para>
7489 <para>Any single-constructor data is eligible for unpacking; for
7493 data T = T {-# UNPACK #-} !(Int,Int)
7496 <para>will store the two <literal>Int</literal>s directly in the
7497 <function>T</function> constructor, by flattening the pair.
7498 Multi-level unpacking is also supported:
7501 data T = T {-# UNPACK #-} !S
7502 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7505 will store two unboxed <literal>Int#</literal>s
7506 directly in the <function>T</function> constructor. The
7507 unpacker can see through newtypes, too.</para>
7509 <para>If a field cannot be unpacked, you will not get a warning,
7510 so it might be an idea to check the generated code with
7511 <option>-ddump-simpl</option>.</para>
7513 <para>See also the <option>-funbox-strict-fields</option> flag,
7514 which essentially has the effect of adding
7515 <literal>{-# UNPACK #-}</literal> to every strict
7516 constructor field.</para>
7519 <sect2 id="source-pragma">
7520 <title>SOURCE pragma</title>
7522 <indexterm><primary>SOURCE</primary></indexterm>
7523 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7524 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7530 <!-- ======================= REWRITE RULES ======================== -->
7532 <sect1 id="rewrite-rules">
7533 <title>Rewrite rules
7535 <indexterm><primary>RULES pragma</primary></indexterm>
7536 <indexterm><primary>pragma, RULES</primary></indexterm>
7537 <indexterm><primary>rewrite rules</primary></indexterm></title>
7540 The programmer can specify rewrite rules as part of the source program
7546 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7551 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7552 If you need more information, then <option>-ddump-rule-firings</option> shows you
7553 each individual rule firing in detail.
7557 <title>Syntax</title>
7560 From a syntactic point of view:
7566 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7567 may be generated by the layout rule).
7573 The layout rule applies in a pragma.
7574 Currently no new indentation level
7575 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7576 you must lay out the starting in the same column as the enclosing definitions.
7579 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7580 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7583 Furthermore, the closing <literal>#-}</literal>
7584 should start in a column to the right of the opening <literal>{-#</literal>.
7590 Each rule has a name, enclosed in double quotes. The name itself has
7591 no significance at all. It is only used when reporting how many times the rule fired.
7597 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7598 immediately after the name of the rule. Thus:
7601 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7604 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7605 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7614 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7615 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7616 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7617 by spaces, just like in a type <literal>forall</literal>.
7623 A pattern variable may optionally have a type signature.
7624 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7625 For example, here is the <literal>foldr/build</literal> rule:
7628 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7629 foldr k z (build g) = g k z
7632 Since <function>g</function> has a polymorphic type, it must have a type signature.
7639 The left hand side of a rule must consist of a top-level variable applied
7640 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7643 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7644 "wrong2" forall f. f True = True
7647 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7654 A rule does not need to be in the same module as (any of) the
7655 variables it mentions, though of course they need to be in scope.
7661 All rules are implicitly exported from the module, and are therefore
7662 in force in any module that imports the module that defined the rule, directly
7663 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7664 in force when compiling A.) The situation is very similar to that for instance
7672 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7673 any other flag settings. Furthermore, inside a RULE, the language extension
7674 <option>-XScopedTypeVariables</option> is automatically enabled; see
7675 <xref linkend="scoped-type-variables"/>.
7681 Like other pragmas, RULE pragmas are always checked for scope errors, and
7682 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7683 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7684 if the <option>-fenable-rewrite-rules</option> flag is
7685 on (see <xref linkend="rule-semantics"/>).
7694 <sect2 id="rule-semantics">
7695 <title>Semantics</title>
7698 From a semantic point of view:
7703 Rules are enabled (that is, used during optimisation)
7704 by the <option>-fenable-rewrite-rules</option> flag.
7705 This flag is implied by <option>-O</option>, and may be switched
7706 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7707 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7708 may not do what you expect, though, because without <option>-O</option> GHC
7709 ignores all optimisation information in interface files;
7710 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7711 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7712 has no effect on parsing or typechecking.
7718 Rules are regarded as left-to-right rewrite rules.
7719 When GHC finds an expression that is a substitution instance of the LHS
7720 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7721 By "a substitution instance" we mean that the LHS can be made equal to the
7722 expression by substituting for the pattern variables.
7729 GHC makes absolutely no attempt to verify that the LHS and RHS
7730 of a rule have the same meaning. That is undecidable in general, and
7731 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7738 GHC makes no attempt to make sure that the rules are confluent or
7739 terminating. For example:
7742 "loop" forall x y. f x y = f y x
7745 This rule will cause the compiler to go into an infinite loop.
7752 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7758 GHC currently uses a very simple, syntactic, matching algorithm
7759 for matching a rule LHS with an expression. It seeks a substitution
7760 which makes the LHS and expression syntactically equal modulo alpha
7761 conversion. The pattern (rule), but not the expression, is eta-expanded if
7762 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7763 But not beta conversion (that's called higher-order matching).
7767 Matching is carried out on GHC's intermediate language, which includes
7768 type abstractions and applications. So a rule only matches if the
7769 types match too. See <xref linkend="rule-spec"/> below.
7775 GHC keeps trying to apply the rules as it optimises the program.
7776 For example, consider:
7785 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7786 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7787 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7788 not be substituted, and the rule would not fire.
7795 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7796 results. Consider this (artificial) example
7799 {-# RULES "f" f True = False #-}
7805 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7810 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7812 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7813 would have been a better chance that <literal>f</literal>'s RULE might fire.
7816 The way to get predictable behaviour is to use a NOINLINE
7817 pragma on <literal>f</literal>, to ensure
7818 that it is not inlined until its RULEs have had a chance to fire.
7828 <title>List fusion</title>
7831 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7832 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7833 intermediate list should be eliminated entirely.
7837 The following are good producers:
7849 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7855 Explicit lists (e.g. <literal>[True, False]</literal>)
7861 The cons constructor (e.g <literal>3:4:[]</literal>)
7867 <function>++</function>
7873 <function>map</function>
7879 <function>take</function>, <function>filter</function>
7885 <function>iterate</function>, <function>repeat</function>
7891 <function>zip</function>, <function>zipWith</function>
7900 The following are good consumers:
7912 <function>array</function> (on its second argument)
7918 <function>++</function> (on its first argument)
7924 <function>foldr</function>
7930 <function>map</function>
7936 <function>take</function>, <function>filter</function>
7942 <function>concat</function>
7948 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7954 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7955 will fuse with one but not the other)
7961 <function>partition</function>
7967 <function>head</function>
7973 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7979 <function>sequence_</function>
7985 <function>msum</function>
7991 <function>sortBy</function>
8000 So, for example, the following should generate no intermediate lists:
8003 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8009 This list could readily be extended; if there are Prelude functions that you use
8010 a lot which are not included, please tell us.
8014 If you want to write your own good consumers or producers, look at the
8015 Prelude definitions of the above functions to see how to do so.
8020 <sect2 id="rule-spec">
8021 <title>Specialisation
8025 Rewrite rules can be used to get the same effect as a feature
8026 present in earlier versions of GHC.
8027 For example, suppose that:
8030 genericLookup :: Ord a => Table a b -> a -> b
8031 intLookup :: Table Int b -> Int -> b
8034 where <function>intLookup</function> is an implementation of
8035 <function>genericLookup</function> that works very fast for
8036 keys of type <literal>Int</literal>. You might wish
8037 to tell GHC to use <function>intLookup</function> instead of
8038 <function>genericLookup</function> whenever the latter was called with
8039 type <literal>Table Int b -> Int -> b</literal>.
8040 It used to be possible to write
8043 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8046 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8049 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8052 This slightly odd-looking rule instructs GHC to replace
8053 <function>genericLookup</function> by <function>intLookup</function>
8054 <emphasis>whenever the types match</emphasis>.
8055 What is more, this rule does not need to be in the same
8056 file as <function>genericLookup</function>, unlike the
8057 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8058 have an original definition available to specialise).
8061 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8062 <function>intLookup</function> really behaves as a specialised version
8063 of <function>genericLookup</function>!!!</para>
8065 <para>An example in which using <literal>RULES</literal> for
8066 specialisation will Win Big:
8069 toDouble :: Real a => a -> Double
8070 toDouble = fromRational . toRational
8072 {-# RULES "toDouble/Int" toDouble = i2d #-}
8073 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8076 The <function>i2d</function> function is virtually one machine
8077 instruction; the default conversion—via an intermediate
8078 <literal>Rational</literal>—is obscenely expensive by
8085 <title>Controlling what's going on</title>
8093 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8099 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8100 If you add <option>-dppr-debug</option> you get a more detailed listing.
8106 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8109 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8110 {-# INLINE build #-}
8114 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8115 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8116 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8117 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8124 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8125 see how to write rules that will do fusion and yet give an efficient
8126 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8136 <sect2 id="core-pragma">
8137 <title>CORE pragma</title>
8139 <indexterm><primary>CORE pragma</primary></indexterm>
8140 <indexterm><primary>pragma, CORE</primary></indexterm>
8141 <indexterm><primary>core, annotation</primary></indexterm>
8144 The external core format supports <quote>Note</quote> annotations;
8145 the <literal>CORE</literal> pragma gives a way to specify what these
8146 should be in your Haskell source code. Syntactically, core
8147 annotations are attached to expressions and take a Haskell string
8148 literal as an argument. The following function definition shows an
8152 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8155 Semantically, this is equivalent to:
8163 However, when external core is generated (via
8164 <option>-fext-core</option>), there will be Notes attached to the
8165 expressions <function>show</function> and <varname>x</varname>.
8166 The core function declaration for <function>f</function> is:
8170 f :: %forall a . GHCziShow.ZCTShow a ->
8171 a -> GHCziBase.ZMZN GHCziBase.Char =
8172 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8174 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8176 (tpl1::GHCziBase.Int ->
8178 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8180 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8181 (tpl3::GHCziBase.ZMZN a ->
8182 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8190 Here, we can see that the function <function>show</function> (which
8191 has been expanded out to a case expression over the Show dictionary)
8192 has a <literal>%note</literal> attached to it, as does the
8193 expression <varname>eta</varname> (which used to be called
8194 <varname>x</varname>).
8201 <sect1 id="special-ids">
8202 <title>Special built-in functions</title>
8203 <para>GHC has a few built-in functions with special behaviour. These
8204 are now described in the module <ulink
8205 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8206 in the library documentation.</para>
8210 <sect1 id="generic-classes">
8211 <title>Generic classes</title>
8214 The ideas behind this extension are described in detail in "Derivable type classes",
8215 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8216 An example will give the idea:
8224 fromBin :: [Int] -> (a, [Int])
8226 toBin {| Unit |} Unit = []
8227 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8228 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8229 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8231 fromBin {| Unit |} bs = (Unit, bs)
8232 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8233 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8234 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8235 (y,bs'') = fromBin bs'
8238 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8239 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8240 which are defined thus in the library module <literal>Generics</literal>:
8244 data a :+: b = Inl a | Inr b
8245 data a :*: b = a :*: b
8248 Now you can make a data type into an instance of Bin like this:
8250 instance (Bin a, Bin b) => Bin (a,b)
8251 instance Bin a => Bin [a]
8253 That is, just leave off the "where" clause. Of course, you can put in the
8254 where clause and over-ride whichever methods you please.
8258 <title> Using generics </title>
8259 <para>To use generics you need to</para>
8262 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8263 <option>-XGenerics</option> (to generate extra per-data-type code),
8264 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8268 <para>Import the module <literal>Generics</literal> from the
8269 <literal>lang</literal> package. This import brings into
8270 scope the data types <literal>Unit</literal>,
8271 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8272 don't need this import if you don't mention these types
8273 explicitly; for example, if you are simply giving instance
8274 declarations.)</para>
8279 <sect2> <title> Changes wrt the paper </title>
8281 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8282 can be written infix (indeed, you can now use
8283 any operator starting in a colon as an infix type constructor). Also note that
8284 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8285 Finally, note that the syntax of the type patterns in the class declaration
8286 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8287 alone would ambiguous when they appear on right hand sides (an extension we
8288 anticipate wanting).
8292 <sect2> <title>Terminology and restrictions</title>
8294 Terminology. A "generic default method" in a class declaration
8295 is one that is defined using type patterns as above.
8296 A "polymorphic default method" is a default method defined as in Haskell 98.
8297 A "generic class declaration" is a class declaration with at least one
8298 generic default method.
8306 Alas, we do not yet implement the stuff about constructor names and
8313 A generic class can have only one parameter; you can't have a generic
8314 multi-parameter class.
8320 A default method must be defined entirely using type patterns, or entirely
8321 without. So this is illegal:
8324 op :: a -> (a, Bool)
8325 op {| Unit |} Unit = (Unit, True)
8328 However it is perfectly OK for some methods of a generic class to have
8329 generic default methods and others to have polymorphic default methods.
8335 The type variable(s) in the type pattern for a generic method declaration
8336 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:
8340 op {| p :*: q |} (x :*: y) = op (x :: p)
8348 The type patterns in a generic default method must take one of the forms:
8354 where "a" and "b" are type variables. Furthermore, all the type patterns for
8355 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8356 must use the same type variables. So this is illegal:
8360 op {| a :+: b |} (Inl x) = True
8361 op {| p :+: q |} (Inr y) = False
8363 The type patterns must be identical, even in equations for different methods of the class.
8364 So this too is illegal:
8368 op1 {| a :*: b |} (x :*: y) = True
8371 op2 {| p :*: q |} (x :*: y) = False
8373 (The reason for this restriction is that we gather all the equations for a particular type constructor
8374 into a single generic instance declaration.)
8380 A generic method declaration must give a case for each of the three type constructors.
8386 The type for a generic method can be built only from:
8388 <listitem> <para> Function arrows </para> </listitem>
8389 <listitem> <para> Type variables </para> </listitem>
8390 <listitem> <para> Tuples </para> </listitem>
8391 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8393 Here are some example type signatures for generic methods:
8396 op2 :: Bool -> (a,Bool)
8397 op3 :: [Int] -> a -> a
8400 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8404 This restriction is an implementation restriction: we just haven't got around to
8405 implementing the necessary bidirectional maps over arbitrary type constructors.
8406 It would be relatively easy to add specific type constructors, such as Maybe and list,
8407 to the ones that are allowed.</para>
8412 In an instance declaration for a generic class, the idea is that the compiler
8413 will fill in the methods for you, based on the generic templates. However it can only
8418 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8423 No constructor of the instance type has unboxed fields.
8427 (Of course, these things can only arise if you are already using GHC extensions.)
8428 However, you can still give an instance declarations for types which break these rules,
8429 provided you give explicit code to override any generic default methods.
8437 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8438 what the compiler does with generic declarations.
8443 <sect2> <title> Another example </title>
8445 Just to finish with, here's another example I rather like:
8449 nCons {| Unit |} _ = 1
8450 nCons {| a :*: b |} _ = 1
8451 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8454 tag {| Unit |} _ = 1
8455 tag {| a :*: b |} _ = 1
8456 tag {| a :+: b |} (Inl x) = tag x
8457 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8463 <sect1 id="monomorphism">
8464 <title>Control over monomorphism</title>
8466 <para>GHC supports two flags that control the way in which generalisation is
8467 carried out at let and where bindings.
8471 <title>Switching off the dreaded Monomorphism Restriction</title>
8472 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8474 <para>Haskell's monomorphism restriction (see
8475 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8477 of the Haskell Report)
8478 can be completely switched off by
8479 <option>-XNoMonomorphismRestriction</option>.
8484 <title>Monomorphic pattern bindings</title>
8485 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8486 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8488 <para> As an experimental change, we are exploring the possibility of
8489 making pattern bindings monomorphic; that is, not generalised at all.
8490 A pattern binding is a binding whose LHS has no function arguments,
8491 and is not a simple variable. For example:
8493 f x = x -- Not a pattern binding
8494 f = \x -> x -- Not a pattern binding
8495 f :: Int -> Int = \x -> x -- Not a pattern binding
8497 (g,h) = e -- A pattern binding
8498 (f) = e -- A pattern binding
8499 [x] = e -- A pattern binding
8501 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8502 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8511 ;;; Local Variables: ***
8513 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8514 ;;; ispell-local-dictionary: "british" ***
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