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 you must make any such pattern-match
214 strict. For example, rather than:
216 data Foo = Foo Int Int#
218 f x = let (Foo a b, w) = ..rhs.. in ..body..
222 data Foo = Foo Int Int#
224 f x = let !(Foo a b, w) = ..rhs.. in ..body..
226 since <literal>b</literal> has type <literal>Int#</literal>.
234 <sect2 id="unboxed-tuples">
235 <title>Unboxed Tuples
239 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
240 they're available by default with <option>-fglasgow-exts</option>. An
241 unboxed tuple looks like this:
253 where <literal>e_1..e_n</literal> are expressions of any
254 type (primitive or non-primitive). The type of an unboxed tuple looks
259 Unboxed tuples are used for functions that need to return multiple
260 values, but they avoid the heap allocation normally associated with
261 using fully-fledged tuples. When an unboxed tuple is returned, the
262 components are put directly into registers or on the stack; the
263 unboxed tuple itself does not have a composite representation. Many
264 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
266 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
267 tuples to avoid unnecessary allocation during sequences of operations.
271 There are some pretty stringent restrictions on the use of unboxed tuples:
276 Values of unboxed tuple types are subject to the same restrictions as
277 other unboxed types; i.e. they may not be stored in polymorphic data
278 structures or passed to polymorphic functions.
285 No variable can have an unboxed tuple type, nor may a constructor or function
286 argument have an unboxed tuple type. The following are all illegal:
290 data Foo = Foo (# Int, Int #)
292 f :: (# Int, Int #) -> (# Int, Int #)
295 g :: (# Int, Int #) -> Int
298 h x = let y = (# x,x #) in ...
305 The typical use of unboxed tuples is simply to return multiple values,
306 binding those multiple results with a <literal>case</literal> expression, thus:
308 f x y = (# x+1, y-1 #)
309 g x = case f x x of { (# a, b #) -> a + b }
311 You can have an unboxed tuple in a pattern binding, thus
313 f x = let (# p,q #) = h x in ..body..
315 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
316 the resulting binding is lazy like any other Haskell pattern binding. The
317 above example desugars like this:
319 f x = let t = case h x o f{ (# p,q #) -> (p,q)
324 Indeed, the bindings can even be recursive.
331 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
333 <sect1 id="syntax-extns">
334 <title>Syntactic extensions</title>
336 <sect2 id="unicode-syntax">
337 <title>Unicode syntax</title>
339 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
340 enables Unicode characters to be used to stand for certain ASCII
341 character sequences. The following alternatives are provided:</para>
344 <tgroup cols="2" align="left" colsep="1" rowsep="1">
348 <entry>Unicode alternative</entry>
349 <entry>Code point</entry>
355 <entry><literal>::</literal></entry>
356 <entry>::</entry> <!-- no special char, apparently -->
357 <entry>0x2237</entry>
358 <entry>PROPORTION</entry>
363 <entry><literal>=></literal></entry>
364 <entry>⇒</entry>
365 <entry>0x21D2</entry>
366 <entry>RIGHTWARDS DOUBLE ARROW</entry>
371 <entry><literal>forall</literal></entry>
372 <entry>∀</entry>
373 <entry>0x2200</entry>
374 <entry>FOR ALL</entry>
379 <entry><literal>-></literal></entry>
380 <entry>→</entry>
381 <entry>0x2192</entry>
382 <entry>RIGHTWARDS ARROW</entry>
387 <entry><literal><-</literal></entry>
388 <entry>←</entry>
389 <entry>0x2190</entry>
390 <entry>LEFTWARDS ARROW</entry>
396 <entry>…</entry>
397 <entry>0x22EF</entry>
398 <entry>MIDLINE HORIZONTAL ELLIPSIS</entry>
405 <sect2 id="magic-hash">
406 <title>The magic hash</title>
407 <para>The language extension <option>-XMagicHash</option> allows "#" as a
408 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
409 a valid type constructor or data constructor.</para>
411 <para>The hash sign does not change sematics at all. We tend to use variable
412 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
413 but there is no requirement to do so; they are just plain ordinary variables.
414 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
415 For example, to bring <literal>Int#</literal> into scope you must
416 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
417 the <option>-XMagicHash</option> extension
418 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
419 that is now in scope.</para>
420 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
422 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
423 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
424 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
425 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
426 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
427 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
428 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
429 is a <literal>Word#</literal>. </para> </listitem>
430 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
431 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
436 <sect2 id="new-qualified-operators">
437 <title>New qualified operator syntax</title>
439 <para>A new syntax for referencing qualified operators is
440 planned to be introduced by Haskell', and is enabled in GHC
442 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
443 option. In the new syntax, the prefix form of a qualified
445 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
446 (in Haskell 98 this would
447 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
448 and the infix form is
449 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
450 (in Haskell 98 this would
451 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
454 add x y = Prelude.(+) x y
455 subtract y = (`Prelude.(-)` y)
457 The new form of qualified operators is intended to regularise
458 the syntax by eliminating odd cases
459 like <literal>Prelude..</literal>. For example,
460 when <literal>NewQualifiedOperators</literal> is on, it is possible to
461 write the enumerated sequence <literal>[Monday..]</literal>
462 without spaces, whereas in Haskell 98 this would be a
463 reference to the operator ‘<literal>.</literal>‘
464 from module <literal>Monday</literal>.</para>
466 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
467 98 syntax for qualified operators is not accepted, so this
468 option may cause existing Haskell 98 code to break.</para>
473 <!-- ====================== HIERARCHICAL MODULES ======================= -->
476 <sect2 id="hierarchical-modules">
477 <title>Hierarchical Modules</title>
479 <para>GHC supports a small extension to the syntax of module
480 names: a module name is allowed to contain a dot
481 <literal>‘.’</literal>. This is also known as the
482 “hierarchical module namespace” extension, because
483 it extends the normally flat Haskell module namespace into a
484 more flexible hierarchy of modules.</para>
486 <para>This extension has very little impact on the language
487 itself; modules names are <emphasis>always</emphasis> fully
488 qualified, so you can just think of the fully qualified module
489 name as <quote>the module name</quote>. In particular, this
490 means that the full module name must be given after the
491 <literal>module</literal> keyword at the beginning of the
492 module; for example, the module <literal>A.B.C</literal> must
495 <programlisting>module A.B.C</programlisting>
498 <para>It is a common strategy to use the <literal>as</literal>
499 keyword to save some typing when using qualified names with
500 hierarchical modules. For example:</para>
503 import qualified Control.Monad.ST.Strict as ST
506 <para>For details on how GHC searches for source and interface
507 files in the presence of hierarchical modules, see <xref
508 linkend="search-path"/>.</para>
510 <para>GHC comes with a large collection of libraries arranged
511 hierarchically; see the accompanying <ulink
512 url="../libraries/index.html">library
513 documentation</ulink>. More libraries to install are available
515 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
518 <!-- ====================== PATTERN GUARDS ======================= -->
520 <sect2 id="pattern-guards">
521 <title>Pattern guards</title>
524 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
525 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.)
529 Suppose we have an abstract data type of finite maps, with a
533 lookup :: FiniteMap -> Int -> Maybe Int
536 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
537 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
541 clunky env var1 var2 | ok1 && ok2 = val1 + val2
542 | otherwise = var1 + var2
553 The auxiliary functions are
557 maybeToBool :: Maybe a -> Bool
558 maybeToBool (Just x) = True
559 maybeToBool Nothing = False
561 expectJust :: Maybe a -> a
562 expectJust (Just x) = x
563 expectJust Nothing = error "Unexpected Nothing"
567 What is <function>clunky</function> doing? The guard <literal>ok1 &&
568 ok2</literal> checks that both lookups succeed, using
569 <function>maybeToBool</function> to convert the <function>Maybe</function>
570 types to booleans. The (lazily evaluated) <function>expectJust</function>
571 calls extract the values from the results of the lookups, and binds the
572 returned values to <varname>val1</varname> and <varname>val2</varname>
573 respectively. If either lookup fails, then clunky takes the
574 <literal>otherwise</literal> case and returns the sum of its arguments.
578 This is certainly legal Haskell, but it is a tremendously verbose and
579 un-obvious way to achieve the desired effect. Arguably, a more direct way
580 to write clunky would be to use case expressions:
584 clunky env var1 var2 = case lookup env var1 of
586 Just val1 -> case lookup env var2 of
588 Just val2 -> val1 + val2
594 This is a bit shorter, but hardly better. Of course, we can rewrite any set
595 of pattern-matching, guarded equations as case expressions; that is
596 precisely what the compiler does when compiling equations! The reason that
597 Haskell provides guarded equations is because they allow us to write down
598 the cases we want to consider, one at a time, independently of each other.
599 This structure is hidden in the case version. Two of the right-hand sides
600 are really the same (<function>fail</function>), and the whole expression
601 tends to become more and more indented.
605 Here is how I would write clunky:
610 | Just val1 <- lookup env var1
611 , Just val2 <- lookup env var2
613 ...other equations for clunky...
617 The semantics should be clear enough. The qualifiers are matched in order.
618 For a <literal><-</literal> qualifier, which I call a pattern guard, the
619 right hand side is evaluated and matched against the pattern on the left.
620 If the match fails then the whole guard fails and the next equation is
621 tried. If it succeeds, then the appropriate binding takes place, and the
622 next qualifier is matched, in the augmented environment. Unlike list
623 comprehensions, however, the type of the expression to the right of the
624 <literal><-</literal> is the same as the type of the pattern to its
625 left. The bindings introduced by pattern guards scope over all the
626 remaining guard qualifiers, and over the right hand side of the equation.
630 Just as with list comprehensions, boolean expressions can be freely mixed
631 with among the pattern guards. For example:
642 Haskell's current guards therefore emerge as a special case, in which the
643 qualifier list has just one element, a boolean expression.
647 <!-- ===================== View patterns =================== -->
649 <sect2 id="view-patterns">
654 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
655 More information and examples of view patterns can be found on the
656 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
661 View patterns are somewhat like pattern guards that can be nested inside
662 of other patterns. They are a convenient way of pattern-matching
663 against values of abstract types. For example, in a programming language
664 implementation, we might represent the syntax of the types of the
673 view :: Type -> TypeView
675 -- additional operations for constructing Typ's ...
678 The representation of Typ is held abstract, permitting implementations
679 to use a fancy representation (e.g., hash-consing to manage sharing).
681 Without view patterns, using this signature a little inconvenient:
683 size :: Typ -> Integer
684 size t = case view t of
686 Arrow t1 t2 -> size t1 + size t2
689 It is necessary to iterate the case, rather than using an equational
690 function definition. And the situation is even worse when the matching
691 against <literal>t</literal> is buried deep inside another pattern.
695 View patterns permit calling the view function inside the pattern and
696 matching against the result:
698 size (view -> Unit) = 1
699 size (view -> Arrow t1 t2) = size t1 + size t2
702 That is, we add a new form of pattern, written
703 <replaceable>expression</replaceable> <literal>-></literal>
704 <replaceable>pattern</replaceable> that means "apply the expression to
705 whatever we're trying to match against, and then match the result of
706 that application against the pattern". The expression can be any Haskell
707 expression of function type, and view patterns can be used wherever
712 The semantics of a pattern <literal>(</literal>
713 <replaceable>exp</replaceable> <literal>-></literal>
714 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
720 <para>The variables bound by the view pattern are the variables bound by
721 <replaceable>pat</replaceable>.
725 Any variables in <replaceable>exp</replaceable> are bound occurrences,
726 but variables bound "to the left" in a pattern are in scope. This
727 feature permits, for example, one argument to a function to be used in
728 the view of another argument. For example, the function
729 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
730 written using view patterns as follows:
733 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
734 ...other equations for clunky...
739 More precisely, the scoping rules are:
743 In a single pattern, variables bound by patterns to the left of a view
744 pattern expression are in scope. For example:
746 example :: Maybe ((String -> Integer,Integer), String) -> Bool
747 example Just ((f,_), f -> 4) = True
750 Additionally, in function definitions, variables bound by matching earlier curried
751 arguments may be used in view pattern expressions in later arguments:
753 example :: (String -> Integer) -> String -> Bool
754 example f (f -> 4) = True
756 That is, the scoping is the same as it would be if the curried arguments
757 were collected into a tuple.
763 In mutually recursive bindings, such as <literal>let</literal>,
764 <literal>where</literal>, or the top level, view patterns in one
765 declaration may not mention variables bound by other declarations. That
766 is, each declaration must be self-contained. For example, the following
767 program is not allowed:
774 restriction in the future; the only cost is that type checking patterns
775 would get a little more complicated.)
785 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
786 <replaceable>T1</replaceable> <literal>-></literal>
787 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
788 a <replaceable>T2</replaceable>, then the whole view pattern matches a
789 <replaceable>T1</replaceable>.
792 <listitem><para> Matching: To the equations in Section 3.17.3 of the
793 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
794 Report</ulink>, add the following:
796 case v of { (e -> p) -> e1 ; _ -> e2 }
798 case (e v) of { p -> e1 ; _ -> e2 }
800 That is, to match a variable <replaceable>v</replaceable> against a pattern
801 <literal>(</literal> <replaceable>exp</replaceable>
802 <literal>-></literal> <replaceable>pat</replaceable>
803 <literal>)</literal>, evaluate <literal>(</literal>
804 <replaceable>exp</replaceable> <replaceable> v</replaceable>
805 <literal>)</literal> and match the result against
806 <replaceable>pat</replaceable>.
809 <listitem><para> Efficiency: When the same view function is applied in
810 multiple branches of a function definition or a case expression (e.g.,
811 in <literal>size</literal> above), GHC makes an attempt to collect these
812 applications into a single nested case expression, so that the view
813 function is only applied once. Pattern compilation in GHC follows the
814 matrix algorithm described in Chapter 4 of <ulink
815 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
816 Implementation of Functional Programming Languages</ulink>. When the
817 top rows of the first column of a matrix are all view patterns with the
818 "same" expression, these patterns are transformed into a single nested
819 case. This includes, for example, adjacent view patterns that line up
822 f ((view -> A, p1), p2) = e1
823 f ((view -> B, p3), p4) = e2
827 <para> The current notion of when two view pattern expressions are "the
828 same" is very restricted: it is not even full syntactic equality.
829 However, it does include variables, literals, applications, and tuples;
830 e.g., two instances of <literal>view ("hi", "there")</literal> will be
831 collected. However, the current implementation does not compare up to
832 alpha-equivalence, so two instances of <literal>(x, view x ->
833 y)</literal> will not be coalesced.
843 <!-- ===================== Recursive do-notation =================== -->
845 <sect2 id="mdo-notation">
846 <title>The recursive do-notation
849 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
850 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
851 by Levent Erkok, John Launchbury,
852 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
853 This paper is essential reading for anyone making non-trivial use of mdo-notation,
854 and we do not repeat it here.
857 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
858 that is, the variables bound in a do-expression are visible only in the textually following
859 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
860 group. It turns out that several applications can benefit from recursive bindings in
861 the do-notation, and this extension provides the necessary syntactic support.
864 Here is a simple (yet contrived) example:
867 import Control.Monad.Fix
869 justOnes = mdo xs <- Just (1:xs)
873 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
877 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
880 class Monad m => MonadFix m where
881 mfix :: (a -> m a) -> m a
884 The function <literal>mfix</literal>
885 dictates how the required recursion operation should be performed. For example,
886 <literal>justOnes</literal> desugars as follows:
888 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
890 For full details of the way in which mdo is typechecked and desugared, see
891 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
892 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
895 If recursive bindings are required for a monad,
896 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
897 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
898 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
899 for Haskell's internal state monad (strict and lazy, respectively).
902 Here are some important points in using the recursive-do notation:
905 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
906 than <literal>do</literal>).
910 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
911 <literal>-fglasgow-exts</literal>.
915 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
916 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
917 be distinct (Section 3.3 of the paper).
921 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
922 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
923 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
924 and improve termination (Section 3.2 of the paper).
930 Historical note: The old implementation of the mdo-notation (and most
931 of the existing documents) used the name
932 <literal>MonadRec</literal> for the class and the corresponding library.
933 This name is not supported by GHC.
939 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
941 <sect2 id="parallel-list-comprehensions">
942 <title>Parallel List Comprehensions</title>
943 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
945 <indexterm><primary>parallel list comprehensions</primary>
948 <para>Parallel list comprehensions are a natural extension to list
949 comprehensions. List comprehensions can be thought of as a nice
950 syntax for writing maps and filters. Parallel comprehensions
951 extend this to include the zipWith family.</para>
953 <para>A parallel list comprehension has multiple independent
954 branches of qualifier lists, each separated by a `|' symbol. For
955 example, the following zips together two lists:</para>
958 [ (x, y) | x <- xs | y <- ys ]
961 <para>The behavior of parallel list comprehensions follows that of
962 zip, in that the resulting list will have the same length as the
963 shortest branch.</para>
965 <para>We can define parallel list comprehensions by translation to
966 regular comprehensions. Here's the basic idea:</para>
968 <para>Given a parallel comprehension of the form: </para>
971 [ e | p1 <- e11, p2 <- e12, ...
972 | q1 <- e21, q2 <- e22, ...
977 <para>This will be translated to: </para>
980 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
981 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
986 <para>where `zipN' is the appropriate zip for the given number of
991 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
993 <sect2 id="generalised-list-comprehensions">
994 <title>Generalised (SQL-Like) List Comprehensions</title>
995 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
997 <indexterm><primary>extended list comprehensions</primary>
999 <indexterm><primary>group</primary></indexterm>
1000 <indexterm><primary>sql</primary></indexterm>
1003 <para>Generalised list comprehensions are a further enhancement to the
1004 list comprehension syntatic sugar to allow operations such as sorting
1005 and grouping which are familiar from SQL. They are fully described in the
1006 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1007 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1008 except that the syntax we use differs slightly from the paper.</para>
1009 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1010 <para>Here is an example:
1012 employees = [ ("Simon", "MS", 80)
1013 , ("Erik", "MS", 100)
1014 , ("Phil", "Ed", 40)
1015 , ("Gordon", "Ed", 45)
1016 , ("Paul", "Yale", 60)]
1018 output = [ (the dept, sum salary)
1019 | (name, dept, salary) <- employees
1020 , then group by dept
1021 , then sortWith by (sum salary)
1024 In this example, the list <literal>output</literal> would take on
1028 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1031 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1032 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1033 function that is exported by <literal>GHC.Exts</literal>.)</para>
1035 <para>There are five new forms of comprehension qualifier,
1036 all introduced by the (existing) keyword <literal>then</literal>:
1044 This statement requires that <literal>f</literal> have the type <literal>
1045 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1046 motivating example, as this form is used to apply <literal>take 5</literal>.
1057 This form is similar to the previous one, but allows you to create a function
1058 which will be passed as the first argument to f. As a consequence f must have
1059 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1060 from the type, this function lets f "project out" some information
1061 from the elements of the list it is transforming.</para>
1063 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1064 is supplied with a function that lets it find out the <literal>sum salary</literal>
1065 for any item in the list comprehension it transforms.</para>
1073 then group by e using f
1076 <para>This is the most general of the grouping-type statements. In this form,
1077 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1078 As with the <literal>then f by e</literal> case above, the first argument
1079 is a function supplied to f by the compiler which lets it compute e on every
1080 element of the list being transformed. However, unlike the non-grouping case,
1081 f additionally partitions the list into a number of sublists: this means that
1082 at every point after this statement, binders occurring before it in the comprehension
1083 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1084 this, let's look at an example:</para>
1087 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1088 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1089 groupRuns f = groupBy (\x y -> f x == f y)
1091 output = [ (the x, y)
1092 | x <- ([1..3] ++ [1..2])
1094 , then group by x using groupRuns ]
1097 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1100 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1103 <para>Note that we have used the <literal>the</literal> function to change the type
1104 of x from a list to its original numeric type. The variable y, in contrast, is left
1105 unchanged from the list form introduced by the grouping.</para>
1115 <para>This form of grouping is essentially the same as the one described above. However,
1116 since no function to use for the grouping has been supplied it will fall back on the
1117 <literal>groupWith</literal> function defined in
1118 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1119 is the form of the group statement that we made use of in the opening example.</para>
1130 <para>With this form of the group statement, f is required to simply have the type
1131 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1132 comprehension so far directly. An example of this form is as follows:</para>
1138 , then group using inits]
1141 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1144 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1152 <!-- ===================== REBINDABLE SYNTAX =================== -->
1154 <sect2 id="rebindable-syntax">
1155 <title>Rebindable syntax and the implicit Prelude import</title>
1157 <para><indexterm><primary>-XNoImplicitPrelude
1158 option</primary></indexterm> GHC normally imports
1159 <filename>Prelude.hi</filename> files for you. If you'd
1160 rather it didn't, then give it a
1161 <option>-XNoImplicitPrelude</option> option. The idea is
1162 that you can then import a Prelude of your own. (But don't
1163 call it <literal>Prelude</literal>; the Haskell module
1164 namespace is flat, and you must not conflict with any
1165 Prelude module.)</para>
1167 <para>Suppose you are importing a Prelude of your own
1168 in order to define your own numeric class
1169 hierarchy. It completely defeats that purpose if the
1170 literal "1" means "<literal>Prelude.fromInteger
1171 1</literal>", which is what the Haskell Report specifies.
1172 So the <option>-XNoImplicitPrelude</option>
1173 flag <emphasis>also</emphasis> causes
1174 the following pieces of built-in syntax to refer to
1175 <emphasis>whatever is in scope</emphasis>, not the Prelude
1179 <para>An integer literal <literal>368</literal> means
1180 "<literal>fromInteger (368::Integer)</literal>", rather than
1181 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1184 <listitem><para>Fractional literals are handed in just the same way,
1185 except that the translation is
1186 <literal>fromRational (3.68::Rational)</literal>.
1189 <listitem><para>The equality test in an overloaded numeric pattern
1190 uses whatever <literal>(==)</literal> is in scope.
1193 <listitem><para>The subtraction operation, and the
1194 greater-than-or-equal test, in <literal>n+k</literal> patterns
1195 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1199 <para>Negation (e.g. "<literal>- (f x)</literal>")
1200 means "<literal>negate (f x)</literal>", both in numeric
1201 patterns, and expressions.
1205 <para>"Do" notation is translated using whatever
1206 functions <literal>(>>=)</literal>,
1207 <literal>(>>)</literal>, and <literal>fail</literal>,
1208 are in scope (not the Prelude
1209 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1210 comprehensions, are unaffected. </para></listitem>
1214 notation (see <xref linkend="arrow-notation"/>)
1215 uses whatever <literal>arr</literal>,
1216 <literal>(>>>)</literal>, <literal>first</literal>,
1217 <literal>app</literal>, <literal>(|||)</literal> and
1218 <literal>loop</literal> functions are in scope. But unlike the
1219 other constructs, the types of these functions must match the
1220 Prelude types very closely. Details are in flux; if you want
1224 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1225 even if that is a little unexpected. For example, the
1226 static semantics of the literal <literal>368</literal>
1227 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1228 <literal>fromInteger</literal> to have any of the types:
1230 fromInteger :: Integer -> Integer
1231 fromInteger :: forall a. Foo a => Integer -> a
1232 fromInteger :: Num a => a -> Integer
1233 fromInteger :: Integer -> Bool -> Bool
1237 <para>Be warned: this is an experimental facility, with
1238 fewer checks than usual. Use <literal>-dcore-lint</literal>
1239 to typecheck the desugared program. If Core Lint is happy
1240 you should be all right.</para>
1244 <sect2 id="postfix-operators">
1245 <title>Postfix operators</title>
1248 The <option>-XPostfixOperators</option> flag enables a small
1249 extension to the syntax of left operator sections, which allows you to
1250 define postfix operators. The extension is this: the left section
1254 is equivalent (from the point of view of both type checking and execution) to the expression
1258 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1259 The strict Haskell 98 interpretation is that the section is equivalent to
1263 That is, the operator must be a function of two arguments. GHC allows it to
1264 take only one argument, and that in turn allows you to write the function
1267 <para>The extension does not extend to the left-hand side of function
1268 definitions; you must define such a function in prefix form.</para>
1272 <sect2 id="disambiguate-fields">
1273 <title>Record field disambiguation</title>
1275 In record construction and record pattern matching
1276 it is entirely unambiguous which field is referred to, even if there are two different
1277 data types in scope with a common field name. For example:
1280 data S = MkS { x :: Int, y :: Bool }
1285 data T = MkT { x :: Int }
1287 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1289 ok2 n = MkT { x = n+1 } -- Unambiguous
1291 bad1 k = k { x = 3 } -- Ambiguous
1292 bad2 k = x k -- Ambiguous
1294 Even though there are two <literal>x</literal>'s in scope,
1295 it is clear that the <literal>x</literal> in the pattern in the
1296 definition of <literal>ok1</literal> can only mean the field
1297 <literal>x</literal> from type <literal>S</literal>. Similarly for
1298 the function <literal>ok2</literal>. However, in the record update
1299 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1300 it is not clear which of the two types is intended.
1303 Haskell 98 regards all four as ambiguous, but with the
1304 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1305 the former two. The rules are precisely the same as those for instance
1306 declarations in Haskell 98, where the method names on the left-hand side
1307 of the method bindings in an instance declaration refer unambiguously
1308 to the method of that class (provided they are in scope at all), even
1309 if there are other variables in scope with the same name.
1310 This reduces the clutter of qualified names when you import two
1311 records from different modules that use the same field name.
1315 <!-- ===================== Record puns =================== -->
1317 <sect2 id="record-puns">
1322 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1326 When using records, it is common to write a pattern that binds a
1327 variable with the same name as a record field, such as:
1330 data C = C {a :: Int}
1336 Record punning permits the variable name to be elided, so one can simply
1343 to mean the same pattern as above. That is, in a record pattern, the
1344 pattern <literal>a</literal> expands into the pattern <literal>a =
1345 a</literal> for the same name <literal>a</literal>.
1349 Note that puns and other patterns can be mixed in the same record:
1351 data C = C {a :: Int, b :: Int}
1352 f (C {a, b = 4}) = a
1354 and that puns can be used wherever record patterns occur (e.g. in
1355 <literal>let</literal> bindings or at the top-level).
1359 Record punning can also be used in an expression, writing, for example,
1365 let a = 1 in C {a = a}
1368 Note that this expansion is purely syntactic, so the record pun
1369 expression refers to the nearest enclosing variable that is spelled the
1370 same as the field name.
1375 <!-- ===================== Record wildcards =================== -->
1377 <sect2 id="record-wildcards">
1378 <title>Record wildcards
1382 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1386 For records with many fields, it can be tiresome to write out each field
1387 individually in a record pattern, as in
1389 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1390 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1395 Record wildcard syntax permits a (<literal>..</literal>) in a record
1396 pattern, where each elided field <literal>f</literal> is replaced by the
1397 pattern <literal>f = f</literal>. For example, the above pattern can be
1400 f (C {a = 1, ..}) = b + c + d
1405 Note that wildcards can be mixed with other patterns, including puns
1406 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1407 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1408 wherever record patterns occur, including in <literal>let</literal>
1409 bindings and at the top-level. For example, the top-level binding
1413 defines <literal>b</literal>, <literal>c</literal>, and
1414 <literal>d</literal>.
1418 Record wildcards can also be used in expressions, writing, for example,
1421 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1427 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1430 Note that this expansion is purely syntactic, so the record wildcard
1431 expression refers to the nearest enclosing variables that are spelled
1432 the same as the omitted field names.
1437 <!-- ===================== Local fixity declarations =================== -->
1439 <sect2 id="local-fixity-declarations">
1440 <title>Local Fixity Declarations
1443 <para>A careful reading of the Haskell 98 Report reveals that fixity
1444 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1445 <literal>infixr</literal>) are permitted to appear inside local bindings
1446 such those introduced by <literal>let</literal> and
1447 <literal>where</literal>. However, the Haskell Report does not specify
1448 the semantics of such bindings very precisely.
1451 <para>In GHC, a fixity declaration may accompany a local binding:
1458 and the fixity declaration applies wherever the binding is in scope.
1459 For example, in a <literal>let</literal>, it applies in the right-hand
1460 sides of other <literal>let</literal>-bindings and the body of the
1461 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1462 expressions (<xref linkend="mdo-notation"/>), the local fixity
1463 declarations of a <literal>let</literal> statement scope over other
1464 statements in the group, just as the bound name does.
1468 Moreover, a local fixity declaration *must* accompany a local binding of
1469 that name: it is not possible to revise the fixity of name bound
1472 let infixr 9 $ in ...
1475 Because local fixity declarations are technically Haskell 98, no flag is
1476 necessary to enable them.
1480 <sect2 id="package-imports">
1481 <title>Package-qualified imports</title>
1483 <para>With the <option>-XPackageImports</option> flag, GHC allows
1484 import declarations to be qualified by the package name that the
1485 module is intended to be imported from. For example:</para>
1488 import "network" Network.Socket
1491 <para>would import the module <literal>Network.Socket</literal> from
1492 the package <literal>network</literal> (any version). This may
1493 be used to disambiguate an import when the same module is
1494 available from multiple packages, or is present in both the
1495 current package being built and an external package.</para>
1497 <para>Note: you probably don't need to use this feature, it was
1498 added mainly so that we can build backwards-compatible versions of
1499 packages when APIs change. It can lead to fragile dependencies in
1500 the common case: modules occasionally move from one package to
1501 another, rendering any package-qualified imports broken.</para>
1504 <sect2 id="syntax-stolen">
1505 <title>Summary of stolen syntax</title>
1507 <para>Turning on an option that enables special syntax
1508 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1509 to compile, perhaps because it uses a variable name which has
1510 become a reserved word. This section lists the syntax that is
1511 "stolen" by language extensions.
1513 notation and nonterminal names from the Haskell 98 lexical syntax
1514 (see the Haskell 98 Report).
1515 We only list syntax changes here that might affect
1516 existing working programs (i.e. "stolen" syntax). Many of these
1517 extensions will also enable new context-free syntax, but in all
1518 cases programs written to use the new syntax would not be
1519 compilable without the option enabled.</para>
1521 <para>There are two classes of special
1526 <para>New reserved words and symbols: character sequences
1527 which are no longer available for use as identifiers in the
1531 <para>Other special syntax: sequences of characters that have
1532 a different meaning when this particular option is turned
1537 The following syntax is stolen:
1542 <literal>forall</literal>
1543 <indexterm><primary><literal>forall</literal></primary></indexterm>
1546 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1547 <option>-XLiberalTypeSynonyms</option>,
1548 <option>-XRank2Types</option>,
1549 <option>-XRankNTypes</option>,
1550 <option>-XPolymorphicComponents</option>,
1551 <option>-XExistentialQuantification</option>
1557 <literal>mdo</literal>
1558 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1561 Stolen by: <option>-XRecursiveDo</option>,
1567 <literal>foreign</literal>
1568 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1571 Stolen by: <option>-XForeignFunctionInterface</option>,
1577 <literal>rec</literal>,
1578 <literal>proc</literal>, <literal>-<</literal>,
1579 <literal>>-</literal>, <literal>-<<</literal>,
1580 <literal>>>-</literal>, and <literal>(|</literal>,
1581 <literal>|)</literal> brackets
1582 <indexterm><primary><literal>proc</literal></primary></indexterm>
1585 Stolen by: <option>-XArrows</option>,
1591 <literal>?<replaceable>varid</replaceable></literal>,
1592 <literal>%<replaceable>varid</replaceable></literal>
1593 <indexterm><primary>implicit parameters</primary></indexterm>
1596 Stolen by: <option>-XImplicitParams</option>,
1602 <literal>[|</literal>,
1603 <literal>[e|</literal>, <literal>[p|</literal>,
1604 <literal>[d|</literal>, <literal>[t|</literal>,
1605 <literal>$(</literal>,
1606 <literal>$<replaceable>varid</replaceable></literal>
1607 <indexterm><primary>Template Haskell</primary></indexterm>
1610 Stolen by: <option>-XTemplateHaskell</option>,
1616 <literal>[:<replaceable>varid</replaceable>|</literal>
1617 <indexterm><primary>quasi-quotation</primary></indexterm>
1620 Stolen by: <option>-XQuasiQuotes</option>,
1626 <replaceable>varid</replaceable>{<literal>#</literal>},
1627 <replaceable>char</replaceable><literal>#</literal>,
1628 <replaceable>string</replaceable><literal>#</literal>,
1629 <replaceable>integer</replaceable><literal>#</literal>,
1630 <replaceable>float</replaceable><literal>#</literal>,
1631 <replaceable>float</replaceable><literal>##</literal>,
1632 <literal>(#</literal>, <literal>#)</literal>,
1635 Stolen by: <option>-XMagicHash</option>,
1644 <!-- TYPE SYSTEM EXTENSIONS -->
1645 <sect1 id="data-type-extensions">
1646 <title>Extensions to data types and type synonyms</title>
1648 <sect2 id="nullary-types">
1649 <title>Data types with no constructors</title>
1651 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1652 a data type with no constructors. For example:</para>
1656 data T a -- T :: * -> *
1659 <para>Syntactically, the declaration lacks the "= constrs" part. The
1660 type can be parameterised over types of any kind, but if the kind is
1661 not <literal>*</literal> then an explicit kind annotation must be used
1662 (see <xref linkend="kinding"/>).</para>
1664 <para>Such data types have only one value, namely bottom.
1665 Nevertheless, they can be useful when defining "phantom types".</para>
1668 <sect2 id="infix-tycons">
1669 <title>Infix type constructors, classes, and type variables</title>
1672 GHC allows type constructors, classes, and type variables to be operators, and
1673 to be written infix, very much like expressions. More specifically:
1676 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1677 The lexical syntax is the same as that for data constructors.
1680 Data type and type-synonym declarations can be written infix, parenthesised
1681 if you want further arguments. E.g.
1683 data a :*: b = Foo a b
1684 type a :+: b = Either a b
1685 class a :=: b where ...
1687 data (a :**: b) x = Baz a b x
1688 type (a :++: b) y = Either (a,b) y
1692 Types, and class constraints, can be written infix. For example
1695 f :: (a :=: b) => a -> b
1699 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1700 The lexical syntax is the same as that for variable operators, excluding "(.)",
1701 "(!)", and "(*)". In a binding position, the operator must be
1702 parenthesised. For example:
1704 type T (+) = Int + Int
1708 liftA2 :: Arrow (~>)
1709 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1715 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1716 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1719 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1720 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1721 sets the fixity for a data constructor and the corresponding type constructor. For example:
1725 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1726 and similarly for <literal>:*:</literal>.
1727 <literal>Int `a` Bool</literal>.
1730 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1737 <sect2 id="type-synonyms">
1738 <title>Liberalised type synonyms</title>
1741 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1742 on individual synonym declarations.
1743 With the <option>-XLiberalTypeSynonyms</option> extension,
1744 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1745 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1748 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1749 in a type synonym, thus:
1751 type Discard a = forall b. Show b => a -> b -> (a, String)
1756 g :: Discard Int -> (Int,String) -- A rank-2 type
1763 If you also use <option>-XUnboxedTuples</option>,
1764 you can write an unboxed tuple in a type synonym:
1766 type Pr = (# Int, Int #)
1774 You can apply a type synonym to a forall type:
1776 type Foo a = a -> a -> Bool
1778 f :: Foo (forall b. b->b)
1780 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1782 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1787 You can apply a type synonym to a partially applied type synonym:
1789 type Generic i o = forall x. i x -> o x
1792 foo :: Generic Id []
1794 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1796 foo :: forall x. x -> [x]
1804 GHC currently does kind checking before expanding synonyms (though even that
1808 After expanding type synonyms, GHC does validity checking on types, looking for
1809 the following mal-formedness which isn't detected simply by kind checking:
1812 Type constructor applied to a type involving for-alls.
1815 Unboxed tuple on left of an arrow.
1818 Partially-applied type synonym.
1822 this will be rejected:
1824 type Pr = (# Int, Int #)
1829 because GHC does not allow unboxed tuples on the left of a function arrow.
1834 <sect2 id="existential-quantification">
1835 <title>Existentially quantified data constructors
1839 The idea of using existential quantification in data type declarations
1840 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1841 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1842 London, 1991). It was later formalised by Laufer and Odersky
1843 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1844 TOPLAS, 16(5), pp1411-1430, 1994).
1845 It's been in Lennart
1846 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1847 proved very useful. Here's the idea. Consider the declaration:
1853 data Foo = forall a. MkFoo a (a -> Bool)
1860 The data type <literal>Foo</literal> has two constructors with types:
1866 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1873 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1874 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1875 For example, the following expression is fine:
1881 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1887 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1888 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1889 isUpper</function> packages a character with a compatible function. These
1890 two things are each of type <literal>Foo</literal> and can be put in a list.
1894 What can we do with a value of type <literal>Foo</literal>?. In particular,
1895 what happens when we pattern-match on <function>MkFoo</function>?
1901 f (MkFoo val fn) = ???
1907 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1908 are compatible, the only (useful) thing we can do with them is to
1909 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1916 f (MkFoo val fn) = fn val
1922 What this allows us to do is to package heterogeneous values
1923 together with a bunch of functions that manipulate them, and then treat
1924 that collection of packages in a uniform manner. You can express
1925 quite a bit of object-oriented-like programming this way.
1928 <sect3 id="existential">
1929 <title>Why existential?
1933 What has this to do with <emphasis>existential</emphasis> quantification?
1934 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1940 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1946 But Haskell programmers can safely think of the ordinary
1947 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1948 adding a new existential quantification construct.
1953 <sect3 id="existential-with-context">
1954 <title>Existentials and type classes</title>
1957 An easy extension is to allow
1958 arbitrary contexts before the constructor. For example:
1964 data Baz = forall a. Eq a => Baz1 a a
1965 | forall b. Show b => Baz2 b (b -> b)
1971 The two constructors have the types you'd expect:
1977 Baz1 :: forall a. Eq a => a -> a -> Baz
1978 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1984 But when pattern matching on <function>Baz1</function> the matched values can be compared
1985 for equality, and when pattern matching on <function>Baz2</function> the first matched
1986 value can be converted to a string (as well as applying the function to it).
1987 So this program is legal:
1994 f (Baz1 p q) | p == q = "Yes"
1996 f (Baz2 v fn) = show (fn v)
2002 Operationally, in a dictionary-passing implementation, the
2003 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2004 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2005 extract it on pattern matching.
2010 <sect3 id="existential-records">
2011 <title>Record Constructors</title>
2014 GHC allows existentials to be used with records syntax as well. For example:
2017 data Counter a = forall self. NewCounter
2019 , _inc :: self -> self
2020 , _display :: self -> IO ()
2024 Here <literal>tag</literal> is a public field, with a well-typed selector
2025 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2026 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2027 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2028 compile-time error. In other words, <emphasis>GHC defines a record selector function
2029 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2030 (This example used an underscore in the fields for which record selectors
2031 will not be defined, but that is only programming style; GHC ignores them.)
2035 To make use of these hidden fields, we need to create some helper functions:
2038 inc :: Counter a -> Counter a
2039 inc (NewCounter x i d t) = NewCounter
2040 { _this = i x, _inc = i, _display = d, tag = t }
2042 display :: Counter a -> IO ()
2043 display NewCounter{ _this = x, _display = d } = d x
2046 Now we can define counters with different underlying implementations:
2049 counterA :: Counter String
2050 counterA = NewCounter
2051 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2053 counterB :: Counter String
2054 counterB = NewCounter
2055 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2058 display (inc counterA) -- prints "1"
2059 display (inc (inc counterB)) -- prints "##"
2062 Record update syntax is supported for existentials (and GADTs):
2064 setTag :: Counter a -> a -> Counter a
2065 setTag obj t = obj{ tag = t }
2067 The rule for record update is this: <emphasis>
2068 the types of the updated fields may
2069 mention only the universally-quantified type variables
2070 of the data constructor. For GADTs, the field may mention only types
2071 that appear as a simple type-variable argument in the constructor's result
2072 type</emphasis>. For example:
2074 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2075 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2076 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2077 -- existentially quantified)
2079 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2080 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2081 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2082 -- type-variable argument in G1's result type)
2090 <title>Restrictions</title>
2093 There are several restrictions on the ways in which existentially-quantified
2094 constructors can be use.
2103 When pattern matching, each pattern match introduces a new,
2104 distinct, type for each existential type variable. These types cannot
2105 be unified with any other type, nor can they escape from the scope of
2106 the pattern match. For example, these fragments are incorrect:
2114 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2115 is the result of <function>f1</function>. One way to see why this is wrong is to
2116 ask what type <function>f1</function> has:
2120 f1 :: Foo -> a -- Weird!
2124 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2129 f1 :: forall a. Foo -> a -- Wrong!
2133 The original program is just plain wrong. Here's another sort of error
2137 f2 (Baz1 a b) (Baz1 p q) = a==q
2141 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2142 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2143 from the two <function>Baz1</function> constructors.
2151 You can't pattern-match on an existentially quantified
2152 constructor in a <literal>let</literal> or <literal>where</literal> group of
2153 bindings. So this is illegal:
2157 f3 x = a==b where { Baz1 a b = x }
2160 Instead, use a <literal>case</literal> expression:
2163 f3 x = case x of Baz1 a b -> a==b
2166 In general, you can only pattern-match
2167 on an existentially-quantified constructor in a <literal>case</literal> expression or
2168 in the patterns of a function definition.
2170 The reason for this restriction is really an implementation one.
2171 Type-checking binding groups is already a nightmare without
2172 existentials complicating the picture. Also an existential pattern
2173 binding at the top level of a module doesn't make sense, because it's
2174 not clear how to prevent the existentially-quantified type "escaping".
2175 So for now, there's a simple-to-state restriction. We'll see how
2183 You can't use existential quantification for <literal>newtype</literal>
2184 declarations. So this is illegal:
2188 newtype T = forall a. Ord a => MkT a
2192 Reason: a value of type <literal>T</literal> must be represented as a
2193 pair of a dictionary for <literal>Ord t</literal> and a value of type
2194 <literal>t</literal>. That contradicts the idea that
2195 <literal>newtype</literal> should have no concrete representation.
2196 You can get just the same efficiency and effect by using
2197 <literal>data</literal> instead of <literal>newtype</literal>. If
2198 there is no overloading involved, then there is more of a case for
2199 allowing an existentially-quantified <literal>newtype</literal>,
2200 because the <literal>data</literal> version does carry an
2201 implementation cost, but single-field existentially quantified
2202 constructors aren't much use. So the simple restriction (no
2203 existential stuff on <literal>newtype</literal>) stands, unless there
2204 are convincing reasons to change it.
2212 You can't use <literal>deriving</literal> to define instances of a
2213 data type with existentially quantified data constructors.
2215 Reason: in most cases it would not make sense. For example:;
2218 data T = forall a. MkT [a] deriving( Eq )
2221 To derive <literal>Eq</literal> in the standard way we would need to have equality
2222 between the single component of two <function>MkT</function> constructors:
2226 (MkT a) == (MkT b) = ???
2229 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2230 It's just about possible to imagine examples in which the derived instance
2231 would make sense, but it seems altogether simpler simply to prohibit such
2232 declarations. Define your own instances!
2243 <!-- ====================== Generalised algebraic data types ======================= -->
2245 <sect2 id="gadt-style">
2246 <title>Declaring data types with explicit constructor signatures</title>
2248 <para>GHC allows you to declare an algebraic data type by
2249 giving the type signatures of constructors explicitly. For example:
2253 Just :: a -> Maybe a
2255 The form is called a "GADT-style declaration"
2256 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2257 can only be declared using this form.</para>
2258 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2259 For example, these two declarations are equivalent:
2261 data Foo = forall a. MkFoo a (a -> Bool)
2262 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2265 <para>Any data type that can be declared in standard Haskell-98 syntax
2266 can also be declared using GADT-style syntax.
2267 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2268 they treat class constraints on the data constructors differently.
2269 Specifically, if the constructor is given a type-class context, that
2270 context is made available by pattern matching. For example:
2273 MkSet :: Eq a => [a] -> Set a
2275 makeSet :: Eq a => [a] -> Set a
2276 makeSet xs = MkSet (nub xs)
2278 insert :: a -> Set a -> Set a
2279 insert a (MkSet as) | a `elem` as = MkSet as
2280 | otherwise = MkSet (a:as)
2282 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2283 gives rise to a <literal>(Eq a)</literal>
2284 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2285 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2286 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2287 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2288 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2289 In the example, the equality dictionary is used to satisfy the equality constraint
2290 generated by the call to <literal>elem</literal>, so that the type of
2291 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2294 For example, one possible application is to reify dictionaries:
2296 data NumInst a where
2297 MkNumInst :: Num a => NumInst a
2299 intInst :: NumInst Int
2302 plus :: NumInst a -> a -> a -> a
2303 plus MkNumInst p q = p + q
2305 Here, a value of type <literal>NumInst a</literal> is equivalent
2306 to an explicit <literal>(Num a)</literal> dictionary.
2309 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2310 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2314 = Num a => MkNumInst (NumInst a)
2316 Notice that, unlike the situation when declaring an existential, there is
2317 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2318 data type's universally quantified type variable <literal>a</literal>.
2319 A constructor may have both universal and existential type variables: for example,
2320 the following two declarations are equivalent:
2323 = forall b. (Num a, Eq b) => MkT1 a b
2325 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2328 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2329 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2330 In Haskell 98 the definition
2332 data Eq a => Set' a = MkSet' [a]
2334 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2335 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2336 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2337 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2338 GHC's behaviour is much more useful, as well as much more intuitive.
2342 The rest of this section gives further details about GADT-style data
2347 The result type of each data constructor must begin with the type constructor being defined.
2348 If the result type of all constructors
2349 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2350 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2351 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2355 As with other type signatures, you can give a single signature for several data constructors.
2356 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2365 The type signature of
2366 each constructor is independent, and is implicitly universally quantified as usual.
2367 Different constructors may have different universally-quantified type variables
2368 and different type-class constraints.
2369 For example, this is fine:
2372 T1 :: Eq b => b -> T b
2373 T2 :: (Show c, Ix c) => c -> [c] -> T c
2378 Unlike a Haskell-98-style
2379 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2380 have no scope. Indeed, one can write a kind signature instead:
2382 data Set :: * -> * where ...
2384 or even a mixture of the two:
2386 data Foo a :: (* -> *) -> * where ...
2388 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2391 data Foo a (b :: * -> *) where ...
2397 You can use strictness annotations, in the obvious places
2398 in the constructor type:
2401 Lit :: !Int -> Term Int
2402 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2403 Pair :: Term a -> Term b -> Term (a,b)
2408 You can use a <literal>deriving</literal> clause on a GADT-style data type
2409 declaration. For example, these two declarations are equivalent
2411 data Maybe1 a where {
2412 Nothing1 :: Maybe1 a ;
2413 Just1 :: a -> Maybe1 a
2414 } deriving( Eq, Ord )
2416 data Maybe2 a = Nothing2 | Just2 a
2422 You can use record syntax on a GADT-style data type declaration:
2426 Adult { name :: String, children :: [Person] } :: Person
2427 Child { name :: String } :: Person
2429 As usual, for every constructor that has a field <literal>f</literal>, the type of
2430 field <literal>f</literal> must be the same (modulo alpha conversion).
2433 At the moment, record updates are not yet possible with GADT-style declarations,
2434 so support is limited to record construction, selection and pattern matching.
2437 aPerson = Adult { name = "Fred", children = [] }
2439 shortName :: Person -> Bool
2440 hasChildren (Adult { children = kids }) = not (null kids)
2441 hasChildren (Child {}) = False
2446 As in the case of existentials declared using the Haskell-98-like record syntax
2447 (<xref linkend="existential-records"/>),
2448 record-selector functions are generated only for those fields that have well-typed
2450 Here is the example of that section, in GADT-style syntax:
2452 data Counter a where
2453 NewCounter { _this :: self
2454 , _inc :: self -> self
2455 , _display :: self -> IO ()
2460 As before, only one selector function is generated here, that for <literal>tag</literal>.
2461 Nevertheless, you can still use all the field names in pattern matching and record construction.
2463 </itemizedlist></para>
2467 <title>Generalised Algebraic Data Types (GADTs)</title>
2469 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2470 by allowing constructors to have richer return types. Here is an example:
2473 Lit :: Int -> Term Int
2474 Succ :: Term Int -> Term Int
2475 IsZero :: Term Int -> Term Bool
2476 If :: Term Bool -> Term a -> Term a -> Term a
2477 Pair :: Term a -> Term b -> Term (a,b)
2479 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2480 case with ordinary data types. This generality allows us to
2481 write a well-typed <literal>eval</literal> function
2482 for these <literal>Terms</literal>:
2486 eval (Succ t) = 1 + eval t
2487 eval (IsZero t) = eval t == 0
2488 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2489 eval (Pair e1 e2) = (eval e1, eval e2)
2491 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2492 For example, in the right hand side of the equation
2497 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2498 A precise specification of the type rules is beyond what this user manual aspires to,
2499 but the design closely follows that described in
2501 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2502 unification-based type inference for GADTs</ulink>,
2504 The general principle is this: <emphasis>type refinement is only carried out
2505 based on user-supplied type annotations</emphasis>.
2506 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2507 and lots of obscure error messages will
2508 occur. However, the refinement is quite general. For example, if we had:
2510 eval :: Term a -> a -> a
2511 eval (Lit i) j = i+j
2513 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2514 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2515 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2518 These and many other examples are given in papers by Hongwei Xi, and
2519 Tim Sheard. There is a longer introduction
2520 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2522 <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
2523 may use different notation to that implemented in GHC.
2526 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2527 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2530 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2531 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2532 The result type of each constructor must begin with the type constructor being defined,
2533 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2534 For example, in the <literal>Term</literal> data
2535 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2536 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2541 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2542 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2543 whose result type is not just <literal>T a b</literal>.
2547 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2548 an ordinary data type.
2552 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2556 Lit { val :: Int } :: Term Int
2557 Succ { num :: Term Int } :: Term Int
2558 Pred { num :: Term Int } :: Term Int
2559 IsZero { arg :: Term Int } :: Term Bool
2560 Pair { arg1 :: Term a
2563 If { cnd :: Term Bool
2568 However, for GADTs there is the following additional constraint:
2569 every constructor that has a field <literal>f</literal> must have
2570 the same result type (modulo alpha conversion)
2571 Hence, in the above example, we cannot merge the <literal>num</literal>
2572 and <literal>arg</literal> fields above into a
2573 single name. Although their field types are both <literal>Term Int</literal>,
2574 their selector functions actually have different types:
2577 num :: Term Int -> Term Int
2578 arg :: Term Bool -> Term Int
2583 When pattern-matching against data constructors drawn from a GADT,
2584 for example in a <literal>case</literal> expression, the following rules apply:
2586 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2587 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2588 <listitem><para>The type of any free variable mentioned in any of
2589 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2591 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2592 way to ensure that a variable a rigid type is to give it a type signature.
2593 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2594 Simple unification-based type inference for GADTs
2595 </ulink>. The criteria implemented by GHC are given in the Appendix.
2605 <!-- ====================== End of Generalised algebraic data types ======================= -->
2607 <sect1 id="deriving">
2608 <title>Extensions to the "deriving" mechanism</title>
2610 <sect2 id="deriving-inferred">
2611 <title>Inferred context for deriving clauses</title>
2614 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2617 data T0 f a = MkT0 a deriving( Eq )
2618 data T1 f a = MkT1 (f a) deriving( Eq )
2619 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2621 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2623 instance Eq a => Eq (T0 f a) where ...
2624 instance Eq (f a) => Eq (T1 f a) where ...
2625 instance Eq (f (f a)) => Eq (T2 f a) where ...
2627 The first of these is obviously fine. The second is still fine, although less obviously.
2628 The third is not Haskell 98, and risks losing termination of instances.
2631 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2632 each constraint in the inferred instance context must consist only of type variables,
2633 with no repetitions.
2636 This rule is applied regardless of flags. If you want a more exotic context, you can write
2637 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2641 <sect2 id="stand-alone-deriving">
2642 <title>Stand-alone deriving declarations</title>
2645 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2647 data Foo a = Bar a | Baz String
2649 deriving instance Eq a => Eq (Foo a)
2651 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2652 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2653 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2654 exactly as you would in an ordinary instance declaration.
2655 (In contrast the context is inferred in a <literal>deriving</literal> clause
2656 attached to a data type declaration.)
2658 A <literal>deriving instance</literal> declaration
2659 must obey the same rules concerning form and termination as ordinary instance declarations,
2660 controlled by the same flags; see <xref linkend="instance-decls"/>.
2663 Unlike a <literal>deriving</literal>
2664 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2665 than the data type (assuming you also use
2666 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2669 data Foo a = Bar a | Baz String
2671 deriving instance Eq a => Eq (Foo [a])
2672 deriving instance Eq a => Eq (Foo (Maybe a))
2674 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2675 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2678 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2679 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2682 newtype Foo a = MkFoo (State Int a)
2684 deriving instance MonadState Int Foo
2686 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2687 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2693 <sect2 id="deriving-typeable">
2694 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2697 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2698 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2699 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2700 classes <literal>Eq</literal>, <literal>Ord</literal>,
2701 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2704 GHC extends this list with several more classes that may be automatically derived:
2706 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2707 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2708 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2710 <para>An instance of <literal>Typeable</literal> can only be derived if the
2711 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2712 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2714 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2715 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2717 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2718 are used, and only <literal>Typeable1</literal> up to
2719 <literal>Typeable7</literal> are provided in the library.)
2720 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2721 class, whose kind suits that of the data type constructor, and
2722 then writing the data type instance by hand.
2726 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2727 the class <literal>Functor</literal>,
2728 defined in <literal>GHC.Base</literal>.
2731 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2732 the class <literal>Foldable</literal>,
2733 defined in <literal>Data.Foldable</literal>.
2736 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2737 the class <literal>Traversable</literal>,
2738 defined in <literal>Data.Traversable</literal>.
2741 In each case the appropriate class must be in scope before it
2742 can be mentioned in the <literal>deriving</literal> clause.
2746 <sect2 id="newtype-deriving">
2747 <title>Generalised derived instances for newtypes</title>
2750 When you define an abstract type using <literal>newtype</literal>, you may want
2751 the new type to inherit some instances from its representation. In
2752 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2753 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2754 other classes you have to write an explicit instance declaration. For
2755 example, if you define
2758 newtype Dollars = Dollars Int
2761 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2762 explicitly define an instance of <literal>Num</literal>:
2765 instance Num Dollars where
2766 Dollars a + Dollars b = Dollars (a+b)
2769 All the instance does is apply and remove the <literal>newtype</literal>
2770 constructor. It is particularly galling that, since the constructor
2771 doesn't appear at run-time, this instance declaration defines a
2772 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2773 dictionary, only slower!
2777 <sect3> <title> Generalising the deriving clause </title>
2779 GHC now permits such instances to be derived instead,
2780 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2783 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2786 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2787 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2788 derives an instance declaration of the form
2791 instance Num Int => Num Dollars
2794 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2798 We can also derive instances of constructor classes in a similar
2799 way. For example, suppose we have implemented state and failure monad
2800 transformers, such that
2803 instance Monad m => Monad (State s m)
2804 instance Monad m => Monad (Failure m)
2806 In Haskell 98, we can define a parsing monad by
2808 type Parser tok m a = State [tok] (Failure m) a
2811 which is automatically a monad thanks to the instance declarations
2812 above. With the extension, we can make the parser type abstract,
2813 without needing to write an instance of class <literal>Monad</literal>, via
2816 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2819 In this case the derived instance declaration is of the form
2821 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2824 Notice that, since <literal>Monad</literal> is a constructor class, the
2825 instance is a <emphasis>partial application</emphasis> of the new type, not the
2826 entire left hand side. We can imagine that the type declaration is
2827 "eta-converted" to generate the context of the instance
2832 We can even derive instances of multi-parameter classes, provided the
2833 newtype is the last class parameter. In this case, a ``partial
2834 application'' of the class appears in the <literal>deriving</literal>
2835 clause. For example, given the class
2838 class StateMonad s m | m -> s where ...
2839 instance Monad m => StateMonad s (State s m) where ...
2841 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2843 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2844 deriving (Monad, StateMonad [tok])
2847 The derived instance is obtained by completing the application of the
2848 class to the new type:
2851 instance StateMonad [tok] (State [tok] (Failure m)) =>
2852 StateMonad [tok] (Parser tok m)
2857 As a result of this extension, all derived instances in newtype
2858 declarations are treated uniformly (and implemented just by reusing
2859 the dictionary for the representation type), <emphasis>except</emphasis>
2860 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2861 the newtype and its representation.
2865 <sect3> <title> A more precise specification </title>
2867 Derived instance declarations are constructed as follows. Consider the
2868 declaration (after expansion of any type synonyms)
2871 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2877 The <literal>ci</literal> are partial applications of
2878 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2879 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2882 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2885 The type <literal>t</literal> is an arbitrary type.
2888 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2889 nor in the <literal>ci</literal>, and
2892 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2893 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2894 should not "look through" the type or its constructor. You can still
2895 derive these classes for a newtype, but it happens in the usual way, not
2896 via this new mechanism.
2899 Then, for each <literal>ci</literal>, the derived instance
2902 instance ci t => ci (T v1...vk)
2904 As an example which does <emphasis>not</emphasis> work, consider
2906 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2908 Here we cannot derive the instance
2910 instance Monad (State s m) => Monad (NonMonad m)
2913 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2914 and so cannot be "eta-converted" away. It is a good thing that this
2915 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2916 not, in fact, a monad --- for the same reason. Try defining
2917 <literal>>>=</literal> with the correct type: you won't be able to.
2921 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2922 important, since we can only derive instances for the last one. If the
2923 <literal>StateMonad</literal> class above were instead defined as
2926 class StateMonad m s | m -> s where ...
2929 then we would not have been able to derive an instance for the
2930 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2931 classes usually have one "main" parameter for which deriving new
2932 instances is most interesting.
2934 <para>Lastly, all of this applies only for classes other than
2935 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2936 and <literal>Data</literal>, for which the built-in derivation applies (section
2937 4.3.3. of the Haskell Report).
2938 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2939 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2940 the standard method is used or the one described here.)
2947 <!-- TYPE SYSTEM EXTENSIONS -->
2948 <sect1 id="type-class-extensions">
2949 <title>Class and instances declarations</title>
2951 <sect2 id="multi-param-type-classes">
2952 <title>Class declarations</title>
2955 This section, and the next one, documents GHC's type-class extensions.
2956 There's lots of background in the paper <ulink
2957 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2958 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2959 Jones, Erik Meijer).
2962 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2966 <title>Multi-parameter type classes</title>
2968 Multi-parameter type classes are permitted. For example:
2972 class Collection c a where
2973 union :: c a -> c a -> c a
2981 <title>The superclasses of a class declaration</title>
2984 There are no restrictions on the context in a class declaration
2985 (which introduces superclasses), except that the class hierarchy must
2986 be acyclic. So these class declarations are OK:
2990 class Functor (m k) => FiniteMap m k where
2993 class (Monad m, Monad (t m)) => Transform t m where
2994 lift :: m a -> (t m) a
3000 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3001 of "acyclic" involves only the superclass relationships. For example,
3007 op :: D b => a -> b -> b
3010 class C a => D a where { ... }
3014 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3015 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3016 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3023 <sect3 id="class-method-types">
3024 <title>Class method types</title>
3027 Haskell 98 prohibits class method types to mention constraints on the
3028 class type variable, thus:
3031 fromList :: [a] -> s a
3032 elem :: Eq a => a -> s a -> Bool
3034 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3035 contains the constraint <literal>Eq a</literal>, constrains only the
3036 class type variable (in this case <literal>a</literal>).
3037 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3044 <sect2 id="functional-dependencies">
3045 <title>Functional dependencies
3048 <para> Functional dependencies are implemented as described by Mark Jones
3049 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3050 In Proceedings of the 9th European Symposium on Programming,
3051 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3055 Functional dependencies are introduced by a vertical bar in the syntax of a
3056 class declaration; e.g.
3058 class (Monad m) => MonadState s m | m -> s where ...
3060 class Foo a b c | a b -> c where ...
3062 There should be more documentation, but there isn't (yet). Yell if you need it.
3065 <sect3><title>Rules for functional dependencies </title>
3067 In a class declaration, all of the class type variables must be reachable (in the sense
3068 mentioned in <xref linkend="type-restrictions"/>)
3069 from the free variables of each method type.
3073 class Coll s a where
3075 insert :: s -> a -> s
3078 is not OK, because the type of <literal>empty</literal> doesn't mention
3079 <literal>a</literal>. Functional dependencies can make the type variable
3082 class Coll s a | s -> a where
3084 insert :: s -> a -> s
3087 Alternatively <literal>Coll</literal> might be rewritten
3090 class Coll s a where
3092 insert :: s a -> a -> s a
3096 which makes the connection between the type of a collection of
3097 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3098 Occasionally this really doesn't work, in which case you can split the
3106 class CollE s => Coll s a where
3107 insert :: s -> a -> s
3114 <title>Background on functional dependencies</title>
3116 <para>The following description of the motivation and use of functional dependencies is taken
3117 from the Hugs user manual, reproduced here (with minor changes) by kind
3118 permission of Mark Jones.
3121 Consider the following class, intended as part of a
3122 library for collection types:
3124 class Collects e ce where
3126 insert :: e -> ce -> ce
3127 member :: e -> ce -> Bool
3129 The type variable e used here represents the element type, while ce is the type
3130 of the container itself. Within this framework, we might want to define
3131 instances of this class for lists or characteristic functions (both of which
3132 can be used to represent collections of any equality type), bit sets (which can
3133 be used to represent collections of characters), or hash tables (which can be
3134 used to represent any collection whose elements have a hash function). Omitting
3135 standard implementation details, this would lead to the following declarations:
3137 instance Eq e => Collects e [e] where ...
3138 instance Eq e => Collects e (e -> Bool) where ...
3139 instance Collects Char BitSet where ...
3140 instance (Hashable e, Collects a ce)
3141 => Collects e (Array Int ce) where ...
3143 All this looks quite promising; we have a class and a range of interesting
3144 implementations. Unfortunately, there are some serious problems with the class
3145 declaration. First, the empty function has an ambiguous type:
3147 empty :: Collects e ce => ce
3149 By "ambiguous" we mean that there is a type variable e that appears on the left
3150 of the <literal>=></literal> symbol, but not on the right. The problem with
3151 this is that, according to the theoretical foundations of Haskell overloading,
3152 we cannot guarantee a well-defined semantics for any term with an ambiguous
3156 We can sidestep this specific problem by removing the empty member from the
3157 class declaration. However, although the remaining members, insert and member,
3158 do not have ambiguous types, we still run into problems when we try to use
3159 them. For example, consider the following two functions:
3161 f x y = insert x . insert y
3164 for which GHC infers the following types:
3166 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3167 g :: (Collects Bool c, Collects Char c) => c -> c
3169 Notice that the type for f allows the two parameters x and y to be assigned
3170 different types, even though it attempts to insert each of the two values, one
3171 after the other, into the same collection. If we're trying to model collections
3172 that contain only one type of value, then this is clearly an inaccurate
3173 type. Worse still, the definition for g is accepted, without causing a type
3174 error. As a result, the error in this code will not be flagged at the point
3175 where it appears. Instead, it will show up only when we try to use g, which
3176 might even be in a different module.
3179 <sect4><title>An attempt to use constructor classes</title>
3182 Faced with the problems described above, some Haskell programmers might be
3183 tempted to use something like the following version of the class declaration:
3185 class Collects e c where
3187 insert :: e -> c e -> c e
3188 member :: e -> c e -> Bool
3190 The key difference here is that we abstract over the type constructor c that is
3191 used to form the collection type c e, and not over that collection type itself,
3192 represented by ce in the original class declaration. This avoids the immediate
3193 problems that we mentioned above: empty has type <literal>Collects e c => c
3194 e</literal>, which is not ambiguous.
3197 The function f from the previous section has a more accurate type:
3199 f :: (Collects e c) => e -> e -> c e -> c e
3201 The function g from the previous section is now rejected with a type error as
3202 we would hope because the type of f does not allow the two arguments to have
3204 This, then, is an example of a multiple parameter class that does actually work
3205 quite well in practice, without ambiguity problems.
3206 There is, however, a catch. This version of the Collects class is nowhere near
3207 as general as the original class seemed to be: only one of the four instances
3208 for <literal>Collects</literal>
3209 given above can be used with this version of Collects because only one of
3210 them---the instance for lists---has a collection type that can be written in
3211 the form c e, for some type constructor c, and element type e.
3215 <sect4><title>Adding functional dependencies</title>
3218 To get a more useful version of the Collects class, Hugs provides a mechanism
3219 that allows programmers to specify dependencies between the parameters of a
3220 multiple parameter class (For readers with an interest in theoretical
3221 foundations and previous work: The use of dependency information can be seen
3222 both as a generalization of the proposal for `parametric type classes' that was
3223 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3224 later framework for "improvement" of qualified types. The
3225 underlying ideas are also discussed in a more theoretical and abstract setting
3226 in a manuscript [implparam], where they are identified as one point in a
3227 general design space for systems of implicit parameterization.).
3229 To start with an abstract example, consider a declaration such as:
3231 class C a b where ...
3233 which tells us simply that C can be thought of as a binary relation on types
3234 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3235 included in the definition of classes to add information about dependencies
3236 between parameters, as in the following examples:
3238 class D a b | a -> b where ...
3239 class E a b | a -> b, b -> a where ...
3241 The notation <literal>a -> b</literal> used here between the | and where
3242 symbols --- not to be
3243 confused with a function type --- indicates that the a parameter uniquely
3244 determines the b parameter, and might be read as "a determines b." Thus D is
3245 not just a relation, but actually a (partial) function. Similarly, from the two
3246 dependencies that are included in the definition of E, we can see that E
3247 represents a (partial) one-one mapping between types.
3250 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3251 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3252 m>=0, meaning that the y parameters are uniquely determined by the x
3253 parameters. Spaces can be used as separators if more than one variable appears
3254 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3255 annotated with multiple dependencies using commas as separators, as in the
3256 definition of E above. Some dependencies that we can write in this notation are
3257 redundant, and will be rejected because they don't serve any useful
3258 purpose, and may instead indicate an error in the program. Examples of
3259 dependencies like this include <literal>a -> a </literal>,
3260 <literal>a -> a a </literal>,
3261 <literal>a -> </literal>, etc. There can also be
3262 some redundancy if multiple dependencies are given, as in
3263 <literal>a->b</literal>,
3264 <literal>b->c </literal>, <literal>a->c </literal>, and
3265 in which some subset implies the remaining dependencies. Examples like this are
3266 not treated as errors. Note that dependencies appear only in class
3267 declarations, and not in any other part of the language. In particular, the
3268 syntax for instance declarations, class constraints, and types is completely
3272 By including dependencies in a class declaration, we provide a mechanism for
3273 the programmer to specify each multiple parameter class more precisely. The
3274 compiler, on the other hand, is responsible for ensuring that the set of
3275 instances that are in scope at any given point in the program is consistent
3276 with any declared dependencies. For example, the following pair of instance
3277 declarations cannot appear together in the same scope because they violate the
3278 dependency for D, even though either one on its own would be acceptable:
3280 instance D Bool Int where ...
3281 instance D Bool Char where ...
3283 Note also that the following declaration is not allowed, even by itself:
3285 instance D [a] b where ...
3287 The problem here is that this instance would allow one particular choice of [a]
3288 to be associated with more than one choice for b, which contradicts the
3289 dependency specified in the definition of D. More generally, this means that,
3290 in any instance of the form:
3292 instance D t s where ...
3294 for some particular types t and s, the only variables that can appear in s are
3295 the ones that appear in t, and hence, if the type t is known, then s will be
3296 uniquely determined.
3299 The benefit of including dependency information is that it allows us to define
3300 more general multiple parameter classes, without ambiguity problems, and with
3301 the benefit of more accurate types. To illustrate this, we return to the
3302 collection class example, and annotate the original definition of <literal>Collects</literal>
3303 with a simple dependency:
3305 class Collects e ce | ce -> e where
3307 insert :: e -> ce -> ce
3308 member :: e -> ce -> Bool
3310 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3311 determined by the type of the collection ce. Note that both parameters of
3312 Collects are of kind *; there are no constructor classes here. Note too that
3313 all of the instances of Collects that we gave earlier can be used
3314 together with this new definition.
3317 What about the ambiguity problems that we encountered with the original
3318 definition? The empty function still has type Collects e ce => ce, but it is no
3319 longer necessary to regard that as an ambiguous type: Although the variable e
3320 does not appear on the right of the => symbol, the dependency for class
3321 Collects tells us that it is uniquely determined by ce, which does appear on
3322 the right of the => symbol. Hence the context in which empty is used can still
3323 give enough information to determine types for both ce and e, without
3324 ambiguity. More generally, we need only regard a type as ambiguous if it
3325 contains a variable on the left of the => that is not uniquely determined
3326 (either directly or indirectly) by the variables on the right.
3329 Dependencies also help to produce more accurate types for user defined
3330 functions, and hence to provide earlier detection of errors, and less cluttered
3331 types for programmers to work with. Recall the previous definition for a
3334 f x y = insert x y = insert x . insert y
3336 for which we originally obtained a type:
3338 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3340 Given the dependency information that we have for Collects, however, we can
3341 deduce that a and b must be equal because they both appear as the second
3342 parameter in a Collects constraint with the same first parameter c. Hence we
3343 can infer a shorter and more accurate type for f:
3345 f :: (Collects a c) => a -> a -> c -> c
3347 In a similar way, the earlier definition of g will now be flagged as a type error.
3350 Although we have given only a few examples here, it should be clear that the
3351 addition of dependency information can help to make multiple parameter classes
3352 more useful in practice, avoiding ambiguity problems, and allowing more general
3353 sets of instance declarations.
3359 <sect2 id="instance-decls">
3360 <title>Instance declarations</title>
3362 <para>An instance declaration has the form
3364 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 ...
3366 The part before the "<literal>=></literal>" is the
3367 <emphasis>context</emphasis>, while the part after the
3368 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3371 <sect3 id="flexible-instance-head">
3372 <title>Relaxed rules for the instance head</title>
3375 In Haskell 98 the head of an instance declaration
3376 must be of the form <literal>C (T a1 ... an)</literal>, where
3377 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3378 and the <literal>a1 ... an</literal> are distinct type variables.
3379 GHC relaxes these rules in two ways.
3383 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3384 declaration to mention arbitrary nested types.
3385 For example, this becomes a legal instance declaration
3387 instance C (Maybe Int) where ...
3389 See also the <link linkend="instance-overlap">rules on overlap</link>.
3392 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3393 synonyms. As always, using a type synonym is just shorthand for
3394 writing the RHS of the type synonym definition. For example:
3398 type Point = (Int,Int)
3399 instance C Point where ...
3400 instance C [Point] where ...
3404 is legal. However, if you added
3408 instance C (Int,Int) where ...
3412 as well, then the compiler will complain about the overlapping
3413 (actually, identical) instance declarations. As always, type synonyms
3414 must be fully applied. You cannot, for example, write:
3418 instance Monad P where ...
3426 <sect3 id="instance-rules">
3427 <title>Relaxed rules for instance contexts</title>
3429 <para>In Haskell 98, the assertions in the context of the instance declaration
3430 must be of the form <literal>C a</literal> where <literal>a</literal>
3431 is a type variable that occurs in the head.
3435 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3436 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3437 With this flag the context of the instance declaration can each consist of arbitrary
3438 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3442 The Paterson Conditions: for each assertion in the context
3444 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3445 <listitem><para>The assertion has fewer constructors and variables (taken together
3446 and counting repetitions) than the head</para></listitem>
3450 <listitem><para>The Coverage Condition. For each functional dependency,
3451 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3452 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3453 every type variable in
3454 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3455 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3456 substitution mapping each type variable in the class declaration to the
3457 corresponding type in the instance declaration.
3460 These restrictions ensure that context reduction terminates: each reduction
3461 step makes the problem smaller by at least one
3462 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3463 if you give the <option>-XUndecidableInstances</option>
3464 flag (<xref linkend="undecidable-instances"/>).
3465 You can find lots of background material about the reason for these
3466 restrictions in the paper <ulink
3467 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3468 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3471 For example, these are OK:
3473 instance C Int [a] -- Multiple parameters
3474 instance Eq (S [a]) -- Structured type in head
3476 -- Repeated type variable in head
3477 instance C4 a a => C4 [a] [a]
3478 instance Stateful (ST s) (MutVar s)
3480 -- Head can consist of type variables only
3482 instance (Eq a, Show b) => C2 a b
3484 -- Non-type variables in context
3485 instance Show (s a) => Show (Sized s a)
3486 instance C2 Int a => C3 Bool [a]
3487 instance C2 Int a => C3 [a] b
3491 -- Context assertion no smaller than head
3492 instance C a => C a where ...
3493 -- (C b b) has more more occurrences of b than the head
3494 instance C b b => Foo [b] where ...
3499 The same restrictions apply to instances generated by
3500 <literal>deriving</literal> clauses. Thus the following is accepted:
3502 data MinHeap h a = H a (h a)
3505 because the derived instance
3507 instance (Show a, Show (h a)) => Show (MinHeap h a)
3509 conforms to the above rules.
3513 A useful idiom permitted by the above rules is as follows.
3514 If one allows overlapping instance declarations then it's quite
3515 convenient to have a "default instance" declaration that applies if
3516 something more specific does not:
3524 <sect3 id="undecidable-instances">
3525 <title>Undecidable instances</title>
3528 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3529 For example, sometimes you might want to use the following to get the
3530 effect of a "class synonym":
3532 class (C1 a, C2 a, C3 a) => C a where { }
3534 instance (C1 a, C2 a, C3 a) => C a where { }
3536 This allows you to write shorter signatures:
3542 f :: (C1 a, C2 a, C3 a) => ...
3544 The restrictions on functional dependencies (<xref
3545 linkend="functional-dependencies"/>) are particularly troublesome.
3546 It is tempting to introduce type variables in the context that do not appear in
3547 the head, something that is excluded by the normal rules. For example:
3549 class HasConverter a b | a -> b where
3552 data Foo a = MkFoo a
3554 instance (HasConverter a b,Show b) => Show (Foo a) where
3555 show (MkFoo value) = show (convert value)
3557 This is dangerous territory, however. Here, for example, is a program that would make the
3562 instance F [a] [[a]]
3563 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3565 Similarly, it can be tempting to lift the coverage condition:
3567 class Mul a b c | a b -> c where
3568 (.*.) :: a -> b -> c
3570 instance Mul Int Int Int where (.*.) = (*)
3571 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3572 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3574 The third instance declaration does not obey the coverage condition;
3575 and indeed the (somewhat strange) definition:
3577 f = \ b x y -> if b then x .*. [y] else y
3579 makes instance inference go into a loop, because it requires the constraint
3580 <literal>(Mul a [b] b)</literal>.
3583 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3584 the experimental flag <option>-XUndecidableInstances</option>
3585 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3586 both the Paterson Conditions and the Coverage Condition
3587 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3588 fixed-depth recursion stack. If you exceed the stack depth you get a
3589 sort of backtrace, and the opportunity to increase the stack depth
3590 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3596 <sect3 id="instance-overlap">
3597 <title>Overlapping instances</title>
3599 In general, <emphasis>GHC requires that that it be unambiguous which instance
3601 should be used to resolve a type-class constraint</emphasis>. This behaviour
3602 can be modified by two flags: <option>-XOverlappingInstances</option>
3603 <indexterm><primary>-XOverlappingInstances
3604 </primary></indexterm>
3605 and <option>-XIncoherentInstances</option>
3606 <indexterm><primary>-XIncoherentInstances
3607 </primary></indexterm>, as this section discusses. Both these
3608 flags are dynamic flags, and can be set on a per-module basis, using
3609 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3611 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3612 it tries to match every instance declaration against the
3614 by instantiating the head of the instance declaration. For example, consider
3617 instance context1 => C Int a where ... -- (A)
3618 instance context2 => C a Bool where ... -- (B)
3619 instance context3 => C Int [a] where ... -- (C)
3620 instance context4 => C Int [Int] where ... -- (D)
3622 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3623 but (C) and (D) do not. When matching, GHC takes
3624 no account of the context of the instance declaration
3625 (<literal>context1</literal> etc).
3626 GHC's default behaviour is that <emphasis>exactly one instance must match the
3627 constraint it is trying to resolve</emphasis>.
3628 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3629 including both declarations (A) and (B), say); an error is only reported if a
3630 particular constraint matches more than one.
3634 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3635 more than one instance to match, provided there is a most specific one. For
3636 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3637 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3638 most-specific match, the program is rejected.
3641 However, GHC is conservative about committing to an overlapping instance. For example:
3646 Suppose that from the RHS of <literal>f</literal> we get the constraint
3647 <literal>C Int [b]</literal>. But
3648 GHC does not commit to instance (C), because in a particular
3649 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3650 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3651 So GHC rejects the program.
3652 (If you add the flag <option>-XIncoherentInstances</option>,
3653 GHC will instead pick (C), without complaining about
3654 the problem of subsequent instantiations.)
3657 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3658 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3659 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3660 it instead. In this case, GHC will refrain from
3661 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3662 as before) but, rather than rejecting the program, it will infer the type
3664 f :: C Int [b] => [b] -> [b]
3666 That postpones the question of which instance to pick to the
3667 call site for <literal>f</literal>
3668 by which time more is known about the type <literal>b</literal>.
3669 You can write this type signature yourself if you use the
3670 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3674 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3678 instance Foo [b] where
3681 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3682 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3683 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3684 declaration. The solution is to postpone the choice by adding the constraint to the context
3685 of the instance declaration, thus:
3687 instance C Int [b] => Foo [b] where
3690 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3693 The willingness to be overlapped or incoherent is a property of
3694 the <emphasis>instance declaration</emphasis> itself, controlled by the
3695 presence or otherwise of the <option>-XOverlappingInstances</option>
3696 and <option>-XIncoherentInstances</option> flags when that module is
3697 being defined. Neither flag is required in a module that imports and uses the
3698 instance declaration. Specifically, during the lookup process:
3701 An instance declaration is ignored during the lookup process if (a) a more specific
3702 match is found, and (b) the instance declaration was compiled with
3703 <option>-XOverlappingInstances</option>. The flag setting for the
3704 more-specific instance does not matter.
3707 Suppose an instance declaration does not match the constraint being looked up, but
3708 does unify with it, so that it might match when the constraint is further
3709 instantiated. Usually GHC will regard this as a reason for not committing to
3710 some other constraint. But if the instance declaration was compiled with
3711 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3712 check for that declaration.
3715 These rules make it possible for a library author to design a library that relies on
3716 overlapping instances without the library client having to know.
3719 If an instance declaration is compiled without
3720 <option>-XOverlappingInstances</option>,
3721 then that instance can never be overlapped. This could perhaps be
3722 inconvenient. Perhaps the rule should instead say that the
3723 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3724 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3725 at a usage site should be permitted regardless of how the instance declarations
3726 are compiled, if the <option>-XOverlappingInstances</option> flag is
3727 used at the usage site. (Mind you, the exact usage site can occasionally be
3728 hard to pin down.) We are interested to receive feedback on these points.
3730 <para>The <option>-XIncoherentInstances</option> flag implies the
3731 <option>-XOverlappingInstances</option> flag, but not vice versa.
3739 <sect2 id="overloaded-strings">
3740 <title>Overloaded string literals
3744 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3745 string literal has type <literal>String</literal>, but with overloaded string
3746 literals enabled (with <literal>-XOverloadedStrings</literal>)
3747 a string literal has type <literal>(IsString a) => a</literal>.
3750 This means that the usual string syntax can be used, e.g., for packed strings
3751 and other variations of string like types. String literals behave very much
3752 like integer literals, i.e., they can be used in both expressions and patterns.
3753 If used in a pattern the literal with be replaced by an equality test, in the same
3754 way as an integer literal is.
3757 The class <literal>IsString</literal> is defined as:
3759 class IsString a where
3760 fromString :: String -> a
3762 The only predefined instance is the obvious one to make strings work as usual:
3764 instance IsString [Char] where
3767 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3768 it explicitly (for example, to give an instance declaration for it), you can import it
3769 from module <literal>GHC.Exts</literal>.
3772 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3776 Each type in a default declaration must be an
3777 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3781 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3782 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3783 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3784 <emphasis>or</emphasis> <literal>IsString</literal>.
3793 import GHC.Exts( IsString(..) )
3795 newtype MyString = MyString String deriving (Eq, Show)
3796 instance IsString MyString where
3797 fromString = MyString
3799 greet :: MyString -> MyString
3800 greet "hello" = "world"
3804 print $ greet "hello"
3805 print $ greet "fool"
3809 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3810 to work since it gets translated into an equality comparison.
3816 <sect1 id="type-families">
3817 <title>Type families</title>
3820 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3821 facilitate type-level
3822 programming. Type families are a generalisation of <firstterm>associated
3823 data types</firstterm>
3824 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3825 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3826 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3827 Symposium on Principles of Programming Languages (POPL'05)”, pages
3828 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3829 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3830 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3832 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3833 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3834 themselves are described in the paper “<ulink
3835 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3836 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3838 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3839 13th ACM SIGPLAN International Conference on Functional
3840 Programming”, ACM Press, pages 51-62, 2008. Type families
3841 essentially provide type-indexed data types and named functions on types,
3842 which are useful for generic programming and highly parameterised library
3843 interfaces as well as interfaces with enhanced static information, much like
3844 dependent types. They might also be regarded as an alternative to functional
3845 dependencies, but provide a more functional style of type-level programming
3846 than the relational style of functional dependencies.
3849 Indexed type families, or type families for short, are type constructors that
3850 represent sets of types. Set members are denoted by supplying the type family
3851 constructor with type parameters, which are called <firstterm>type
3852 indices</firstterm>. The
3853 difference between vanilla parametrised type constructors and family
3854 constructors is much like between parametrically polymorphic functions and
3855 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3856 behave the same at all type instances, whereas class methods can change their
3857 behaviour in dependence on the class type parameters. Similarly, vanilla type
3858 constructors imply the same data representation for all type instances, but
3859 family constructors can have varying representation types for varying type
3863 Indexed type families come in two flavours: <firstterm>data
3864 families</firstterm> and <firstterm>type synonym
3865 families</firstterm>. They are the indexed family variants of algebraic
3866 data types and type synonyms, respectively. The instances of data families
3867 can be data types and newtypes.
3870 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3871 Additional information on the use of type families in GHC is available on
3872 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3873 Haskell wiki page on type families</ulink>.
3876 <sect2 id="data-families">
3877 <title>Data families</title>
3880 Data families appear in two flavours: (1) they can be defined on the
3882 or (2) they can appear inside type classes (in which case they are known as
3883 associated types). The former is the more general variant, as it lacks the
3884 requirement for the type-indexes to coincide with the class
3885 parameters. However, the latter can lead to more clearly structured code and
3886 compiler warnings if some type instances were - possibly accidentally -
3887 omitted. In the following, we always discuss the general toplevel form first
3888 and then cover the additional constraints placed on associated types.
3891 <sect3 id="data-family-declarations">
3892 <title>Data family declarations</title>
3895 Indexed data families are introduced by a signature, such as
3897 data family GMap k :: * -> *
3899 The special <literal>family</literal> distinguishes family from standard
3900 data declarations. The result kind annotation is optional and, as
3901 usual, defaults to <literal>*</literal> if omitted. An example is
3905 Named arguments can also be given explicit kind signatures if needed.
3907 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3908 declarations] named arguments are entirely optional, so that we can
3909 declare <literal>Array</literal> alternatively with
3911 data family Array :: * -> *
3915 <sect4 id="assoc-data-family-decl">
3916 <title>Associated data family declarations</title>
3918 When a data family is declared as part of a type class, we drop
3919 the <literal>family</literal> special. The <literal>GMap</literal>
3920 declaration takes the following form
3922 class GMapKey k where
3923 data GMap k :: * -> *
3926 In contrast to toplevel declarations, named arguments must be used for
3927 all type parameters that are to be used as type-indexes. Moreover,
3928 the argument names must be class parameters. Each class parameter may
3929 only be used at most once per associated type, but some may be omitted
3930 and they may be in an order other than in the class head. Hence, the
3931 following contrived example is admissible:
3940 <sect3 id="data-instance-declarations">
3941 <title>Data instance declarations</title>
3944 Instance declarations of data and newtype families are very similar to
3945 standard data and newtype declarations. The only two differences are
3946 that the keyword <literal>data</literal> or <literal>newtype</literal>
3947 is followed by <literal>instance</literal> and that some or all of the
3948 type arguments can be non-variable types, but may not contain forall
3949 types or type synonym families. However, data families are generally
3950 allowed in type parameters, and type synonyms are allowed as long as
3951 they are fully applied and expand to a type that is itself admissible -
3952 exactly as this is required for occurrences of type synonyms in class
3953 instance parameters. For example, the <literal>Either</literal>
3954 instance for <literal>GMap</literal> is
3956 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3958 In this example, the declaration has only one variant. In general, it
3962 Data and newtype instance declarations are only permitted when an
3963 appropriate family declaration is in scope - just as a class instance declaratoin
3964 requires the class declaration to be visible. Moreover, each instance
3965 declaration has to conform to the kind determined by its family
3966 declaration. This implies that the number of parameters of an instance
3967 declaration matches the arity determined by the kind of the family.
3970 A data family instance declaration can use the full exprssiveness of
3971 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
3973 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
3974 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
3975 use either <literal>data</literal> or <literal>newtype</literal>. For example:
3978 data instance T Int = T1 Int | T2 Bool
3979 newtype instance T Char = TC Bool
3982 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
3983 and indeed can define a GADT. For example:
3986 data instance G [a] b where
3987 G1 :: c -> G [Int] b
3991 <listitem><para> You can use a <literal>deriving</literal> clause on a
3992 <literal>data instance</literal> or <literal>newtype instance</literal>
3999 Even if type families are defined as toplevel declarations, functions
4000 that perform different computations for different family instances may still
4001 need to be defined as methods of type classes. In particular, the
4002 following is not possible:
4005 data instance T Int = A
4006 data instance T Char = B
4008 foo A = 1 -- WRONG: These two equations together...
4009 foo B = 2 -- ...will produce a type error.
4011 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4015 instance Foo Int where
4017 instance Foo Char where
4020 (Given the functionality provided by GADTs (Generalised Algebraic Data
4021 Types), it might seem as if a definition, such as the above, should be
4022 feasible. However, type families are - in contrast to GADTs - are
4023 <emphasis>open;</emphasis> i.e., new instances can always be added,
4025 modules. Supporting pattern matching across different data instances
4026 would require a form of extensible case construct.)
4029 <sect4 id="assoc-data-inst">
4030 <title>Associated data instances</title>
4032 When an associated data family instance is declared within a type
4033 class instance, we drop the <literal>instance</literal> keyword in the
4034 family instance. So, the <literal>Either</literal> instance
4035 for <literal>GMap</literal> becomes:
4037 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4038 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4041 The most important point about associated family instances is that the
4042 type indexes corresponding to class parameters must be identical to
4043 the type given in the instance head; here this is the first argument
4044 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4045 which coincides with the only class parameter. Any parameters to the
4046 family constructor that do not correspond to class parameters, need to
4047 be variables in every instance; here this is the
4048 variable <literal>v</literal>.
4051 Instances for an associated family can only appear as part of
4052 instances declarations of the class in which the family was declared -
4053 just as with the equations of the methods of a class. Also in
4054 correspondence to how methods are handled, declarations of associated
4055 types can be omitted in class instances. If an associated family
4056 instance is omitted, the corresponding instance type is not inhabited;
4057 i.e., only diverging expressions, such
4058 as <literal>undefined</literal>, can assume the type.
4062 <sect4 id="scoping-class-params">
4063 <title>Scoping of class parameters</title>
4065 In the case of multi-parameter type classes, the visibility of class
4066 parameters in the right-hand side of associated family instances
4067 depends <emphasis>solely</emphasis> on the parameters of the data
4068 family. As an example, consider the simple class declaration
4073 Only one of the two class parameters is a parameter to the data
4074 family. Hence, the following instance declaration is invalid:
4076 instance C [c] d where
4077 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4079 Here, the right-hand side of the data instance mentions the type
4080 variable <literal>d</literal> that does not occur in its left-hand
4081 side. We cannot admit such data instances as they would compromise
4086 <sect4 id="family-class-inst">
4087 <title>Type class instances of family instances</title>
4089 Type class instances of instances of data families can be defined as
4090 usual, and in particular data instance declarations can
4091 have <literal>deriving</literal> clauses. For example, we can write
4093 data GMap () v = GMapUnit (Maybe v)
4096 which implicitly defines an instance of the form
4098 instance Show v => Show (GMap () v) where ...
4102 Note that class instances are always for
4103 particular <emphasis>instances</emphasis> of a data family and never
4104 for an entire family as a whole. This is for essentially the same
4105 reasons that we cannot define a toplevel function that performs
4106 pattern matching on the data constructors
4107 of <emphasis>different</emphasis> instances of a single type family.
4108 It would require a form of extensible case construct.
4112 <sect4 id="data-family-overlap">
4113 <title>Overlap of data instances</title>
4115 The instance declarations of a data family used in a single program
4116 may not overlap at all, independent of whether they are associated or
4117 not. In contrast to type class instances, this is not only a matter
4118 of consistency, but one of type safety.
4124 <sect3 id="data-family-import-export">
4125 <title>Import and export</title>
4128 The association of data constructors with type families is more dynamic
4129 than that is the case with standard data and newtype declarations. In
4130 the standard case, the notation <literal>T(..)</literal> in an import or
4131 export list denotes the type constructor and all the data constructors
4132 introduced in its declaration. However, a family declaration never
4133 introduces any data constructors; instead, data constructors are
4134 introduced by family instances. As a result, which data constructors
4135 are associated with a type family depends on the currently visible
4136 instance declarations for that family. Consequently, an import or
4137 export item of the form <literal>T(..)</literal> denotes the family
4138 constructor and all currently visible data constructors - in the case of
4139 an export item, these may be either imported or defined in the current
4140 module. The treatment of import and export items that explicitly list
4141 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4145 <sect4 id="data-family-impexp-assoc">
4146 <title>Associated families</title>
4148 As expected, an import or export item of the
4149 form <literal>C(..)</literal> denotes all of the class' methods and
4150 associated types. However, when associated types are explicitly
4151 listed as subitems of a class, we need some new syntax, as uppercase
4152 identifiers as subitems are usually data constructors, not type
4153 constructors. To clarify that we denote types here, each associated
4154 type name needs to be prefixed by the keyword <literal>type</literal>.
4155 So for example, when explicitly listing the components of
4156 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4157 GMap, empty, lookup, insert)</literal>.
4161 <sect4 id="data-family-impexp-examples">
4162 <title>Examples</title>
4164 Assuming our running <literal>GMapKey</literal> class example, let us
4165 look at some export lists and their meaning:
4168 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4169 just the class name.</para>
4172 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4173 Exports the class, the associated type <literal>GMap</literal>
4175 functions <literal>empty</literal>, <literal>lookup</literal>,
4176 and <literal>insert</literal>. None of the data constructors is
4180 <para><literal>module GMap (GMapKey(..), GMap(..))
4181 where...</literal>: As before, but also exports all the data
4182 constructors <literal>GMapInt</literal>,
4183 <literal>GMapChar</literal>,
4184 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4185 and <literal>GMapUnit</literal>.</para>
4188 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4189 GMap(..)) where...</literal>: As before.</para>
4192 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4193 where...</literal>: As before.</para>
4198 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4199 both the class <literal>GMapKey</literal> as well as its associated
4200 type <literal>GMap</literal>. However, you cannot
4201 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4202 sub-component specifications cannot be nested. To
4203 specify <literal>GMap</literal>'s data constructors, you have to list
4208 <sect4 id="data-family-impexp-instances">
4209 <title>Instances</title>
4211 Family instances are implicitly exported, just like class instances.
4212 However, this applies only to the heads of instances, not to the data
4213 constructors an instance defines.
4221 <sect2 id="synonym-families">
4222 <title>Synonym families</title>
4225 Type families appear in two flavours: (1) they can be defined on the
4226 toplevel or (2) they can appear inside type classes (in which case they
4227 are known as associated type synonyms). The former is the more general
4228 variant, as it lacks the requirement for the type-indexes to coincide with
4229 the class parameters. However, the latter can lead to more clearly
4230 structured code and compiler warnings if some type instances were -
4231 possibly accidentally - omitted. In the following, we always discuss the
4232 general toplevel form first and then cover the additional constraints
4233 placed on associated types.
4236 <sect3 id="type-family-declarations">
4237 <title>Type family declarations</title>
4240 Indexed type families are introduced by a signature, such as
4242 type family Elem c :: *
4244 The special <literal>family</literal> distinguishes family from standard
4245 type declarations. The result kind annotation is optional and, as
4246 usual, defaults to <literal>*</literal> if omitted. An example is
4250 Parameters can also be given explicit kind signatures if needed. We
4251 call the number of parameters in a type family declaration, the family's
4252 arity, and all applications of a type family must be fully saturated
4253 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4254 and it implies that the kind of a type family is not sufficient to
4255 determine a family's arity, and hence in general, also insufficient to
4256 determine whether a type family application is well formed. As an
4257 example, consider the following declaration:
4259 type family F a b :: * -> * -- F's arity is 2,
4260 -- although it's overall kind is * -> * -> * -> *
4262 Given this declaration the following are examples of well-formed and
4265 F Char [Int] -- OK! Kind: * -> *
4266 F Char [Int] Bool -- OK! Kind: *
4267 F IO Bool -- WRONG: kind mismatch in the first argument
4268 F Bool -- WRONG: unsaturated application
4272 <sect4 id="assoc-type-family-decl">
4273 <title>Associated type family declarations</title>
4275 When a type family is declared as part of a type class, we drop
4276 the <literal>family</literal> special. The <literal>Elem</literal>
4277 declaration takes the following form
4279 class Collects ce where
4283 The argument names of the type family must be class parameters. Each
4284 class parameter may only be used at most once per associated type, but
4285 some may be omitted and they may be in an order other than in the
4286 class head. Hence, the following contrived example is admissible:
4291 These rules are exactly as for associated data families.
4296 <sect3 id="type-instance-declarations">
4297 <title>Type instance declarations</title>
4299 Instance declarations of type families are very similar to standard type
4300 synonym declarations. The only two differences are that the
4301 keyword <literal>type</literal> is followed
4302 by <literal>instance</literal> and that some or all of the type
4303 arguments can be non-variable types, but may not contain forall types or
4304 type synonym families. However, data families are generally allowed, and
4305 type synonyms are allowed as long as they are fully applied and expand
4306 to a type that is admissible - these are the exact same requirements as
4307 for data instances. For example, the <literal>[e]</literal> instance
4308 for <literal>Elem</literal> is
4310 type instance Elem [e] = e
4314 Type family instance declarations are only legitimate when an
4315 appropriate family declaration is in scope - just like class instances
4316 require the class declaration to be visible. Moreover, each instance
4317 declaration has to conform to the kind determined by its family
4318 declaration, and the number of type parameters in an instance
4319 declaration must match the number of type parameters in the family
4320 declaration. Finally, the right-hand side of a type instance must be a
4321 monotype (i.e., it may not include foralls) and after the expansion of
4322 all saturated vanilla type synonyms, no synonyms, except family synonyms
4323 may remain. Here are some examples of admissible and illegal type
4326 type family F a :: *
4327 type instance F [Int] = Int -- OK!
4328 type instance F String = Char -- OK!
4329 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4330 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4331 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4333 type family G a b :: * -> *
4334 type instance G Int = (,) -- WRONG: must be two type parameters
4335 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4339 <sect4 id="assoc-type-instance">
4340 <title>Associated type instance declarations</title>
4342 When an associated family instance is declared within a type class
4343 instance, we drop the <literal>instance</literal> keyword in the family
4344 instance. So, the <literal>[e]</literal> instance
4345 for <literal>Elem</literal> becomes:
4347 instance (Eq (Elem [e])) => Collects ([e]) where
4351 The most important point about associated family instances is that the
4352 type indexes corresponding to class parameters must be identical to the
4353 type given in the instance head; here this is <literal>[e]</literal>,
4354 which coincides with the only class parameter.
4357 Instances for an associated family can only appear as part of instances
4358 declarations of the class in which the family was declared - just as
4359 with the equations of the methods of a class. Also in correspondence to
4360 how methods are handled, declarations of associated types can be omitted
4361 in class instances. If an associated family instance is omitted, the
4362 corresponding instance type is not inhabited; i.e., only diverging
4363 expressions, such as <literal>undefined</literal>, can assume the type.
4367 <sect4 id="type-family-overlap">
4368 <title>Overlap of type synonym instances</title>
4370 The instance declarations of a type family used in a single program
4371 may only overlap if the right-hand sides of the overlapping instances
4372 coincide for the overlapping types. More formally, two instance
4373 declarations overlap if there is a substitution that makes the
4374 left-hand sides of the instances syntactically the same. Whenever
4375 that is the case, the right-hand sides of the instances must also be
4376 syntactically equal under the same substitution. This condition is
4377 independent of whether the type family is associated or not, and it is
4378 not only a matter of consistency, but one of type safety.
4381 Here are two example to illustrate the condition under which overlap
4384 type instance F (a, Int) = [a]
4385 type instance F (Int, b) = [b] -- overlap permitted
4387 type instance G (a, Int) = [a]
4388 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4393 <sect4 id="type-family-decidability">
4394 <title>Decidability of type synonym instances</title>
4396 In order to guarantee that type inference in the presence of type
4397 families decidable, we need to place a number of additional
4398 restrictions on the formation of type instance declarations (c.f.,
4399 Definition 5 (Relaxed Conditions) of “<ulink
4400 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4401 Checking with Open Type Functions</ulink>”). Instance
4402 declarations have the general form
4404 type instance F t1 .. tn = t
4406 where we require that for every type family application <literal>(G s1
4407 .. sm)</literal> in <literal>t</literal>,
4410 <para><literal>s1 .. sm</literal> do not contain any type family
4411 constructors,</para>
4414 <para>the total number of symbols (data type constructors and type
4415 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4416 in <literal>t1 .. tn</literal>, and</para>
4419 <para>for every type
4420 variable <literal>a</literal>, <literal>a</literal> occurs
4421 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4422 .. tn</literal>.</para>
4425 These restrictions are easily verified and ensure termination of type
4426 inference. However, they are not sufficient to guarantee completeness
4427 of type inference in the presence of, so called, ''loopy equalities'',
4428 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4429 a type variable is underneath a family application and data
4430 constructor application - see the above mentioned paper for details.
4433 If the option <option>-XUndecidableInstances</option> is passed to the
4434 compiler, the above restrictions are not enforced and it is on the
4435 programmer to ensure termination of the normalisation of type families
4436 during type inference.
4441 <sect3 id-="equality-constraints">
4442 <title>Equality constraints</title>
4444 Type context can include equality constraints of the form <literal>t1 ~
4445 t2</literal>, which denote that the types <literal>t1</literal>
4446 and <literal>t2</literal> need to be the same. In the presence of type
4447 families, whether two types are equal cannot generally be decided
4448 locally. Hence, the contexts of function signatures may include
4449 equality constraints, as in the following example:
4451 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4453 where we require that the element type of <literal>c1</literal>
4454 and <literal>c2</literal> are the same. In general, the
4455 types <literal>t1</literal> and <literal>t2</literal> of an equality
4456 constraint may be arbitrary monotypes; i.e., they may not contain any
4457 quantifiers, independent of whether higher-rank types are otherwise
4461 Equality constraints can also appear in class and instance contexts.
4462 The former enable a simple translation of programs using functional
4463 dependencies into programs using family synonyms instead. The general
4464 idea is to rewrite a class declaration of the form
4466 class C a b | a -> b
4470 class (F a ~ b) => C a b where
4473 That is, we represent every functional dependency (FD) <literal>a1 .. an
4474 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4475 superclass context equality <literal>F a1 .. an ~ b</literal>,
4476 essentially giving a name to the functional dependency. In class
4477 instances, we define the type instances of FD families in accordance
4478 with the class head. Method signatures are not affected by that
4482 NB: Equalities in superclass contexts are not fully implemented in
4487 <sect3 id-="ty-fams-in-instances">
4488 <title>Type families and instance declarations</title>
4489 <para>Type families require us to extend the rules for
4490 the form of instance heads, which are given
4491 in <xref linkend="flexible-instance-head"/>.
4494 <listitem><para>Data type families may appear in an instance head</para></listitem>
4495 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4497 The reason for the latter restriction is that there is no way to check for. Consider
4500 type instance F Bool = Int
4507 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4508 The situation is especially bad because the type instance for <literal>F Bool</literal>
4509 might be in another module, or even in a module that is not yet written.
4516 <sect1 id="other-type-extensions">
4517 <title>Other type system extensions</title>
4519 <sect2 id="type-restrictions">
4520 <title>Type signatures</title>
4522 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4524 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4525 that the type-class constraints in a type signature must have the
4526 form <emphasis>(class type-variable)</emphasis> or
4527 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4528 With <option>-XFlexibleContexts</option>
4529 these type signatures are perfectly OK
4532 g :: Ord (T a ()) => ...
4536 GHC imposes the following restrictions on the constraints in a type signature.
4540 forall tv1..tvn (c1, ...,cn) => type
4543 (Here, we write the "foralls" explicitly, although the Haskell source
4544 language omits them; in Haskell 98, all the free type variables of an
4545 explicit source-language type signature are universally quantified,
4546 except for the class type variables in a class declaration. However,
4547 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4556 <emphasis>Each universally quantified type variable
4557 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4559 A type variable <literal>a</literal> is "reachable" if it appears
4560 in the same constraint as either a type variable free in
4561 <literal>type</literal>, or another reachable type variable.
4562 A value with a type that does not obey
4563 this reachability restriction cannot be used without introducing
4564 ambiguity; that is why the type is rejected.
4565 Here, for example, is an illegal type:
4569 forall a. Eq a => Int
4573 When a value with this type was used, the constraint <literal>Eq tv</literal>
4574 would be introduced where <literal>tv</literal> is a fresh type variable, and
4575 (in the dictionary-translation implementation) the value would be
4576 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4577 can never know which instance of <literal>Eq</literal> to use because we never
4578 get any more information about <literal>tv</literal>.
4582 that the reachability condition is weaker than saying that <literal>a</literal> is
4583 functionally dependent on a type variable free in
4584 <literal>type</literal> (see <xref
4585 linkend="functional-dependencies"/>). The reason for this is there
4586 might be a "hidden" dependency, in a superclass perhaps. So
4587 "reachable" is a conservative approximation to "functionally dependent".
4588 For example, consider:
4590 class C a b | a -> b where ...
4591 class C a b => D a b where ...
4592 f :: forall a b. D a b => a -> a
4594 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4595 but that is not immediately apparent from <literal>f</literal>'s type.
4601 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4602 universally quantified type variables <literal>tvi</literal></emphasis>.
4604 For example, this type is OK because <literal>C a b</literal> mentions the
4605 universally quantified type variable <literal>b</literal>:
4609 forall a. C a b => burble
4613 The next type is illegal because the constraint <literal>Eq b</literal> does not
4614 mention <literal>a</literal>:
4618 forall a. Eq b => burble
4622 The reason for this restriction is milder than the other one. The
4623 excluded types are never useful or necessary (because the offending
4624 context doesn't need to be witnessed at this point; it can be floated
4625 out). Furthermore, floating them out increases sharing. Lastly,
4626 excluding them is a conservative choice; it leaves a patch of
4627 territory free in case we need it later.
4641 <sect2 id="implicit-parameters">
4642 <title>Implicit parameters</title>
4644 <para> Implicit parameters are implemented as described in
4645 "Implicit parameters: dynamic scoping with static types",
4646 J Lewis, MB Shields, E Meijer, J Launchbury,
4647 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4651 <para>(Most of the following, still rather incomplete, documentation is
4652 due to Jeff Lewis.)</para>
4654 <para>Implicit parameter support is enabled with the option
4655 <option>-XImplicitParams</option>.</para>
4658 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4659 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4660 context. In Haskell, all variables are statically bound. Dynamic
4661 binding of variables is a notion that goes back to Lisp, but was later
4662 discarded in more modern incarnations, such as Scheme. Dynamic binding
4663 can be very confusing in an untyped language, and unfortunately, typed
4664 languages, in particular Hindley-Milner typed languages like Haskell,
4665 only support static scoping of variables.
4668 However, by a simple extension to the type class system of Haskell, we
4669 can support dynamic binding. Basically, we express the use of a
4670 dynamically bound variable as a constraint on the type. These
4671 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4672 function uses a dynamically-bound variable <literal>?x</literal>
4673 of type <literal>t'</literal>". For
4674 example, the following expresses the type of a sort function,
4675 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4677 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4679 The dynamic binding constraints are just a new form of predicate in the type class system.
4682 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4683 where <literal>x</literal> is
4684 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4685 Use of this construct also introduces a new
4686 dynamic-binding constraint in the type of the expression.
4687 For example, the following definition
4688 shows how we can define an implicitly parameterized sort function in
4689 terms of an explicitly parameterized <literal>sortBy</literal> function:
4691 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4693 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4699 <title>Implicit-parameter type constraints</title>
4701 Dynamic binding constraints behave just like other type class
4702 constraints in that they are automatically propagated. Thus, when a
4703 function is used, its implicit parameters are inherited by the
4704 function that called it. For example, our <literal>sort</literal> function might be used
4705 to pick out the least value in a list:
4707 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4708 least xs = head (sort xs)
4710 Without lifting a finger, the <literal>?cmp</literal> parameter is
4711 propagated to become a parameter of <literal>least</literal> as well. With explicit
4712 parameters, the default is that parameters must always be explicit
4713 propagated. With implicit parameters, the default is to always
4717 An implicit-parameter type constraint differs from other type class constraints in the
4718 following way: All uses of a particular implicit parameter must have
4719 the same type. This means that the type of <literal>(?x, ?x)</literal>
4720 is <literal>(?x::a) => (a,a)</literal>, and not
4721 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4725 <para> You can't have an implicit parameter in the context of a class or instance
4726 declaration. For example, both these declarations are illegal:
4728 class (?x::Int) => C a where ...
4729 instance (?x::a) => Foo [a] where ...
4731 Reason: exactly which implicit parameter you pick up depends on exactly where
4732 you invoke a function. But the ``invocation'' of instance declarations is done
4733 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4734 Easiest thing is to outlaw the offending types.</para>
4736 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4738 f :: (?x :: [a]) => Int -> Int
4741 g :: (Read a, Show a) => String -> String
4744 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4745 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4746 quite unambiguous, and fixes the type <literal>a</literal>.
4751 <title>Implicit-parameter bindings</title>
4754 An implicit parameter is <emphasis>bound</emphasis> using the standard
4755 <literal>let</literal> or <literal>where</literal> binding forms.
4756 For example, we define the <literal>min</literal> function by binding
4757 <literal>cmp</literal>.
4760 min = let ?cmp = (<=) in least
4764 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4765 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4766 (including in a list comprehension, or do-notation, or pattern guards),
4767 or a <literal>where</literal> clause.
4768 Note the following points:
4771 An implicit-parameter binding group must be a
4772 collection of simple bindings to implicit-style variables (no
4773 function-style bindings, and no type signatures); these bindings are
4774 neither polymorphic or recursive.
4777 You may not mix implicit-parameter bindings with ordinary bindings in a
4778 single <literal>let</literal>
4779 expression; use two nested <literal>let</literal>s instead.
4780 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4784 You may put multiple implicit-parameter bindings in a
4785 single binding group; but they are <emphasis>not</emphasis> treated
4786 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4787 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4788 parameter. The bindings are not nested, and may be re-ordered without changing
4789 the meaning of the program.
4790 For example, consider:
4792 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4794 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4795 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4797 f :: (?x::Int) => Int -> Int
4805 <sect3><title>Implicit parameters and polymorphic recursion</title>
4808 Consider these two definitions:
4811 len1 xs = let ?acc = 0 in len_acc1 xs
4814 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4819 len2 xs = let ?acc = 0 in len_acc2 xs
4821 len_acc2 :: (?acc :: Int) => [a] -> Int
4823 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4825 The only difference between the two groups is that in the second group
4826 <literal>len_acc</literal> is given a type signature.
4827 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4828 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4829 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4830 has a type signature, the recursive call is made to the
4831 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4832 as an implicit parameter. So we get the following results in GHCi:
4839 Adding a type signature dramatically changes the result! This is a rather
4840 counter-intuitive phenomenon, worth watching out for.
4844 <sect3><title>Implicit parameters and monomorphism</title>
4846 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4847 Haskell Report) to implicit parameters. For example, consider:
4855 Since the binding for <literal>y</literal> falls under the Monomorphism
4856 Restriction it is not generalised, so the type of <literal>y</literal> is
4857 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4858 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4859 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4860 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4861 <literal>y</literal> in the body of the <literal>let</literal> will see the
4862 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4863 <literal>14</literal>.
4868 <!-- ======================= COMMENTED OUT ========================
4870 We intend to remove linear implicit parameters, so I'm at least removing
4871 them from the 6.6 user manual
4873 <sect2 id="linear-implicit-parameters">
4874 <title>Linear implicit parameters</title>
4876 Linear implicit parameters are an idea developed by Koen Claessen,
4877 Mark Shields, and Simon PJ. They address the long-standing
4878 problem that monads seem over-kill for certain sorts of problem, notably:
4881 <listitem> <para> distributing a supply of unique names </para> </listitem>
4882 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4883 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4887 Linear implicit parameters are just like ordinary implicit parameters,
4888 except that they are "linear"; that is, they cannot be copied, and
4889 must be explicitly "split" instead. Linear implicit parameters are
4890 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4891 (The '/' in the '%' suggests the split!)
4896 import GHC.Exts( Splittable )
4898 data NameSupply = ...
4900 splitNS :: NameSupply -> (NameSupply, NameSupply)
4901 newName :: NameSupply -> Name
4903 instance Splittable NameSupply where
4907 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4908 f env (Lam x e) = Lam x' (f env e)
4911 env' = extend env x x'
4912 ...more equations for f...
4914 Notice that the implicit parameter %ns is consumed
4916 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4917 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4921 So the translation done by the type checker makes
4922 the parameter explicit:
4924 f :: NameSupply -> Env -> Expr -> Expr
4925 f ns env (Lam x e) = Lam x' (f ns1 env e)
4927 (ns1,ns2) = splitNS ns
4929 env = extend env x x'
4931 Notice the call to 'split' introduced by the type checker.
4932 How did it know to use 'splitNS'? Because what it really did
4933 was to introduce a call to the overloaded function 'split',
4934 defined by the class <literal>Splittable</literal>:
4936 class Splittable a where
4939 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4940 split for name supplies. But we can simply write
4946 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4948 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4949 <literal>GHC.Exts</literal>.
4954 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4955 are entirely distinct implicit parameters: you
4956 can use them together and they won't interfere with each other. </para>
4959 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4961 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4962 in the context of a class or instance declaration. </para></listitem>
4966 <sect3><title>Warnings</title>
4969 The monomorphism restriction is even more important than usual.
4970 Consider the example above:
4972 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4973 f env (Lam x e) = Lam x' (f env e)
4976 env' = extend env x x'
4978 If we replaced the two occurrences of x' by (newName %ns), which is
4979 usually a harmless thing to do, we get:
4981 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4982 f env (Lam x e) = Lam (newName %ns) (f env e)
4984 env' = extend env x (newName %ns)
4986 But now the name supply is consumed in <emphasis>three</emphasis> places
4987 (the two calls to newName,and the recursive call to f), so
4988 the result is utterly different. Urk! We don't even have
4992 Well, this is an experimental change. With implicit
4993 parameters we have already lost beta reduction anyway, and
4994 (as John Launchbury puts it) we can't sensibly reason about
4995 Haskell programs without knowing their typing.
5000 <sect3><title>Recursive functions</title>
5001 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5004 foo :: %x::T => Int -> [Int]
5006 foo n = %x : foo (n-1)
5008 where T is some type in class Splittable.</para>
5010 Do you get a list of all the same T's or all different T's
5011 (assuming that split gives two distinct T's back)?
5013 If you supply the type signature, taking advantage of polymorphic
5014 recursion, you get what you'd probably expect. Here's the
5015 translated term, where the implicit param is made explicit:
5018 foo x n = let (x1,x2) = split x
5019 in x1 : foo x2 (n-1)
5021 But if you don't supply a type signature, GHC uses the Hindley
5022 Milner trick of using a single monomorphic instance of the function
5023 for the recursive calls. That is what makes Hindley Milner type inference
5024 work. So the translation becomes
5028 foom n = x : foom (n-1)
5032 Result: 'x' is not split, and you get a list of identical T's. So the
5033 semantics of the program depends on whether or not foo has a type signature.
5036 You may say that this is a good reason to dislike linear implicit parameters
5037 and you'd be right. That is why they are an experimental feature.
5043 ================ END OF Linear Implicit Parameters commented out -->
5045 <sect2 id="kinding">
5046 <title>Explicitly-kinded quantification</title>
5049 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5050 to give the kind explicitly as (machine-checked) documentation,
5051 just as it is nice to give a type signature for a function. On some occasions,
5052 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5053 John Hughes had to define the data type:
5055 data Set cxt a = Set [a]
5056 | Unused (cxt a -> ())
5058 The only use for the <literal>Unused</literal> constructor was to force the correct
5059 kind for the type variable <literal>cxt</literal>.
5062 GHC now instead allows you to specify the kind of a type variable directly, wherever
5063 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5066 This flag enables kind signatures in the following places:
5068 <listitem><para><literal>data</literal> declarations:
5070 data Set (cxt :: * -> *) a = Set [a]
5071 </screen></para></listitem>
5072 <listitem><para><literal>type</literal> declarations:
5074 type T (f :: * -> *) = f Int
5075 </screen></para></listitem>
5076 <listitem><para><literal>class</literal> declarations:
5078 class (Eq a) => C (f :: * -> *) a where ...
5079 </screen></para></listitem>
5080 <listitem><para><literal>forall</literal>'s in type signatures:
5082 f :: forall (cxt :: * -> *). Set cxt Int
5083 </screen></para></listitem>
5088 The parentheses are required. Some of the spaces are required too, to
5089 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5090 will get a parse error, because "<literal>::*->*</literal>" is a
5091 single lexeme in Haskell.
5095 As part of the same extension, you can put kind annotations in types
5098 f :: (Int :: *) -> Int
5099 g :: forall a. a -> (a :: *)
5103 atype ::= '(' ctype '::' kind ')
5105 The parentheses are required.
5110 <sect2 id="universal-quantification">
5111 <title>Arbitrary-rank polymorphism
5115 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5116 allows us to say exactly what this means. For example:
5124 g :: forall b. (b -> b)
5126 The two are treated identically.
5130 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5131 explicit universal quantification in
5133 For example, all the following types are legal:
5135 f1 :: forall a b. a -> b -> a
5136 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5138 f2 :: (forall a. a->a) -> Int -> Int
5139 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5141 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5143 f4 :: Int -> (forall a. a -> a)
5145 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5146 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5147 The <literal>forall</literal> makes explicit the universal quantification that
5148 is implicitly added by Haskell.
5151 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5152 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5153 shows, the polymorphic type on the left of the function arrow can be overloaded.
5156 The function <literal>f3</literal> has a rank-3 type;
5157 it has rank-2 types on the left of a function arrow.
5160 GHC has three flags to control higher-rank types:
5163 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5166 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5169 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5170 That is, you can nest <literal>forall</literal>s
5171 arbitrarily deep in function arrows.
5172 In particular, a forall-type (also called a "type scheme"),
5173 including an operational type class context, is legal:
5175 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5176 of a function arrow </para> </listitem>
5177 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5178 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5179 field type signatures.</para> </listitem>
5180 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5181 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5185 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5186 a type variable any more!
5195 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5196 the types of the constructor arguments. Here are several examples:
5202 data T a = T1 (forall b. b -> b -> b) a
5204 data MonadT m = MkMonad { return :: forall a. a -> m a,
5205 bind :: forall a b. m a -> (a -> m b) -> m b
5208 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5214 The constructors have rank-2 types:
5220 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5221 MkMonad :: forall m. (forall a. a -> m a)
5222 -> (forall a b. m a -> (a -> m b) -> m b)
5224 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5230 Notice that you don't need to use a <literal>forall</literal> if there's an
5231 explicit context. For example in the first argument of the
5232 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5233 prefixed to the argument type. The implicit <literal>forall</literal>
5234 quantifies all type variables that are not already in scope, and are
5235 mentioned in the type quantified over.
5239 As for type signatures, implicit quantification happens for non-overloaded
5240 types too. So if you write this:
5243 data T a = MkT (Either a b) (b -> b)
5246 it's just as if you had written this:
5249 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5252 That is, since the type variable <literal>b</literal> isn't in scope, it's
5253 implicitly universally quantified. (Arguably, it would be better
5254 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5255 where that is what is wanted. Feedback welcomed.)
5259 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5260 the constructor to suitable values, just as usual. For example,
5271 a3 = MkSwizzle reverse
5274 a4 = let r x = Just x
5281 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5282 mkTs f x y = [T1 f x, T1 f y]
5288 The type of the argument can, as usual, be more general than the type
5289 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5290 does not need the <literal>Ord</literal> constraint.)
5294 When you use pattern matching, the bound variables may now have
5295 polymorphic types. For example:
5301 f :: T a -> a -> (a, Char)
5302 f (T1 w k) x = (w k x, w 'c' 'd')
5304 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5305 g (MkSwizzle s) xs f = s (map f (s xs))
5307 h :: MonadT m -> [m a] -> m [a]
5308 h m [] = return m []
5309 h m (x:xs) = bind m x $ \y ->
5310 bind m (h m xs) $ \ys ->
5317 In the function <function>h</function> we use the record selectors <literal>return</literal>
5318 and <literal>bind</literal> to extract the polymorphic bind and return functions
5319 from the <literal>MonadT</literal> data structure, rather than using pattern
5325 <title>Type inference</title>
5328 In general, type inference for arbitrary-rank types is undecidable.
5329 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5330 to get a decidable algorithm by requiring some help from the programmer.
5331 We do not yet have a formal specification of "some help" but the rule is this:
5334 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5335 provides an explicit polymorphic type for x, or GHC's type inference will assume
5336 that x's type has no foralls in it</emphasis>.
5339 What does it mean to "provide" an explicit type for x? You can do that by
5340 giving a type signature for x directly, using a pattern type signature
5341 (<xref linkend="scoped-type-variables"/>), thus:
5343 \ f :: (forall a. a->a) -> (f True, f 'c')
5345 Alternatively, you can give a type signature to the enclosing
5346 context, which GHC can "push down" to find the type for the variable:
5348 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5350 Here the type signature on the expression can be pushed inwards
5351 to give a type signature for f. Similarly, and more commonly,
5352 one can give a type signature for the function itself:
5354 h :: (forall a. a->a) -> (Bool,Char)
5355 h f = (f True, f 'c')
5357 You don't need to give a type signature if the lambda bound variable
5358 is a constructor argument. Here is an example we saw earlier:
5360 f :: T a -> a -> (a, Char)
5361 f (T1 w k) x = (w k x, w 'c' 'd')
5363 Here we do not need to give a type signature to <literal>w</literal>, because
5364 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5371 <sect3 id="implicit-quant">
5372 <title>Implicit quantification</title>
5375 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5376 user-written types, if and only if there is no explicit <literal>forall</literal>,
5377 GHC finds all the type variables mentioned in the type that are not already
5378 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5382 f :: forall a. a -> a
5389 h :: forall b. a -> b -> b
5395 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5398 f :: (a -> a) -> Int
5400 f :: forall a. (a -> a) -> Int
5402 f :: (forall a. a -> a) -> Int
5405 g :: (Ord a => a -> a) -> Int
5406 -- MEANS the illegal type
5407 g :: forall a. (Ord a => a -> a) -> Int
5409 g :: (forall a. Ord a => a -> a) -> Int
5411 The latter produces an illegal type, which you might think is silly,
5412 but at least the rule is simple. If you want the latter type, you
5413 can write your for-alls explicitly. Indeed, doing so is strongly advised
5420 <sect2 id="impredicative-polymorphism">
5421 <title>Impredicative polymorphism
5423 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5424 enabled with <option>-XImpredicativeTypes</option>.
5426 that you can call a polymorphic function at a polymorphic type, and
5427 parameterise data structures over polymorphic types. For example:
5429 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5430 f (Just g) = Just (g [3], g "hello")
5433 Notice here that the <literal>Maybe</literal> type is parameterised by the
5434 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5437 <para>The technical details of this extension are described in the paper
5438 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5439 type inference for higher-rank types and impredicativity</ulink>,
5440 which appeared at ICFP 2006.
5444 <sect2 id="scoped-type-variables">
5445 <title>Lexically scoped type variables
5449 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5450 which some type signatures are simply impossible to write. For example:
5452 f :: forall a. [a] -> [a]
5458 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5459 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5460 The type variables bound by a <literal>forall</literal> scope over
5461 the entire definition of the accompanying value declaration.
5462 In this example, the type variable <literal>a</literal> scopes over the whole
5463 definition of <literal>f</literal>, including over
5464 the type signature for <varname>ys</varname>.
5465 In Haskell 98 it is not possible to declare
5466 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5467 it becomes possible to do so.
5469 <para>Lexically-scoped type variables are enabled by
5470 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5472 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5473 variables work, compared to earlier releases. Read this section
5477 <title>Overview</title>
5479 <para>The design follows the following principles
5481 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5482 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5483 design.)</para></listitem>
5484 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5485 type variables. This means that every programmer-written type signature
5486 (including one that contains free scoped type variables) denotes a
5487 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5488 checker, and no inference is involved.</para></listitem>
5489 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5490 changing the program.</para></listitem>
5494 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5496 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5497 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5498 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5499 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5503 In Haskell, a programmer-written type signature is implicitly quantified over
5504 its free type variables (<ulink
5505 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5507 of the Haskell Report).
5508 Lexically scoped type variables affect this implicit quantification rules
5509 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5510 quantified. For example, if type variable <literal>a</literal> is in scope,
5513 (e :: a -> a) means (e :: a -> a)
5514 (e :: b -> b) means (e :: forall b. b->b)
5515 (e :: a -> b) means (e :: forall b. a->b)
5523 <sect3 id="decl-type-sigs">
5524 <title>Declaration type signatures</title>
5525 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5526 quantification (using <literal>forall</literal>) brings into scope the
5527 explicitly-quantified
5528 type variables, in the definition of the named function. For example:
5530 f :: forall a. [a] -> [a]
5531 f (x:xs) = xs ++ [ x :: a ]
5533 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5534 the definition of "<literal>f</literal>".
5536 <para>This only happens if:
5538 <listitem><para> The quantification in <literal>f</literal>'s type
5539 signature is explicit. For example:
5542 g (x:xs) = xs ++ [ x :: a ]
5544 This program will be rejected, because "<literal>a</literal>" does not scope
5545 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5546 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5547 quantification rules.
5549 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5550 not a pattern binding.
5553 f1 :: forall a. [a] -> [a]
5554 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5556 f2 :: forall a. [a] -> [a]
5557 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5559 f3 :: forall a. [a] -> [a]
5560 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5562 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5563 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5564 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5565 the type signature brings <literal>a</literal> into scope.
5571 <sect3 id="exp-type-sigs">
5572 <title>Expression type signatures</title>
5574 <para>An expression type signature that has <emphasis>explicit</emphasis>
5575 quantification (using <literal>forall</literal>) brings into scope the
5576 explicitly-quantified
5577 type variables, in the annotated expression. For example:
5579 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5581 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5582 type variable <literal>s</literal> into scope, in the annotated expression
5583 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5588 <sect3 id="pattern-type-sigs">
5589 <title>Pattern type signatures</title>
5591 A type signature may occur in any pattern; this is a <emphasis>pattern type
5592 signature</emphasis>.
5595 -- f and g assume that 'a' is already in scope
5596 f = \(x::Int, y::a) -> x
5598 h ((x,y) :: (Int,Bool)) = (y,x)
5600 In the case where all the type variables in the pattern type signature are
5601 already in scope (i.e. bound by the enclosing context), matters are simple: the
5602 signature simply constrains the type of the pattern in the obvious way.
5605 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5606 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5607 that are already in scope. For example:
5609 f :: forall a. [a] -> (Int, [a])
5612 (ys::[a], n) = (reverse xs, length xs) -- OK
5613 zs::[a] = xs ++ ys -- OK
5615 Just (v::b) = ... -- Not OK; b is not in scope
5617 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5618 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5622 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5623 type signature may mention a type variable that is not in scope; in this case,
5624 <emphasis>the signature brings that type variable into scope</emphasis>.
5625 This is particularly important for existential data constructors. For example:
5627 data T = forall a. MkT [a]
5630 k (MkT [t::a]) = MkT t3
5634 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5635 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5636 because it is bound by the pattern match. GHC's rule is that in this situation
5637 (and only then), a pattern type signature can mention a type variable that is
5638 not already in scope; the effect is to bring it into scope, standing for the
5639 existentially-bound type variable.
5642 When a pattern type signature binds a type variable in this way, GHC insists that the
5643 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5644 This means that any user-written type signature always stands for a completely known type.
5647 If all this seems a little odd, we think so too. But we must have
5648 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5649 could not name existentially-bound type variables in subsequent type signatures.
5652 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5653 signature is allowed to mention a lexical variable that is not already in
5655 For example, both <literal>f</literal> and <literal>g</literal> would be
5656 illegal if <literal>a</literal> was not already in scope.
5662 <!-- ==================== Commented out part about result type signatures
5664 <sect3 id="result-type-sigs">
5665 <title>Result type signatures</title>
5668 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5671 {- f assumes that 'a' is already in scope -}
5672 f x y :: [a] = [x,y,x]
5674 g = \ x :: [Int] -> [3,4]
5676 h :: forall a. [a] -> a
5680 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5681 the result of the function. Similarly, the body of the lambda in the RHS of
5682 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5683 alternative in <literal>h</literal> is <literal>a</literal>.
5685 <para> A result type signature never brings new type variables into scope.</para>
5687 There are a couple of syntactic wrinkles. First, notice that all three
5688 examples would parse quite differently with parentheses:
5690 {- f assumes that 'a' is already in scope -}
5691 f x (y :: [a]) = [x,y,x]
5693 g = \ (x :: [Int]) -> [3,4]
5695 h :: forall a. [a] -> a
5699 Now the signature is on the <emphasis>pattern</emphasis>; and
5700 <literal>h</literal> would certainly be ill-typed (since the pattern
5701 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5703 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5704 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5705 token or a parenthesised type of some sort). To see why,
5706 consider how one would parse this:
5715 <sect3 id="cls-inst-scoped-tyvars">
5716 <title>Class and instance declarations</title>
5719 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5720 scope over the methods defined in the <literal>where</literal> part. For example:
5738 <sect2 id="typing-binds">
5739 <title>Generalised typing of mutually recursive bindings</title>
5742 The Haskell Report specifies that a group of bindings (at top level, or in a
5743 <literal>let</literal> or <literal>where</literal>) should be sorted into
5744 strongly-connected components, and then type-checked in dependency order
5745 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5746 Report, Section 4.5.1</ulink>).
5747 As each group is type-checked, any binders of the group that
5749 an explicit type signature are put in the type environment with the specified
5751 and all others are monomorphic until the group is generalised
5752 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5755 <para>Following a suggestion of Mark Jones, in his paper
5756 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5758 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5760 <emphasis>the dependency analysis ignores references to variables that have an explicit
5761 type signature</emphasis>.
5762 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5763 typecheck. For example, consider:
5765 f :: Eq a => a -> Bool
5766 f x = (x == x) || g True || g "Yes"
5768 g y = (y <= y) || f True
5770 This is rejected by Haskell 98, but under Jones's scheme the definition for
5771 <literal>g</literal> is typechecked first, separately from that for
5772 <literal>f</literal>,
5773 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5774 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5775 type is generalised, to get
5777 g :: Ord a => a -> Bool
5779 Now, the definition for <literal>f</literal> is typechecked, with this type for
5780 <literal>g</literal> in the type environment.
5784 The same refined dependency analysis also allows the type signatures of
5785 mutually-recursive functions to have different contexts, something that is illegal in
5786 Haskell 98 (Section 4.5.2, last sentence). With
5787 <option>-XRelaxedPolyRec</option>
5788 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5789 type signatures; in practice this means that only variables bound by the same
5790 pattern binding must have the same context. For example, this is fine:
5792 f :: Eq a => a -> Bool
5793 f x = (x == x) || g True
5795 g :: Ord a => a -> Bool
5796 g y = (y <= y) || f True
5802 <!-- ==================== End of type system extensions ================= -->
5804 <!-- ====================== TEMPLATE HASKELL ======================= -->
5806 <sect1 id="template-haskell">
5807 <title>Template Haskell</title>
5809 <para>Template Haskell allows you to do compile-time meta-programming in
5812 the main technical innovations is discussed in "<ulink
5813 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5814 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5817 There is a Wiki page about
5818 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5819 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5823 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5824 Haskell library reference material</ulink>
5825 (look for module <literal>Language.Haskell.TH</literal>).
5826 Many changes to the original design are described in
5827 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5828 Notes on Template Haskell version 2</ulink>.
5829 Not all of these changes are in GHC, however.
5832 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5833 as a worked example to help get you started.
5837 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5838 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5843 <title>Syntax</title>
5845 <para> Template Haskell has the following new syntactic
5846 constructions. You need to use the flag
5847 <option>-XTemplateHaskell</option>
5848 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5849 </indexterm>to switch these syntactic extensions on
5850 (<option>-XTemplateHaskell</option> is no longer implied by
5851 <option>-fglasgow-exts</option>).</para>
5855 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5856 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5857 There must be no space between the "$" and the identifier or parenthesis. This use
5858 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5859 of "." as an infix operator. If you want the infix operator, put spaces around it.
5861 <para> A splice can occur in place of
5863 <listitem><para> an expression; the spliced expression must
5864 have type <literal>Q Exp</literal></para></listitem>
5865 <listitem><para> an type; the spliced expression must
5866 have type <literal>Q Typ</literal></para></listitem>
5867 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5870 Inside a splice you can can only call functions defined in imported modules,
5871 not functions defined elsewhere in the same module.</listitem>
5875 A expression quotation is written in Oxford brackets, thus:
5877 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5878 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5879 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5880 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5881 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5882 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5883 </itemizedlist></para></listitem>
5886 A quasi-quotation can appear in either a pattern context or an
5887 expression context and is also written in Oxford brackets:
5889 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5890 where the "..." is an arbitrary string; a full description of the
5891 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5892 </itemizedlist></para></listitem>
5895 A name can be quoted with either one or two prefix single quotes:
5897 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5898 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5899 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5901 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5902 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5905 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5906 may also be given as an argument to the <literal>reify</literal> function.
5912 (Compared to the original paper, there are many differences of detail.
5913 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5914 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5915 Pattern splices and quotations are not implemented.)
5919 <sect2> <title> Using Template Haskell </title>
5923 The data types and monadic constructor functions for Template Haskell are in the library
5924 <literal>Language.Haskell.THSyntax</literal>.
5928 You can only run a function at compile time if it is imported from another module. That is,
5929 you can't define a function in a module, and call it from within a splice in the same module.
5930 (It would make sense to do so, but it's hard to implement.)
5934 You can only run a function at compile time if it is imported
5935 from another module <emphasis>that is not part of a mutually-recursive group of modules
5936 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5937 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5938 splice is to be run.</para>
5940 For example, when compiling module A,
5941 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5942 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5946 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5949 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5950 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5951 compiles and runs a program, and then looks at the result. So it's important that
5952 the program it compiles produces results whose representations are identical to
5953 those of the compiler itself.
5957 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5958 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5963 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5964 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5965 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5972 -- Import our template "pr"
5973 import Printf ( pr )
5975 -- The splice operator $ takes the Haskell source code
5976 -- generated at compile time by "pr" and splices it into
5977 -- the argument of "putStrLn".
5978 main = putStrLn ( $(pr "Hello") )
5984 -- Skeletal printf from the paper.
5985 -- It needs to be in a separate module to the one where
5986 -- you intend to use it.
5988 -- Import some Template Haskell syntax
5989 import Language.Haskell.TH
5991 -- Describe a format string
5992 data Format = D | S | L String
5994 -- Parse a format string. This is left largely to you
5995 -- as we are here interested in building our first ever
5996 -- Template Haskell program and not in building printf.
5997 parse :: String -> [Format]
6000 -- Generate Haskell source code from a parsed representation
6001 -- of the format string. This code will be spliced into
6002 -- the module which calls "pr", at compile time.
6003 gen :: [Format] -> Q Exp
6004 gen [D] = [| \n -> show n |]
6005 gen [S] = [| \s -> s |]
6006 gen [L s] = stringE s
6008 -- Here we generate the Haskell code for the splice
6009 -- from an input format string.
6010 pr :: String -> Q Exp
6011 pr s = gen (parse s)
6014 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6017 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6020 <para>Run "main.exe" and here is your output:</para>
6030 <title>Using Template Haskell with Profiling</title>
6031 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6033 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6034 interpreter to run the splice expressions. The bytecode interpreter
6035 runs the compiled expression on top of the same runtime on which GHC
6036 itself is running; this means that the compiled code referred to by
6037 the interpreted expression must be compatible with this runtime, and
6038 in particular this means that object code that is compiled for
6039 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6040 expression, because profiled object code is only compatible with the
6041 profiling version of the runtime.</para>
6043 <para>This causes difficulties if you have a multi-module program
6044 containing Template Haskell code and you need to compile it for
6045 profiling, because GHC cannot load the profiled object code and use it
6046 when executing the splices. Fortunately GHC provides a workaround.
6047 The basic idea is to compile the program twice:</para>
6051 <para>Compile the program or library first the normal way, without
6052 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6055 <para>Then compile it again with <option>-prof</option>, and
6056 additionally use <option>-osuf
6057 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6058 to name the object files differently (you can choose any suffix
6059 that isn't the normal object suffix here). GHC will automatically
6060 load the object files built in the first step when executing splice
6061 expressions. If you omit the <option>-osuf</option> flag when
6062 building with <option>-prof</option> and Template Haskell is used,
6063 GHC will emit an error message. </para>
6068 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6069 <para>Quasi-quotation allows patterns and expressions to be written using
6070 programmer-defined concrete syntax; the motivation behind the extension and
6071 several examples are documented in
6072 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6073 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6074 2007). The example below shows how to write a quasiquoter for a simple
6075 expression language.</para>
6078 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6079 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6080 functions for quoting expressions and patterns, respectively. The first argument
6081 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6082 context of the quasi-quotation statement determines which of the two parsers is
6083 called: if the quasi-quotation occurs in an expression context, the expression
6084 parser is called, and if it occurs in a pattern context, the pattern parser is
6088 Note that in the example we make use of an antiquoted
6089 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6090 (this syntax for anti-quotation was defined by the parser's
6091 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6092 integer value argument of the constructor <literal>IntExpr</literal> when
6093 pattern matching. Please see the referenced paper for further details regarding
6094 anti-quotation as well as the description of a technique that uses SYB to
6095 leverage a single parser of type <literal>String -> a</literal> to generate both
6096 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6097 pattern parser that returns a value of type <literal>Q Pat</literal>.
6100 <para>In general, a quasi-quote has the form
6101 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6102 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6103 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6104 can be arbitrary, and may contain newlines.
6107 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6108 the example, <literal>expr</literal> cannot be defined
6109 in <literal>Main.hs</literal> where it is used, but must be imported.
6120 main = do { print $ eval [$expr|1 + 2|]
6122 { [$expr|'int:n|] -> print n
6131 import qualified Language.Haskell.TH as TH
6132 import Language.Haskell.TH.Quote
6134 data Expr = IntExpr Integer
6135 | AntiIntExpr String
6136 | BinopExpr BinOp Expr Expr
6138 deriving(Show, Typeable, Data)
6144 deriving(Show, Typeable, Data)
6146 eval :: Expr -> Integer
6147 eval (IntExpr n) = n
6148 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6155 expr = QuasiQuoter parseExprExp parseExprPat
6157 -- Parse an Expr, returning its representation as
6158 -- either a Q Exp or a Q Pat. See the referenced paper
6159 -- for how to use SYB to do this by writing a single
6160 -- parser of type String -> Expr instead of two
6161 -- separate parsers.
6163 parseExprExp :: String -> Q Exp
6166 parseExprPat :: String -> Q Pat
6170 <para>Now run the compiler:
6173 $ ghc --make -XQuasiQuotes Main.hs -o main
6176 <para>Run "main" and here is your output:</para>
6188 <!-- ===================== Arrow notation =================== -->
6190 <sect1 id="arrow-notation">
6191 <title>Arrow notation
6194 <para>Arrows are a generalization of monads introduced by John Hughes.
6195 For more details, see
6200 “Generalising Monads to Arrows”,
6201 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6202 pp67–111, May 2000.
6203 The paper that introduced arrows: a friendly introduction, motivated with
6204 programming examples.
6210 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6211 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6212 Introduced the notation described here.
6218 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6219 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6226 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6227 John Hughes, in <citetitle>5th International Summer School on
6228 Advanced Functional Programming</citetitle>,
6229 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6231 This paper includes another introduction to the notation,
6232 with practical examples.
6238 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6239 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6240 A terse enumeration of the formal rules used
6241 (extracted from comments in the source code).
6247 The arrows web page at
6248 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6253 With the <option>-XArrows</option> flag, GHC supports the arrow
6254 notation described in the second of these papers,
6255 translating it using combinators from the
6256 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6258 What follows is a brief introduction to the notation;
6259 it won't make much sense unless you've read Hughes's paper.
6262 <para>The extension adds a new kind of expression for defining arrows:
6264 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6265 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6267 where <literal>proc</literal> is a new keyword.
6268 The variables of the pattern are bound in the body of the
6269 <literal>proc</literal>-expression,
6270 which is a new sort of thing called a <firstterm>command</firstterm>.
6271 The syntax of commands is as follows:
6273 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6274 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6275 | <replaceable>cmd</replaceable><superscript>0</superscript>
6277 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6278 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6279 infix operators as for expressions, and
6281 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6282 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6283 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6284 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6285 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6286 | <replaceable>fcmd</replaceable>
6288 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6289 | ( <replaceable>cmd</replaceable> )
6290 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6292 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6293 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6294 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6295 | <replaceable>cmd</replaceable>
6297 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6298 except that the bodies are commands instead of expressions.
6302 Commands produce values, but (like monadic computations)
6303 may yield more than one value,
6304 or none, and may do other things as well.
6305 For the most part, familiarity with monadic notation is a good guide to
6307 However the values of expressions, even monadic ones,
6308 are determined by the values of the variables they contain;
6309 this is not necessarily the case for commands.
6313 A simple example of the new notation is the expression
6315 proc x -> f -< x+1
6317 We call this a <firstterm>procedure</firstterm> or
6318 <firstterm>arrow abstraction</firstterm>.
6319 As with a lambda expression, the variable <literal>x</literal>
6320 is a new variable bound within the <literal>proc</literal>-expression.
6321 It refers to the input to the arrow.
6322 In the above example, <literal>-<</literal> is not an identifier but an
6323 new reserved symbol used for building commands from an expression of arrow
6324 type and an expression to be fed as input to that arrow.
6325 (The weird look will make more sense later.)
6326 It may be read as analogue of application for arrows.
6327 The above example is equivalent to the Haskell expression
6329 arr (\ x -> x+1) >>> f
6331 That would make no sense if the expression to the left of
6332 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6333 More generally, the expression to the left of <literal>-<</literal>
6334 may not involve any <firstterm>local variable</firstterm>,
6335 i.e. a variable bound in the current arrow abstraction.
6336 For such a situation there is a variant <literal>-<<</literal>, as in
6338 proc x -> f x -<< x+1
6340 which is equivalent to
6342 arr (\ x -> (f x, x+1)) >>> app
6344 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6346 Such an arrow is equivalent to a monad, so if you're using this form
6347 you may find a monadic formulation more convenient.
6351 <title>do-notation for commands</title>
6354 Another form of command is a form of <literal>do</literal>-notation.
6355 For example, you can write
6364 You can read this much like ordinary <literal>do</literal>-notation,
6365 but with commands in place of monadic expressions.
6366 The first line sends the value of <literal>x+1</literal> as an input to
6367 the arrow <literal>f</literal>, and matches its output against
6368 <literal>y</literal>.
6369 In the next line, the output is discarded.
6370 The arrow <function>returnA</function> is defined in the
6371 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6372 module as <literal>arr id</literal>.
6373 The above example is treated as an abbreviation for
6375 arr (\ x -> (x, x)) >>>
6376 first (arr (\ x -> x+1) >>> f) >>>
6377 arr (\ (y, x) -> (y, (x, y))) >>>
6378 first (arr (\ y -> 2*y) >>> g) >>>
6380 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6381 first (arr (\ (x, z) -> x*z) >>> h) >>>
6382 arr (\ (t, z) -> t+z) >>>
6385 Note that variables not used later in the composition are projected out.
6386 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6388 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6389 module, this reduces to
6391 arr (\ x -> (x+1, x)) >>>
6393 arr (\ (y, x) -> (2*y, (x, y))) >>>
6395 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6397 arr (\ (t, z) -> t+z)
6399 which is what you might have written by hand.
6400 With arrow notation, GHC keeps track of all those tuples of variables for you.
6404 Note that although the above translation suggests that
6405 <literal>let</literal>-bound variables like <literal>z</literal> must be
6406 monomorphic, the actual translation produces Core,
6407 so polymorphic variables are allowed.
6411 It's also possible to have mutually recursive bindings,
6412 using the new <literal>rec</literal> keyword, as in the following example:
6414 counter :: ArrowCircuit a => a Bool Int
6415 counter = proc reset -> do
6416 rec output <- returnA -< if reset then 0 else next
6417 next <- delay 0 -< output+1
6418 returnA -< output
6420 The translation of such forms uses the <function>loop</function> combinator,
6421 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6427 <title>Conditional commands</title>
6430 In the previous example, we used a conditional expression to construct the
6432 Sometimes we want to conditionally execute different commands, as in
6439 which is translated to
6441 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6442 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6444 Since the translation uses <function>|||</function>,
6445 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6449 There are also <literal>case</literal> commands, like
6455 y <- h -< (x1, x2)
6459 The syntax is the same as for <literal>case</literal> expressions,
6460 except that the bodies of the alternatives are commands rather than expressions.
6461 The translation is similar to that of <literal>if</literal> commands.
6467 <title>Defining your own control structures</title>
6470 As we're seen, arrow notation provides constructs,
6471 modelled on those for expressions,
6472 for sequencing, value recursion and conditionals.
6473 But suitable combinators,
6474 which you can define in ordinary Haskell,
6475 may also be used to build new commands out of existing ones.
6476 The basic idea is that a command defines an arrow from environments to values.
6477 These environments assign values to the free local variables of the command.
6478 Thus combinators that produce arrows from arrows
6479 may also be used to build commands from commands.
6480 For example, the <literal>ArrowChoice</literal> class includes a combinator
6482 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6484 so we can use it to build commands:
6486 expr' = proc x -> do
6489 symbol Plus -< ()
6490 y <- term -< ()
6493 symbol Minus -< ()
6494 y <- term -< ()
6497 (The <literal>do</literal> on the first line is needed to prevent the first
6498 <literal><+> ...</literal> from being interpreted as part of the
6499 expression on the previous line.)
6500 This is equivalent to
6502 expr' = (proc x -> returnA -< x)
6503 <+> (proc x -> do
6504 symbol Plus -< ()
6505 y <- term -< ()
6507 <+> (proc x -> do
6508 symbol Minus -< ()
6509 y <- term -< ()
6512 It is essential that this operator be polymorphic in <literal>e</literal>
6513 (representing the environment input to the command
6514 and thence to its subcommands)
6515 and satisfy the corresponding naturality property
6517 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6519 at least for strict <literal>k</literal>.
6520 (This should be automatic if you're not using <function>seq</function>.)
6521 This ensures that environments seen by the subcommands are environments
6522 of the whole command,
6523 and also allows the translation to safely trim these environments.
6524 The operator must also not use any variable defined within the current
6529 We could define our own operator
6531 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6532 untilA body cond = proc x ->
6533 b <- cond -< x
6534 if b then returnA -< ()
6537 untilA body cond -< x
6539 and use it in the same way.
6540 Of course this infix syntax only makes sense for binary operators;
6541 there is also a more general syntax involving special brackets:
6545 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6552 <title>Primitive constructs</title>
6555 Some operators will need to pass additional inputs to their subcommands.
6556 For example, in an arrow type supporting exceptions,
6557 the operator that attaches an exception handler will wish to pass the
6558 exception that occurred to the handler.
6559 Such an operator might have a type
6561 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6563 where <literal>Ex</literal> is the type of exceptions handled.
6564 You could then use this with arrow notation by writing a command
6566 body `handleA` \ ex -> handler
6568 so that if an exception is raised in the command <literal>body</literal>,
6569 the variable <literal>ex</literal> is bound to the value of the exception
6570 and the command <literal>handler</literal>,
6571 which typically refers to <literal>ex</literal>, is entered.
6572 Though the syntax here looks like a functional lambda,
6573 we are talking about commands, and something different is going on.
6574 The input to the arrow represented by a command consists of values for
6575 the free local variables in the command, plus a stack of anonymous values.
6576 In all the prior examples, this stack was empty.
6577 In the second argument to <function>handleA</function>,
6578 this stack consists of one value, the value of the exception.
6579 The command form of lambda merely gives this value a name.
6584 the values on the stack are paired to the right of the environment.
6585 So operators like <function>handleA</function> that pass
6586 extra inputs to their subcommands can be designed for use with the notation
6587 by pairing the values with the environment in this way.
6588 More precisely, the type of each argument of the operator (and its result)
6589 should have the form
6591 a (...(e,t1), ... tn) t
6593 where <replaceable>e</replaceable> is a polymorphic variable
6594 (representing the environment)
6595 and <replaceable>ti</replaceable> are the types of the values on the stack,
6596 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6597 The polymorphic variable <replaceable>e</replaceable> must not occur in
6598 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6599 <replaceable>t</replaceable>.
6600 However the arrows involved need not be the same.
6601 Here are some more examples of suitable operators:
6603 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6604 runReader :: ... => a e c -> a' (e,State) c
6605 runState :: ... => a e c -> a' (e,State) (c,State)
6607 We can supply the extra input required by commands built with the last two
6608 by applying them to ordinary expressions, as in
6612 (|runReader (do { ... })|) s
6614 which adds <literal>s</literal> to the stack of inputs to the command
6615 built using <function>runReader</function>.
6619 The command versions of lambda abstraction and application are analogous to
6620 the expression versions.
6621 In particular, the beta and eta rules describe equivalences of commands.
6622 These three features (operators, lambda abstraction and application)
6623 are the core of the notation; everything else can be built using them,
6624 though the results would be somewhat clumsy.
6625 For example, we could simulate <literal>do</literal>-notation by defining
6627 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6628 u `bind` f = returnA &&& u >>> f
6630 bind_ :: Arrow a => a e b -> a e c -> a e c
6631 u `bind_` f = u `bind` (arr fst >>> f)
6633 We could simulate <literal>if</literal> by defining
6635 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6636 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6643 <title>Differences with the paper</title>
6648 <para>Instead of a single form of arrow application (arrow tail) with two
6649 translations, the implementation provides two forms
6650 <quote><literal>-<</literal></quote> (first-order)
6651 and <quote><literal>-<<</literal></quote> (higher-order).
6656 <para>User-defined operators are flagged with banana brackets instead of
6657 a new <literal>form</literal> keyword.
6666 <title>Portability</title>
6669 Although only GHC implements arrow notation directly,
6670 there is also a preprocessor
6672 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6673 that translates arrow notation into Haskell 98
6674 for use with other Haskell systems.
6675 You would still want to check arrow programs with GHC;
6676 tracing type errors in the preprocessor output is not easy.
6677 Modules intended for both GHC and the preprocessor must observe some
6678 additional restrictions:
6683 The module must import
6684 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6690 The preprocessor cannot cope with other Haskell extensions.
6691 These would have to go in separate modules.
6697 Because the preprocessor targets Haskell (rather than Core),
6698 <literal>let</literal>-bound variables are monomorphic.
6709 <!-- ==================== BANG PATTERNS ================= -->
6711 <sect1 id="bang-patterns">
6712 <title>Bang patterns
6713 <indexterm><primary>Bang patterns</primary></indexterm>
6715 <para>GHC supports an extension of pattern matching called <emphasis>bang
6716 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6717 Bang patterns are under consideration for Haskell Prime.
6719 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6720 prime feature description</ulink> contains more discussion and examples
6721 than the material below.
6724 The key change is the addition of a new rule to the
6725 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6726 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6727 against a value <replaceable>v</replaceable> behaves as follows:
6729 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6730 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6734 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6737 <sect2 id="bang-patterns-informal">
6738 <title>Informal description of bang patterns
6741 The main idea is to add a single new production to the syntax of patterns:
6745 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6746 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6751 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6752 whereas without the bang it would be lazy.
6753 Bang patterns can be nested of course:
6757 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6758 <literal>y</literal>.
6759 A bang only really has an effect if it precedes a variable or wild-card pattern:
6764 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6765 putting a bang before a pattern that
6766 forces evaluation anyway does nothing.
6769 There is one (apparent) exception to this general rule that a bang only
6770 makes a difference when it precedes a variable or wild-card: a bang at the
6771 top level of a <literal>let</literal> or <literal>where</literal>
6772 binding makes the binding strict, regardless of the pattern. For example:
6776 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6777 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6778 (We say "apparent" exception because the Right Way to think of it is that the bang
6779 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6780 is part of the syntax of the <emphasis>binding</emphasis>.)
6781 Nested bangs in a pattern binding behave uniformly with all other forms of
6782 pattern matching. For example
6784 let (!x,[y]) = e in b
6786 is equivalent to this:
6788 let { t = case e of (x,[y]) -> x `seq` (x,y)
6793 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6794 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6795 evaluation of <literal>x</literal>.
6798 Bang patterns work in <literal>case</literal> expressions too, of course:
6800 g5 x = let y = f x in body
6801 g6 x = case f x of { y -> body }
6802 g7 x = case f x of { !y -> body }
6804 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6805 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6806 result, and then evaluates <literal>body</literal>.
6811 <sect2 id="bang-patterns-sem">
6812 <title>Syntax and semantics
6816 We add a single new production to the syntax of patterns:
6820 There is one problem with syntactic ambiguity. Consider:
6824 Is this a definition of the infix function "<literal>(!)</literal>",
6825 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6826 ambiguity in favour of the latter. If you want to define
6827 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6832 The semantics of Haskell pattern matching is described in <ulink
6833 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6834 Section 3.17.2</ulink> of the Haskell Report. To this description add
6835 one extra item 10, saying:
6836 <itemizedlist><listitem><para>Matching
6837 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6838 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6839 <listitem><para>otherwise, <literal>pat</literal> is matched against
6840 <literal>v</literal></para></listitem>
6842 </para></listitem></itemizedlist>
6843 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6844 Section 3.17.3</ulink>, add a new case (t):
6846 case v of { !pat -> e; _ -> e' }
6847 = v `seq` case v of { pat -> e; _ -> e' }
6850 That leaves let expressions, whose translation is given in
6851 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6853 of the Haskell Report.
6854 In the translation box, first apply
6855 the following transformation: for each pattern <literal>pi</literal> that is of
6856 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6857 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6858 have a bang at the top, apply the rules in the existing box.
6860 <para>The effect of the let rule is to force complete matching of the pattern
6861 <literal>qi</literal> before evaluation of the body is begun. The bang is
6862 retained in the translated form in case <literal>qi</literal> is a variable,
6870 The let-binding can be recursive. However, it is much more common for
6871 the let-binding to be non-recursive, in which case the following law holds:
6872 <literal>(let !p = rhs in body)</literal>
6874 <literal>(case rhs of !p -> body)</literal>
6877 A pattern with a bang at the outermost level is not allowed at the top level of
6883 <!-- ==================== ASSERTIONS ================= -->
6885 <sect1 id="assertions">
6887 <indexterm><primary>Assertions</primary></indexterm>
6891 If you want to make use of assertions in your standard Haskell code, you
6892 could define a function like the following:
6898 assert :: Bool -> a -> a
6899 assert False x = error "assertion failed!"
6906 which works, but gives you back a less than useful error message --
6907 an assertion failed, but which and where?
6911 One way out is to define an extended <function>assert</function> function which also
6912 takes a descriptive string to include in the error message and
6913 perhaps combine this with the use of a pre-processor which inserts
6914 the source location where <function>assert</function> was used.
6918 Ghc offers a helping hand here, doing all of this for you. For every
6919 use of <function>assert</function> in the user's source:
6925 kelvinToC :: Double -> Double
6926 kelvinToC k = assert (k >= 0.0) (k+273.15)
6932 Ghc will rewrite this to also include the source location where the
6939 assert pred val ==> assertError "Main.hs|15" pred val
6945 The rewrite is only performed by the compiler when it spots
6946 applications of <function>Control.Exception.assert</function>, so you
6947 can still define and use your own versions of
6948 <function>assert</function>, should you so wish. If not, import
6949 <literal>Control.Exception</literal> to make use
6950 <function>assert</function> in your code.
6954 GHC ignores assertions when optimisation is turned on with the
6955 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6956 <literal>assert pred e</literal> will be rewritten to
6957 <literal>e</literal>. You can also disable assertions using the
6958 <option>-fignore-asserts</option>
6959 option<indexterm><primary><option>-fignore-asserts</option></primary>
6960 </indexterm>.</para>
6963 Assertion failures can be caught, see the documentation for the
6964 <literal>Control.Exception</literal> library for the details.
6970 <!-- =============================== PRAGMAS =========================== -->
6972 <sect1 id="pragmas">
6973 <title>Pragmas</title>
6975 <indexterm><primary>pragma</primary></indexterm>
6977 <para>GHC supports several pragmas, or instructions to the
6978 compiler placed in the source code. Pragmas don't normally affect
6979 the meaning of the program, but they might affect the efficiency
6980 of the generated code.</para>
6982 <para>Pragmas all take the form
6984 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6986 where <replaceable>word</replaceable> indicates the type of
6987 pragma, and is followed optionally by information specific to that
6988 type of pragma. Case is ignored in
6989 <replaceable>word</replaceable>. The various values for
6990 <replaceable>word</replaceable> that GHC understands are described
6991 in the following sections; any pragma encountered with an
6992 unrecognised <replaceable>word</replaceable> is
6993 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6994 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6996 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7000 pragma must precede the <literal>module</literal> keyword in the file.
7003 There can be as many file-header pragmas as you please, and they can be
7004 preceded or followed by comments.
7007 File-header pragmas are read once only, before
7008 pre-processing the file (e.g. with cpp).
7011 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7012 <literal>{-# OPTIONS_GHC #-}</literal>, and
7013 <literal>{-# INCLUDE #-}</literal>.
7018 <sect2 id="language-pragma">
7019 <title>LANGUAGE pragma</title>
7021 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7022 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7024 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7026 It is the intention that all Haskell compilers support the
7027 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7028 all extensions are supported by all compilers, of
7029 course. The <literal>LANGUAGE</literal> pragma should be used instead
7030 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7032 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7034 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7036 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7038 <para>Every language extension can also be turned into a command-line flag
7039 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7040 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7043 <para>A list of all supported language extensions can be obtained by invoking
7044 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7046 <para>Any extension from the <literal>Extension</literal> type defined in
7048 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7049 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7053 <sect2 id="options-pragma">
7054 <title>OPTIONS_GHC pragma</title>
7055 <indexterm><primary>OPTIONS_GHC</primary>
7057 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7060 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7061 additional options that are given to the compiler when compiling
7062 this source file. See <xref linkend="source-file-options"/> for
7065 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7066 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7069 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7071 <sect2 id="include-pragma">
7072 <title>INCLUDE pragma</title>
7074 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
7075 of C header files that should be <literal>#include</literal>'d into
7076 the C source code generated by the compiler for the current module (if
7077 compiling via C). For example:</para>
7080 {-# INCLUDE "foo.h" #-}
7081 {-# INCLUDE <stdio.h> #-}</programlisting>
7083 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7085 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
7086 to the <option>-#include</option> option (<xref
7087 linkend="options-C-compiler" />), because the
7088 <literal>INCLUDE</literal> pragma is understood by other
7089 compilers. Yet another alternative is to add the include file to each
7090 <literal>foreign import</literal> declaration in your code, but we
7091 don't recommend using this approach with GHC.</para>
7094 <sect2 id="warning-deprecated-pragma">
7095 <title>WARNING and DEPRECATED pragmas</title>
7096 <indexterm><primary>WARNING</primary></indexterm>
7097 <indexterm><primary>DEPRECATED</primary></indexterm>
7099 <para>The WARNING pragma allows you to attach an arbitrary warning
7100 to a particular function, class, or type.
7101 A DEPRECATED pragma lets you specify that
7102 a particular function, class, or type is deprecated.
7103 There are two ways of using these pragmas.
7107 <para>You can work on an entire module thus:</para>
7109 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7114 module Wibble {-# WARNING "This is an unstable interface." #-} where
7117 <para>When you compile any module that import
7118 <literal>Wibble</literal>, GHC will print the specified
7123 <para>You can attach a warning to a function, class, type, or data constructor, with the
7124 following top-level declarations:</para>
7126 {-# DEPRECATED f, C, T "Don't use these" #-}
7127 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7129 <para>When you compile any module that imports and uses any
7130 of the specified entities, GHC will print the specified
7132 <para> You can only attach to entities declared at top level in the module
7133 being compiled, and you can only use unqualified names in the list of
7134 entities. A capitalised name, such as <literal>T</literal>
7135 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7136 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7137 both are in scope. If both are in scope, there is currently no way to
7138 specify one without the other (c.f. fixities
7139 <xref linkend="infix-tycons"/>).</para>
7142 Warnings and deprecations are not reported for
7143 (a) uses within the defining module, and
7144 (b) uses in an export list.
7145 The latter reduces spurious complaints within a library
7146 in which one module gathers together and re-exports
7147 the exports of several others.
7149 <para>You can suppress the warnings with the flag
7150 <option>-fno-warn-warnings-deprecations</option>.</para>
7153 <sect2 id="inline-noinline-pragma">
7154 <title>INLINE and NOINLINE pragmas</title>
7156 <para>These pragmas control the inlining of function
7159 <sect3 id="inline-pragma">
7160 <title>INLINE pragma</title>
7161 <indexterm><primary>INLINE</primary></indexterm>
7163 <para>GHC (with <option>-O</option>, as always) tries to
7164 inline (or “unfold”) functions/values that are
7165 “small enough,” thus avoiding the call overhead
7166 and possibly exposing other more-wonderful optimisations.
7167 Normally, if GHC decides a function is “too
7168 expensive” to inline, it will not do so, nor will it
7169 export that unfolding for other modules to use.</para>
7171 <para>The sledgehammer you can bring to bear is the
7172 <literal>INLINE</literal><indexterm><primary>INLINE
7173 pragma</primary></indexterm> pragma, used thusly:</para>
7176 key_function :: Int -> String -> (Bool, Double)
7177 {-# INLINE key_function #-}
7180 <para>The major effect of an <literal>INLINE</literal> pragma
7181 is to declare a function's “cost” to be very low.
7182 The normal unfolding machinery will then be very keen to
7183 inline it. However, an <literal>INLINE</literal> pragma for a
7184 function "<literal>f</literal>" has a number of other effects:
7187 No functions are inlined into <literal>f</literal>. Otherwise
7188 GHC might inline a big function into <literal>f</literal>'s right hand side,
7189 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7192 The float-in, float-out, and common-sub-expression transformations are not
7193 applied to the body of <literal>f</literal>.
7196 An INLINE function is not worker/wrappered by strictness analysis.
7197 It's going to be inlined wholesale instead.
7200 All of these effects are aimed at ensuring that what gets inlined is
7201 exactly what you asked for, no more and no less.
7203 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7204 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7205 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7206 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7207 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7208 when there is no choice even an INLINE function can be selected, in which case
7209 the INLINE pragma is ignored.
7210 For example, for a self-recursive function, the loop breaker can only be the function
7211 itself, so an INLINE pragma is always ignored.</para>
7213 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7214 function can be put anywhere its type signature could be
7217 <para><literal>INLINE</literal> pragmas are a particularly
7219 <literal>then</literal>/<literal>return</literal> (or
7220 <literal>bind</literal>/<literal>unit</literal>) functions in
7221 a monad. For example, in GHC's own
7222 <literal>UniqueSupply</literal> monad code, we have:</para>
7225 {-# INLINE thenUs #-}
7226 {-# INLINE returnUs #-}
7229 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7230 linkend="noinline-pragma"/>).</para>
7232 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7233 so if you want your code to be HBC-compatible you'll have to surround
7234 the pragma with C pre-processor directives
7235 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7239 <sect3 id="noinline-pragma">
7240 <title>NOINLINE pragma</title>
7242 <indexterm><primary>NOINLINE</primary></indexterm>
7243 <indexterm><primary>NOTINLINE</primary></indexterm>
7245 <para>The <literal>NOINLINE</literal> pragma does exactly what
7246 you'd expect: it stops the named function from being inlined
7247 by the compiler. You shouldn't ever need to do this, unless
7248 you're very cautious about code size.</para>
7250 <para><literal>NOTINLINE</literal> is a synonym for
7251 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7252 specified by Haskell 98 as the standard way to disable
7253 inlining, so it should be used if you want your code to be
7257 <sect3 id="phase-control">
7258 <title>Phase control</title>
7260 <para> Sometimes you want to control exactly when in GHC's
7261 pipeline the INLINE pragma is switched on. Inlining happens
7262 only during runs of the <emphasis>simplifier</emphasis>. Each
7263 run of the simplifier has a different <emphasis>phase
7264 number</emphasis>; the phase number decreases towards zero.
7265 If you use <option>-dverbose-core2core</option> you'll see the
7266 sequence of phase numbers for successive runs of the
7267 simplifier. In an INLINE pragma you can optionally specify a
7271 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7272 <literal>f</literal>
7273 until phase <literal>k</literal>, but from phase
7274 <literal>k</literal> onwards be very keen to inline it.
7277 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7278 <literal>f</literal>
7279 until phase <literal>k</literal>, but from phase
7280 <literal>k</literal> onwards do not inline it.
7283 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7284 <literal>f</literal>
7285 until phase <literal>k</literal>, but from phase
7286 <literal>k</literal> onwards be willing to inline it (as if
7287 there was no pragma).
7290 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7291 <literal>f</literal>
7292 until phase <literal>k</literal>, but from phase
7293 <literal>k</literal> onwards do not inline it.
7296 The same information is summarised here:
7298 -- Before phase 2 Phase 2 and later
7299 {-# INLINE [2] f #-} -- No Yes
7300 {-# INLINE [~2] f #-} -- Yes No
7301 {-# NOINLINE [2] f #-} -- No Maybe
7302 {-# NOINLINE [~2] f #-} -- Maybe No
7304 {-# INLINE f #-} -- Yes Yes
7305 {-# NOINLINE f #-} -- No No
7307 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7308 function body is small, or it is applied to interesting-looking arguments etc).
7309 Another way to understand the semantics is this:
7311 <listitem><para>For both INLINE and NOINLINE, the phase number says
7312 when inlining is allowed at all.</para></listitem>
7313 <listitem><para>The INLINE pragma has the additional effect of making the
7314 function body look small, so that when inlining is allowed it is very likely to
7319 <para>The same phase-numbering control is available for RULES
7320 (<xref linkend="rewrite-rules"/>).</para>
7324 <sect2 id="annotation-pragmas">
7325 <title>ANN pragmas</title>
7327 <para>GHC offers the ability to annotate various code constructs with additional
7328 data by using three pragmas. This data can then be inspected at a later date by
7329 using GHC-as-a-library.</para>
7331 <sect3 id="ann-pragma">
7332 <title>Annotating values</title>
7334 <indexterm><primary>ANN</primary></indexterm>
7336 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7337 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7338 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7339 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7340 you would do this:</para>
7343 {-# ANN foo (Just "Hello") #-}
7348 A number of restrictions apply to use of annotations:
7350 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7351 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7352 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7353 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7354 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7356 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7357 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7360 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7361 please give the GHC team a shout</ulink>.
7364 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7365 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7368 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7373 <sect3 id="typeann-pragma">
7374 <title>Annotating types</title>
7376 <indexterm><primary>ANN type</primary></indexterm>
7377 <indexterm><primary>ANN</primary></indexterm>
7379 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7382 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7387 <sect3 id="modann-pragma">
7388 <title>Annotating modules</title>
7390 <indexterm><primary>ANN module</primary></indexterm>
7391 <indexterm><primary>ANN</primary></indexterm>
7393 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7396 {-# ANN module (Just "A `Maybe String' annotation") #-}
7401 <sect2 id="line-pragma">
7402 <title>LINE pragma</title>
7404 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7405 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7406 <para>This pragma is similar to C's <literal>#line</literal>
7407 pragma, and is mainly for use in automatically generated Haskell
7408 code. It lets you specify the line number and filename of the
7409 original code; for example</para>
7411 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7413 <para>if you'd generated the current file from something called
7414 <filename>Foo.vhs</filename> and this line corresponds to line
7415 42 in the original. GHC will adjust its error messages to refer
7416 to the line/file named in the <literal>LINE</literal>
7421 <title>RULES pragma</title>
7423 <para>The RULES pragma lets you specify rewrite rules. It is
7424 described in <xref linkend="rewrite-rules"/>.</para>
7427 <sect2 id="specialize-pragma">
7428 <title>SPECIALIZE pragma</title>
7430 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7431 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7432 <indexterm><primary>overloading, death to</primary></indexterm>
7434 <para>(UK spelling also accepted.) For key overloaded
7435 functions, you can create extra versions (NB: more code space)
7436 specialised to particular types. Thus, if you have an
7437 overloaded function:</para>
7440 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7443 <para>If it is heavily used on lists with
7444 <literal>Widget</literal> keys, you could specialise it as
7448 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7451 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7452 be put anywhere its type signature could be put.</para>
7454 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7455 (a) a specialised version of the function and (b) a rewrite rule
7456 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7457 un-specialised function into a call to the specialised one.</para>
7459 <para>The type in a SPECIALIZE pragma can be any type that is less
7460 polymorphic than the type of the original function. In concrete terms,
7461 if the original function is <literal>f</literal> then the pragma
7463 {-# SPECIALIZE f :: <type> #-}
7465 is valid if and only if the definition
7467 f_spec :: <type>
7470 is valid. Here are some examples (where we only give the type signature
7471 for the original function, not its code):
7473 f :: Eq a => a -> b -> b
7474 {-# SPECIALISE f :: Int -> b -> b #-}
7476 g :: (Eq a, Ix b) => a -> b -> b
7477 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7479 h :: Eq a => a -> a -> a
7480 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7482 The last of these examples will generate a
7483 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7484 well. If you use this kind of specialisation, let us know how well it works.
7487 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7488 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7489 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7490 The <literal>INLINE</literal> pragma affects the specialised version of the
7491 function (only), and applies even if the function is recursive. The motivating
7494 -- A GADT for arrays with type-indexed representation
7496 ArrInt :: !Int -> ByteArray# -> Arr Int
7497 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7499 (!:) :: Arr e -> Int -> e
7500 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7501 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7502 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7503 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7505 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7506 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7507 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7508 the specialised function will be inlined. It has two calls to
7509 <literal>(!:)</literal>,
7510 both at type <literal>Int</literal>. Both these calls fire the first
7511 specialisation, whose body is also inlined. The result is a type-based
7512 unrolling of the indexing function.</para>
7513 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7514 on an ordinarily-recursive function.</para>
7516 <para>Note: In earlier versions of GHC, it was possible to provide your own
7517 specialised function for a given type:
7520 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7523 This feature has been removed, as it is now subsumed by the
7524 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7528 <sect2 id="specialize-instance-pragma">
7529 <title>SPECIALIZE instance pragma
7533 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7534 <indexterm><primary>overloading, death to</primary></indexterm>
7535 Same idea, except for instance declarations. For example:
7538 instance (Eq a) => Eq (Foo a) where {
7539 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7543 The pragma must occur inside the <literal>where</literal> part
7544 of the instance declaration.
7547 Compatible with HBC, by the way, except perhaps in the placement
7553 <sect2 id="unpack-pragma">
7554 <title>UNPACK pragma</title>
7556 <indexterm><primary>UNPACK</primary></indexterm>
7558 <para>The <literal>UNPACK</literal> indicates to the compiler
7559 that it should unpack the contents of a constructor field into
7560 the constructor itself, removing a level of indirection. For
7564 data T = T {-# UNPACK #-} !Float
7565 {-# UNPACK #-} !Float
7568 <para>will create a constructor <literal>T</literal> containing
7569 two unboxed floats. This may not always be an optimisation: if
7570 the <function>T</function> constructor is scrutinised and the
7571 floats passed to a non-strict function for example, they will
7572 have to be reboxed (this is done automatically by the
7575 <para>Unpacking constructor fields should only be used in
7576 conjunction with <option>-O</option>, in order to expose
7577 unfoldings to the compiler so the reboxing can be removed as
7578 often as possible. For example:</para>
7582 f (T f1 f2) = f1 + f2
7585 <para>The compiler will avoid reboxing <function>f1</function>
7586 and <function>f2</function> by inlining <function>+</function>
7587 on floats, but only when <option>-O</option> is on.</para>
7589 <para>Any single-constructor data is eligible for unpacking; for
7593 data T = T {-# UNPACK #-} !(Int,Int)
7596 <para>will store the two <literal>Int</literal>s directly in the
7597 <function>T</function> constructor, by flattening the pair.
7598 Multi-level unpacking is also supported:
7601 data T = T {-# UNPACK #-} !S
7602 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7605 will store two unboxed <literal>Int#</literal>s
7606 directly in the <function>T</function> constructor. The
7607 unpacker can see through newtypes, too.</para>
7609 <para>If a field cannot be unpacked, you will not get a warning,
7610 so it might be an idea to check the generated code with
7611 <option>-ddump-simpl</option>.</para>
7613 <para>See also the <option>-funbox-strict-fields</option> flag,
7614 which essentially has the effect of adding
7615 <literal>{-# UNPACK #-}</literal> to every strict
7616 constructor field.</para>
7619 <sect2 id="source-pragma">
7620 <title>SOURCE pragma</title>
7622 <indexterm><primary>SOURCE</primary></indexterm>
7623 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7624 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7630 <!-- ======================= REWRITE RULES ======================== -->
7632 <sect1 id="rewrite-rules">
7633 <title>Rewrite rules
7635 <indexterm><primary>RULES pragma</primary></indexterm>
7636 <indexterm><primary>pragma, RULES</primary></indexterm>
7637 <indexterm><primary>rewrite rules</primary></indexterm></title>
7640 The programmer can specify rewrite rules as part of the source program
7646 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7651 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7652 If you need more information, then <option>-ddump-rule-firings</option> shows you
7653 each individual rule firing in detail.
7657 <title>Syntax</title>
7660 From a syntactic point of view:
7666 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7667 may be generated by the layout rule).
7673 The layout rule applies in a pragma.
7674 Currently no new indentation level
7675 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7676 you must lay out the starting in the same column as the enclosing definitions.
7679 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7680 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7683 Furthermore, the closing <literal>#-}</literal>
7684 should start in a column to the right of the opening <literal>{-#</literal>.
7690 Each rule has a name, enclosed in double quotes. The name itself has
7691 no significance at all. It is only used when reporting how many times the rule fired.
7697 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7698 immediately after the name of the rule. Thus:
7701 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7704 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7705 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7714 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7715 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7716 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7717 by spaces, just like in a type <literal>forall</literal>.
7723 A pattern variable may optionally have a type signature.
7724 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7725 For example, here is the <literal>foldr/build</literal> rule:
7728 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7729 foldr k z (build g) = g k z
7732 Since <function>g</function> has a polymorphic type, it must have a type signature.
7739 The left hand side of a rule must consist of a top-level variable applied
7740 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7743 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7744 "wrong2" forall f. f True = True
7747 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7754 A rule does not need to be in the same module as (any of) the
7755 variables it mentions, though of course they need to be in scope.
7761 All rules are implicitly exported from the module, and are therefore
7762 in force in any module that imports the module that defined the rule, directly
7763 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7764 in force when compiling A.) The situation is very similar to that for instance
7772 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7773 any other flag settings. Furthermore, inside a RULE, the language extension
7774 <option>-XScopedTypeVariables</option> is automatically enabled; see
7775 <xref linkend="scoped-type-variables"/>.
7781 Like other pragmas, RULE pragmas are always checked for scope errors, and
7782 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7783 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7784 if the <option>-fenable-rewrite-rules</option> flag is
7785 on (see <xref linkend="rule-semantics"/>).
7794 <sect2 id="rule-semantics">
7795 <title>Semantics</title>
7798 From a semantic point of view:
7803 Rules are enabled (that is, used during optimisation)
7804 by the <option>-fenable-rewrite-rules</option> flag.
7805 This flag is implied by <option>-O</option>, and may be switched
7806 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7807 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7808 may not do what you expect, though, because without <option>-O</option> GHC
7809 ignores all optimisation information in interface files;
7810 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7811 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7812 has no effect on parsing or typechecking.
7818 Rules are regarded as left-to-right rewrite rules.
7819 When GHC finds an expression that is a substitution instance of the LHS
7820 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7821 By "a substitution instance" we mean that the LHS can be made equal to the
7822 expression by substituting for the pattern variables.
7829 GHC makes absolutely no attempt to verify that the LHS and RHS
7830 of a rule have the same meaning. That is undecidable in general, and
7831 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7838 GHC makes no attempt to make sure that the rules are confluent or
7839 terminating. For example:
7842 "loop" forall x y. f x y = f y x
7845 This rule will cause the compiler to go into an infinite loop.
7852 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7858 GHC currently uses a very simple, syntactic, matching algorithm
7859 for matching a rule LHS with an expression. It seeks a substitution
7860 which makes the LHS and expression syntactically equal modulo alpha
7861 conversion. The pattern (rule), but not the expression, is eta-expanded if
7862 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7863 But not beta conversion (that's called higher-order matching).
7867 Matching is carried out on GHC's intermediate language, which includes
7868 type abstractions and applications. So a rule only matches if the
7869 types match too. See <xref linkend="rule-spec"/> below.
7875 GHC keeps trying to apply the rules as it optimises the program.
7876 For example, consider:
7885 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7886 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7887 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7888 not be substituted, and the rule would not fire.
7895 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7896 results. Consider this (artificial) example
7899 {-# RULES "f" f True = False #-}
7905 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7910 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7912 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7913 would have been a better chance that <literal>f</literal>'s RULE might fire.
7916 The way to get predictable behaviour is to use a NOINLINE
7917 pragma on <literal>f</literal>, to ensure
7918 that it is not inlined until its RULEs have had a chance to fire.
7928 <title>List fusion</title>
7931 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7932 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7933 intermediate list should be eliminated entirely.
7937 The following are good producers:
7949 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7955 Explicit lists (e.g. <literal>[True, False]</literal>)
7961 The cons constructor (e.g <literal>3:4:[]</literal>)
7967 <function>++</function>
7973 <function>map</function>
7979 <function>take</function>, <function>filter</function>
7985 <function>iterate</function>, <function>repeat</function>
7991 <function>zip</function>, <function>zipWith</function>
8000 The following are good consumers:
8012 <function>array</function> (on its second argument)
8018 <function>++</function> (on its first argument)
8024 <function>foldr</function>
8030 <function>map</function>
8036 <function>take</function>, <function>filter</function>
8042 <function>concat</function>
8048 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8054 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8055 will fuse with one but not the other)
8061 <function>partition</function>
8067 <function>head</function>
8073 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8079 <function>sequence_</function>
8085 <function>msum</function>
8091 <function>sortBy</function>
8100 So, for example, the following should generate no intermediate lists:
8103 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8109 This list could readily be extended; if there are Prelude functions that you use
8110 a lot which are not included, please tell us.
8114 If you want to write your own good consumers or producers, look at the
8115 Prelude definitions of the above functions to see how to do so.
8120 <sect2 id="rule-spec">
8121 <title>Specialisation
8125 Rewrite rules can be used to get the same effect as a feature
8126 present in earlier versions of GHC.
8127 For example, suppose that:
8130 genericLookup :: Ord a => Table a b -> a -> b
8131 intLookup :: Table Int b -> Int -> b
8134 where <function>intLookup</function> is an implementation of
8135 <function>genericLookup</function> that works very fast for
8136 keys of type <literal>Int</literal>. You might wish
8137 to tell GHC to use <function>intLookup</function> instead of
8138 <function>genericLookup</function> whenever the latter was called with
8139 type <literal>Table Int b -> Int -> b</literal>.
8140 It used to be possible to write
8143 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8146 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8149 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8152 This slightly odd-looking rule instructs GHC to replace
8153 <function>genericLookup</function> by <function>intLookup</function>
8154 <emphasis>whenever the types match</emphasis>.
8155 What is more, this rule does not need to be in the same
8156 file as <function>genericLookup</function>, unlike the
8157 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8158 have an original definition available to specialise).
8161 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8162 <function>intLookup</function> really behaves as a specialised version
8163 of <function>genericLookup</function>!!!</para>
8165 <para>An example in which using <literal>RULES</literal> for
8166 specialisation will Win Big:
8169 toDouble :: Real a => a -> Double
8170 toDouble = fromRational . toRational
8172 {-# RULES "toDouble/Int" toDouble = i2d #-}
8173 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8176 The <function>i2d</function> function is virtually one machine
8177 instruction; the default conversion—via an intermediate
8178 <literal>Rational</literal>—is obscenely expensive by
8185 <title>Controlling what's going on</title>
8193 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8199 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8200 If you add <option>-dppr-debug</option> you get a more detailed listing.
8206 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8209 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8210 {-# INLINE build #-}
8214 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8215 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8216 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8217 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8224 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8225 see how to write rules that will do fusion and yet give an efficient
8226 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8236 <sect2 id="core-pragma">
8237 <title>CORE pragma</title>
8239 <indexterm><primary>CORE pragma</primary></indexterm>
8240 <indexterm><primary>pragma, CORE</primary></indexterm>
8241 <indexterm><primary>core, annotation</primary></indexterm>
8244 The external core format supports <quote>Note</quote> annotations;
8245 the <literal>CORE</literal> pragma gives a way to specify what these
8246 should be in your Haskell source code. Syntactically, core
8247 annotations are attached to expressions and take a Haskell string
8248 literal as an argument. The following function definition shows an
8252 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8255 Semantically, this is equivalent to:
8263 However, when external core is generated (via
8264 <option>-fext-core</option>), there will be Notes attached to the
8265 expressions <function>show</function> and <varname>x</varname>.
8266 The core function declaration for <function>f</function> is:
8270 f :: %forall a . GHCziShow.ZCTShow a ->
8271 a -> GHCziBase.ZMZN GHCziBase.Char =
8272 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8274 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8276 (tpl1::GHCziBase.Int ->
8278 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8280 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8281 (tpl3::GHCziBase.ZMZN a ->
8282 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8290 Here, we can see that the function <function>show</function> (which
8291 has been expanded out to a case expression over the Show dictionary)
8292 has a <literal>%note</literal> attached to it, as does the
8293 expression <varname>eta</varname> (which used to be called
8294 <varname>x</varname>).
8301 <sect1 id="special-ids">
8302 <title>Special built-in functions</title>
8303 <para>GHC has a few built-in functions with special behaviour. These
8304 are now described in the module <ulink
8305 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8306 in the library documentation.</para>
8310 <sect1 id="generic-classes">
8311 <title>Generic classes</title>
8314 The ideas behind this extension are described in detail in "Derivable type classes",
8315 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8316 An example will give the idea:
8324 fromBin :: [Int] -> (a, [Int])
8326 toBin {| Unit |} Unit = []
8327 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8328 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8329 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8331 fromBin {| Unit |} bs = (Unit, bs)
8332 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8333 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8334 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8335 (y,bs'') = fromBin bs'
8338 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8339 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8340 which are defined thus in the library module <literal>Generics</literal>:
8344 data a :+: b = Inl a | Inr b
8345 data a :*: b = a :*: b
8348 Now you can make a data type into an instance of Bin like this:
8350 instance (Bin a, Bin b) => Bin (a,b)
8351 instance Bin a => Bin [a]
8353 That is, just leave off the "where" clause. Of course, you can put in the
8354 where clause and over-ride whichever methods you please.
8358 <title> Using generics </title>
8359 <para>To use generics you need to</para>
8362 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8363 <option>-XGenerics</option> (to generate extra per-data-type code),
8364 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8368 <para>Import the module <literal>Generics</literal> from the
8369 <literal>lang</literal> package. This import brings into
8370 scope the data types <literal>Unit</literal>,
8371 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8372 don't need this import if you don't mention these types
8373 explicitly; for example, if you are simply giving instance
8374 declarations.)</para>
8379 <sect2> <title> Changes wrt the paper </title>
8381 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8382 can be written infix (indeed, you can now use
8383 any operator starting in a colon as an infix type constructor). Also note that
8384 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8385 Finally, note that the syntax of the type patterns in the class declaration
8386 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8387 alone would ambiguous when they appear on right hand sides (an extension we
8388 anticipate wanting).
8392 <sect2> <title>Terminology and restrictions</title>
8394 Terminology. A "generic default method" in a class declaration
8395 is one that is defined using type patterns as above.
8396 A "polymorphic default method" is a default method defined as in Haskell 98.
8397 A "generic class declaration" is a class declaration with at least one
8398 generic default method.
8406 Alas, we do not yet implement the stuff about constructor names and
8413 A generic class can have only one parameter; you can't have a generic
8414 multi-parameter class.
8420 A default method must be defined entirely using type patterns, or entirely
8421 without. So this is illegal:
8424 op :: a -> (a, Bool)
8425 op {| Unit |} Unit = (Unit, True)
8428 However it is perfectly OK for some methods of a generic class to have
8429 generic default methods and others to have polymorphic default methods.
8435 The type variable(s) in the type pattern for a generic method declaration
8436 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:
8440 op {| p :*: q |} (x :*: y) = op (x :: p)
8448 The type patterns in a generic default method must take one of the forms:
8454 where "a" and "b" are type variables. Furthermore, all the type patterns for
8455 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8456 must use the same type variables. So this is illegal:
8460 op {| a :+: b |} (Inl x) = True
8461 op {| p :+: q |} (Inr y) = False
8463 The type patterns must be identical, even in equations for different methods of the class.
8464 So this too is illegal:
8468 op1 {| a :*: b |} (x :*: y) = True
8471 op2 {| p :*: q |} (x :*: y) = False
8473 (The reason for this restriction is that we gather all the equations for a particular type constructor
8474 into a single generic instance declaration.)
8480 A generic method declaration must give a case for each of the three type constructors.
8486 The type for a generic method can be built only from:
8488 <listitem> <para> Function arrows </para> </listitem>
8489 <listitem> <para> Type variables </para> </listitem>
8490 <listitem> <para> Tuples </para> </listitem>
8491 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8493 Here are some example type signatures for generic methods:
8496 op2 :: Bool -> (a,Bool)
8497 op3 :: [Int] -> a -> a
8500 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8504 This restriction is an implementation restriction: we just haven't got around to
8505 implementing the necessary bidirectional maps over arbitrary type constructors.
8506 It would be relatively easy to add specific type constructors, such as Maybe and list,
8507 to the ones that are allowed.</para>
8512 In an instance declaration for a generic class, the idea is that the compiler
8513 will fill in the methods for you, based on the generic templates. However it can only
8518 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8523 No constructor of the instance type has unboxed fields.
8527 (Of course, these things can only arise if you are already using GHC extensions.)
8528 However, you can still give an instance declarations for types which break these rules,
8529 provided you give explicit code to override any generic default methods.
8537 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8538 what the compiler does with generic declarations.
8543 <sect2> <title> Another example </title>
8545 Just to finish with, here's another example I rather like:
8549 nCons {| Unit |} _ = 1
8550 nCons {| a :*: b |} _ = 1
8551 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8554 tag {| Unit |} _ = 1
8555 tag {| a :*: b |} _ = 1
8556 tag {| a :+: b |} (Inl x) = tag x
8557 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8563 <sect1 id="monomorphism">
8564 <title>Control over monomorphism</title>
8566 <para>GHC supports two flags that control the way in which generalisation is
8567 carried out at let and where bindings.
8571 <title>Switching off the dreaded Monomorphism Restriction</title>
8572 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8574 <para>Haskell's monomorphism restriction (see
8575 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8577 of the Haskell Report)
8578 can be completely switched off by
8579 <option>-XNoMonomorphismRestriction</option>.
8584 <title>Monomorphic pattern bindings</title>
8585 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8586 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8588 <para> As an experimental change, we are exploring the possibility of
8589 making pattern bindings monomorphic; that is, not generalised at all.
8590 A pattern binding is a binding whose LHS has no function arguments,
8591 and is not a simple variable. For example:
8593 f x = x -- Not a pattern binding
8594 f = \x -> x -- Not a pattern binding
8595 f :: Int -> Int = \x -> x -- Not a pattern binding
8597 (g,h) = e -- A pattern binding
8598 (f) = e -- A pattern binding
8599 [x] = e -- A pattern binding
8601 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8602 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8611 ;;; Local Variables: ***
8613 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8614 ;;; ispell-local-dictionary: "british" ***
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