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 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2368 have no scope, and different constructors may have different universally-quantified type variables:
2370 data T a where -- The 'a' has no scope
2371 T1,T2 :: b -> T b -- Means forall b. b -> T b
2372 T3 :: T a -- Means forall a. T a
2377 A constructor signature may mention type class constraints, which can differ for
2378 different constructors. For example, this is fine:
2381 T1 :: Eq b => b -> b -> T b
2382 T2 :: (Show c, Ix c) => c -> [c] -> T c
2384 When patten matching, these constraints are made available to discharge constraints
2385 in the body of the match. For example:
2388 f (T1 x y) | x==y = "yes"
2392 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2393 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2394 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2398 Unlike a Haskell-98-style
2399 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2400 have no scope. Indeed, one can write a kind signature instead:
2402 data Set :: * -> * where ...
2404 or even a mixture of the two:
2406 data Bar a :: (* -> *) -> * where ...
2408 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2411 data Bar a (b :: * -> *) where ...
2417 You can use strictness annotations, in the obvious places
2418 in the constructor type:
2421 Lit :: !Int -> Term Int
2422 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2423 Pair :: Term a -> Term b -> Term (a,b)
2428 You can use a <literal>deriving</literal> clause on a GADT-style data type
2429 declaration. For example, these two declarations are equivalent
2431 data Maybe1 a where {
2432 Nothing1 :: Maybe1 a ;
2433 Just1 :: a -> Maybe1 a
2434 } deriving( Eq, Ord )
2436 data Maybe2 a = Nothing2 | Just2 a
2442 The type signature may have quantified type variables that do not appear
2446 MkFoo :: a -> (a->Bool) -> Foo
2449 Here the type variable <literal>a</literal> does not appear in the result type
2450 of either constructor.
2451 Although it is universally quantified in the type of the constructor, such
2452 a type variable is often called "existential".
2453 Indeed, the above declaration declares precisely the same type as
2454 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2456 The type may contain a class context too, of course:
2459 MkShowable :: Show a => a -> Showable
2464 You can use record syntax on a GADT-style data type declaration:
2468 Adult :: { name :: String, children :: [Person] } -> Person
2469 Child :: Show a => { name :: !String, funny :: a } -> Person
2471 As usual, for every constructor that has a field <literal>f</literal>, the type of
2472 field <literal>f</literal> must be the same (modulo alpha conversion).
2473 The <literal>Child</literal> constructor above shows that the signature
2474 may have a context, existentially-quantified variables, and strictness annotations,
2475 just as in the non-record case. (NB: the "type" that follows the double-colon
2476 is not really a type, because of the record syntax and strictness annotations.
2477 A "type" of this form can appear only in a constructor signature.)
2481 Record updates are allowed with GADT-style declarations,
2482 only fields that have the following property: the type of the field
2483 mentions no existential type variables.
2487 As in the case of existentials declared using the Haskell-98-like record syntax
2488 (<xref linkend="existential-records"/>),
2489 record-selector functions are generated only for those fields that have well-typed
2491 Here is the example of that section, in GADT-style syntax:
2493 data Counter a where
2494 NewCounter { _this :: self
2495 , _inc :: self -> self
2496 , _display :: self -> IO ()
2501 As before, only one selector function is generated here, that for <literal>tag</literal>.
2502 Nevertheless, you can still use all the field names in pattern matching and record construction.
2504 </itemizedlist></para>
2508 <title>Generalised Algebraic Data Types (GADTs)</title>
2510 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2511 by allowing constructors to have richer return types. Here is an example:
2514 Lit :: Int -> Term Int
2515 Succ :: Term Int -> Term Int
2516 IsZero :: Term Int -> Term Bool
2517 If :: Term Bool -> Term a -> Term a -> Term a
2518 Pair :: Term a -> Term b -> Term (a,b)
2520 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2521 case with ordinary data types. This generality allows us to
2522 write a well-typed <literal>eval</literal> function
2523 for these <literal>Terms</literal>:
2527 eval (Succ t) = 1 + eval t
2528 eval (IsZero t) = eval t == 0
2529 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2530 eval (Pair e1 e2) = (eval e1, eval e2)
2532 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2533 For example, in the right hand side of the equation
2538 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2539 A precise specification of the type rules is beyond what this user manual aspires to,
2540 but the design closely follows that described in
2542 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2543 unification-based type inference for GADTs</ulink>,
2545 The general principle is this: <emphasis>type refinement is only carried out
2546 based on user-supplied type annotations</emphasis>.
2547 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2548 and lots of obscure error messages will
2549 occur. However, the refinement is quite general. For example, if we had:
2551 eval :: Term a -> a -> a
2552 eval (Lit i) j = i+j
2554 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2555 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2556 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2559 These and many other examples are given in papers by Hongwei Xi, and
2560 Tim Sheard. There is a longer introduction
2561 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2563 <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
2564 may use different notation to that implemented in GHC.
2567 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2568 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2571 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2572 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2573 The result type of each constructor must begin with the type constructor being defined,
2574 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2575 For example, in the <literal>Term</literal> data
2576 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2577 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2582 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2583 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2584 whose result type is not just <literal>T a b</literal>.
2588 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2589 an ordinary data type.
2593 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2597 Lit { val :: Int } :: Term Int
2598 Succ { num :: Term Int } :: Term Int
2599 Pred { num :: Term Int } :: Term Int
2600 IsZero { arg :: Term Int } :: Term Bool
2601 Pair { arg1 :: Term a
2604 If { cnd :: Term Bool
2609 However, for GADTs there is the following additional constraint:
2610 every constructor that has a field <literal>f</literal> must have
2611 the same result type (modulo alpha conversion)
2612 Hence, in the above example, we cannot merge the <literal>num</literal>
2613 and <literal>arg</literal> fields above into a
2614 single name. Although their field types are both <literal>Term Int</literal>,
2615 their selector functions actually have different types:
2618 num :: Term Int -> Term Int
2619 arg :: Term Bool -> Term Int
2624 When pattern-matching against data constructors drawn from a GADT,
2625 for example in a <literal>case</literal> expression, the following rules apply:
2627 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2628 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2629 <listitem><para>The type of any free variable mentioned in any of
2630 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2632 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2633 way to ensure that a variable a rigid type is to give it a type signature.
2634 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2635 Simple unification-based type inference for GADTs
2636 </ulink>. The criteria implemented by GHC are given in the Appendix.
2646 <!-- ====================== End of Generalised algebraic data types ======================= -->
2648 <sect1 id="deriving">
2649 <title>Extensions to the "deriving" mechanism</title>
2651 <sect2 id="deriving-inferred">
2652 <title>Inferred context for deriving clauses</title>
2655 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2658 data T0 f a = MkT0 a deriving( Eq )
2659 data T1 f a = MkT1 (f a) deriving( Eq )
2660 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2662 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2664 instance Eq a => Eq (T0 f a) where ...
2665 instance Eq (f a) => Eq (T1 f a) where ...
2666 instance Eq (f (f a)) => Eq (T2 f a) where ...
2668 The first of these is obviously fine. The second is still fine, although less obviously.
2669 The third is not Haskell 98, and risks losing termination of instances.
2672 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2673 each constraint in the inferred instance context must consist only of type variables,
2674 with no repetitions.
2677 This rule is applied regardless of flags. If you want a more exotic context, you can write
2678 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2682 <sect2 id="stand-alone-deriving">
2683 <title>Stand-alone deriving declarations</title>
2686 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2688 data Foo a = Bar a | Baz String
2690 deriving instance Eq a => Eq (Foo a)
2692 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2693 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2694 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2695 exactly as you would in an ordinary instance declaration.
2696 (In contrast the context is inferred in a <literal>deriving</literal> clause
2697 attached to a data type declaration.)
2699 A <literal>deriving instance</literal> declaration
2700 must obey the same rules concerning form and termination as ordinary instance declarations,
2701 controlled by the same flags; see <xref linkend="instance-decls"/>.
2704 Unlike a <literal>deriving</literal>
2705 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2706 than the data type (assuming you also use
2707 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2710 data Foo a = Bar a | Baz String
2712 deriving instance Eq a => Eq (Foo [a])
2713 deriving instance Eq a => Eq (Foo (Maybe a))
2715 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2716 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2719 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2720 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2723 newtype Foo a = MkFoo (State Int a)
2725 deriving instance MonadState Int Foo
2727 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2728 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2734 <sect2 id="deriving-typeable">
2735 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2738 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2739 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2740 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2741 classes <literal>Eq</literal>, <literal>Ord</literal>,
2742 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2745 GHC extends this list with several more classes that may be automatically derived:
2747 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2748 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2749 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2751 <para>An instance of <literal>Typeable</literal> can only be derived if the
2752 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2753 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2755 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2756 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2758 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2759 are used, and only <literal>Typeable1</literal> up to
2760 <literal>Typeable7</literal> are provided in the library.)
2761 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2762 class, whose kind suits that of the data type constructor, and
2763 then writing the data type instance by hand.
2767 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2768 the class <literal>Functor</literal>,
2769 defined in <literal>GHC.Base</literal>.
2772 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2773 the class <literal>Foldable</literal>,
2774 defined in <literal>Data.Foldable</literal>.
2777 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2778 the class <literal>Traversable</literal>,
2779 defined in <literal>Data.Traversable</literal>.
2782 In each case the appropriate class must be in scope before it
2783 can be mentioned in the <literal>deriving</literal> clause.
2787 <sect2 id="newtype-deriving">
2788 <title>Generalised derived instances for newtypes</title>
2791 When you define an abstract type using <literal>newtype</literal>, you may want
2792 the new type to inherit some instances from its representation. In
2793 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2794 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2795 other classes you have to write an explicit instance declaration. For
2796 example, if you define
2799 newtype Dollars = Dollars Int
2802 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2803 explicitly define an instance of <literal>Num</literal>:
2806 instance Num Dollars where
2807 Dollars a + Dollars b = Dollars (a+b)
2810 All the instance does is apply and remove the <literal>newtype</literal>
2811 constructor. It is particularly galling that, since the constructor
2812 doesn't appear at run-time, this instance declaration defines a
2813 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2814 dictionary, only slower!
2818 <sect3> <title> Generalising the deriving clause </title>
2820 GHC now permits such instances to be derived instead,
2821 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2824 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2827 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2828 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2829 derives an instance declaration of the form
2832 instance Num Int => Num Dollars
2835 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2839 We can also derive instances of constructor classes in a similar
2840 way. For example, suppose we have implemented state and failure monad
2841 transformers, such that
2844 instance Monad m => Monad (State s m)
2845 instance Monad m => Monad (Failure m)
2847 In Haskell 98, we can define a parsing monad by
2849 type Parser tok m a = State [tok] (Failure m) a
2852 which is automatically a monad thanks to the instance declarations
2853 above. With the extension, we can make the parser type abstract,
2854 without needing to write an instance of class <literal>Monad</literal>, via
2857 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2860 In this case the derived instance declaration is of the form
2862 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2865 Notice that, since <literal>Monad</literal> is a constructor class, the
2866 instance is a <emphasis>partial application</emphasis> of the new type, not the
2867 entire left hand side. We can imagine that the type declaration is
2868 "eta-converted" to generate the context of the instance
2873 We can even derive instances of multi-parameter classes, provided the
2874 newtype is the last class parameter. In this case, a ``partial
2875 application'' of the class appears in the <literal>deriving</literal>
2876 clause. For example, given the class
2879 class StateMonad s m | m -> s where ...
2880 instance Monad m => StateMonad s (State s m) where ...
2882 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2884 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2885 deriving (Monad, StateMonad [tok])
2888 The derived instance is obtained by completing the application of the
2889 class to the new type:
2892 instance StateMonad [tok] (State [tok] (Failure m)) =>
2893 StateMonad [tok] (Parser tok m)
2898 As a result of this extension, all derived instances in newtype
2899 declarations are treated uniformly (and implemented just by reusing
2900 the dictionary for the representation type), <emphasis>except</emphasis>
2901 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2902 the newtype and its representation.
2906 <sect3> <title> A more precise specification </title>
2908 Derived instance declarations are constructed as follows. Consider the
2909 declaration (after expansion of any type synonyms)
2912 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2918 The <literal>ci</literal> are partial applications of
2919 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2920 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2923 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2926 The type <literal>t</literal> is an arbitrary type.
2929 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2930 nor in the <literal>ci</literal>, and
2933 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2934 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2935 should not "look through" the type or its constructor. You can still
2936 derive these classes for a newtype, but it happens in the usual way, not
2937 via this new mechanism.
2940 Then, for each <literal>ci</literal>, the derived instance
2943 instance ci t => ci (T v1...vk)
2945 As an example which does <emphasis>not</emphasis> work, consider
2947 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2949 Here we cannot derive the instance
2951 instance Monad (State s m) => Monad (NonMonad m)
2954 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2955 and so cannot be "eta-converted" away. It is a good thing that this
2956 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2957 not, in fact, a monad --- for the same reason. Try defining
2958 <literal>>>=</literal> with the correct type: you won't be able to.
2962 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2963 important, since we can only derive instances for the last one. If the
2964 <literal>StateMonad</literal> class above were instead defined as
2967 class StateMonad m s | m -> s where ...
2970 then we would not have been able to derive an instance for the
2971 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2972 classes usually have one "main" parameter for which deriving new
2973 instances is most interesting.
2975 <para>Lastly, all of this applies only for classes other than
2976 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2977 and <literal>Data</literal>, for which the built-in derivation applies (section
2978 4.3.3. of the Haskell Report).
2979 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2980 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2981 the standard method is used or the one described here.)
2988 <!-- TYPE SYSTEM EXTENSIONS -->
2989 <sect1 id="type-class-extensions">
2990 <title>Class and instances declarations</title>
2992 <sect2 id="multi-param-type-classes">
2993 <title>Class declarations</title>
2996 This section, and the next one, documents GHC's type-class extensions.
2997 There's lots of background in the paper <ulink
2998 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2999 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3000 Jones, Erik Meijer).
3003 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3007 <title>Multi-parameter type classes</title>
3009 Multi-parameter type classes are permitted. For example:
3013 class Collection c a where
3014 union :: c a -> c a -> c a
3022 <title>The superclasses of a class declaration</title>
3025 There are no restrictions on the context in a class declaration
3026 (which introduces superclasses), except that the class hierarchy must
3027 be acyclic. So these class declarations are OK:
3031 class Functor (m k) => FiniteMap m k where
3034 class (Monad m, Monad (t m)) => Transform t m where
3035 lift :: m a -> (t m) a
3041 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3042 of "acyclic" involves only the superclass relationships. For example,
3048 op :: D b => a -> b -> b
3051 class C a => D a where { ... }
3055 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3056 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3057 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3064 <sect3 id="class-method-types">
3065 <title>Class method types</title>
3068 Haskell 98 prohibits class method types to mention constraints on the
3069 class type variable, thus:
3072 fromList :: [a] -> s a
3073 elem :: Eq a => a -> s a -> Bool
3075 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3076 contains the constraint <literal>Eq a</literal>, constrains only the
3077 class type variable (in this case <literal>a</literal>).
3078 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3085 <sect2 id="functional-dependencies">
3086 <title>Functional dependencies
3089 <para> Functional dependencies are implemented as described by Mark Jones
3090 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3091 In Proceedings of the 9th European Symposium on Programming,
3092 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3096 Functional dependencies are introduced by a vertical bar in the syntax of a
3097 class declaration; e.g.
3099 class (Monad m) => MonadState s m | m -> s where ...
3101 class Foo a b c | a b -> c where ...
3103 There should be more documentation, but there isn't (yet). Yell if you need it.
3106 <sect3><title>Rules for functional dependencies </title>
3108 In a class declaration, all of the class type variables must be reachable (in the sense
3109 mentioned in <xref linkend="type-restrictions"/>)
3110 from the free variables of each method type.
3114 class Coll s a where
3116 insert :: s -> a -> s
3119 is not OK, because the type of <literal>empty</literal> doesn't mention
3120 <literal>a</literal>. Functional dependencies can make the type variable
3123 class Coll s a | s -> a where
3125 insert :: s -> a -> s
3128 Alternatively <literal>Coll</literal> might be rewritten
3131 class Coll s a where
3133 insert :: s a -> a -> s a
3137 which makes the connection between the type of a collection of
3138 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3139 Occasionally this really doesn't work, in which case you can split the
3147 class CollE s => Coll s a where
3148 insert :: s -> a -> s
3155 <title>Background on functional dependencies</title>
3157 <para>The following description of the motivation and use of functional dependencies is taken
3158 from the Hugs user manual, reproduced here (with minor changes) by kind
3159 permission of Mark Jones.
3162 Consider the following class, intended as part of a
3163 library for collection types:
3165 class Collects e ce where
3167 insert :: e -> ce -> ce
3168 member :: e -> ce -> Bool
3170 The type variable e used here represents the element type, while ce is the type
3171 of the container itself. Within this framework, we might want to define
3172 instances of this class for lists or characteristic functions (both of which
3173 can be used to represent collections of any equality type), bit sets (which can
3174 be used to represent collections of characters), or hash tables (which can be
3175 used to represent any collection whose elements have a hash function). Omitting
3176 standard implementation details, this would lead to the following declarations:
3178 instance Eq e => Collects e [e] where ...
3179 instance Eq e => Collects e (e -> Bool) where ...
3180 instance Collects Char BitSet where ...
3181 instance (Hashable e, Collects a ce)
3182 => Collects e (Array Int ce) where ...
3184 All this looks quite promising; we have a class and a range of interesting
3185 implementations. Unfortunately, there are some serious problems with the class
3186 declaration. First, the empty function has an ambiguous type:
3188 empty :: Collects e ce => ce
3190 By "ambiguous" we mean that there is a type variable e that appears on the left
3191 of the <literal>=></literal> symbol, but not on the right. The problem with
3192 this is that, according to the theoretical foundations of Haskell overloading,
3193 we cannot guarantee a well-defined semantics for any term with an ambiguous
3197 We can sidestep this specific problem by removing the empty member from the
3198 class declaration. However, although the remaining members, insert and member,
3199 do not have ambiguous types, we still run into problems when we try to use
3200 them. For example, consider the following two functions:
3202 f x y = insert x . insert y
3205 for which GHC infers the following types:
3207 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3208 g :: (Collects Bool c, Collects Char c) => c -> c
3210 Notice that the type for f allows the two parameters x and y to be assigned
3211 different types, even though it attempts to insert each of the two values, one
3212 after the other, into the same collection. If we're trying to model collections
3213 that contain only one type of value, then this is clearly an inaccurate
3214 type. Worse still, the definition for g is accepted, without causing a type
3215 error. As a result, the error in this code will not be flagged at the point
3216 where it appears. Instead, it will show up only when we try to use g, which
3217 might even be in a different module.
3220 <sect4><title>An attempt to use constructor classes</title>
3223 Faced with the problems described above, some Haskell programmers might be
3224 tempted to use something like the following version of the class declaration:
3226 class Collects e c where
3228 insert :: e -> c e -> c e
3229 member :: e -> c e -> Bool
3231 The key difference here is that we abstract over the type constructor c that is
3232 used to form the collection type c e, and not over that collection type itself,
3233 represented by ce in the original class declaration. This avoids the immediate
3234 problems that we mentioned above: empty has type <literal>Collects e c => c
3235 e</literal>, which is not ambiguous.
3238 The function f from the previous section has a more accurate type:
3240 f :: (Collects e c) => e -> e -> c e -> c e
3242 The function g from the previous section is now rejected with a type error as
3243 we would hope because the type of f does not allow the two arguments to have
3245 This, then, is an example of a multiple parameter class that does actually work
3246 quite well in practice, without ambiguity problems.
3247 There is, however, a catch. This version of the Collects class is nowhere near
3248 as general as the original class seemed to be: only one of the four instances
3249 for <literal>Collects</literal>
3250 given above can be used with this version of Collects because only one of
3251 them---the instance for lists---has a collection type that can be written in
3252 the form c e, for some type constructor c, and element type e.
3256 <sect4><title>Adding functional dependencies</title>
3259 To get a more useful version of the Collects class, Hugs provides a mechanism
3260 that allows programmers to specify dependencies between the parameters of a
3261 multiple parameter class (For readers with an interest in theoretical
3262 foundations and previous work: The use of dependency information can be seen
3263 both as a generalization of the proposal for `parametric type classes' that was
3264 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3265 later framework for "improvement" of qualified types. The
3266 underlying ideas are also discussed in a more theoretical and abstract setting
3267 in a manuscript [implparam], where they are identified as one point in a
3268 general design space for systems of implicit parameterization.).
3270 To start with an abstract example, consider a declaration such as:
3272 class C a b where ...
3274 which tells us simply that C can be thought of as a binary relation on types
3275 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3276 included in the definition of classes to add information about dependencies
3277 between parameters, as in the following examples:
3279 class D a b | a -> b where ...
3280 class E a b | a -> b, b -> a where ...
3282 The notation <literal>a -> b</literal> used here between the | and where
3283 symbols --- not to be
3284 confused with a function type --- indicates that the a parameter uniquely
3285 determines the b parameter, and might be read as "a determines b." Thus D is
3286 not just a relation, but actually a (partial) function. Similarly, from the two
3287 dependencies that are included in the definition of E, we can see that E
3288 represents a (partial) one-one mapping between types.
3291 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3292 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3293 m>=0, meaning that the y parameters are uniquely determined by the x
3294 parameters. Spaces can be used as separators if more than one variable appears
3295 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3296 annotated with multiple dependencies using commas as separators, as in the
3297 definition of E above. Some dependencies that we can write in this notation are
3298 redundant, and will be rejected because they don't serve any useful
3299 purpose, and may instead indicate an error in the program. Examples of
3300 dependencies like this include <literal>a -> a </literal>,
3301 <literal>a -> a a </literal>,
3302 <literal>a -> </literal>, etc. There can also be
3303 some redundancy if multiple dependencies are given, as in
3304 <literal>a->b</literal>,
3305 <literal>b->c </literal>, <literal>a->c </literal>, and
3306 in which some subset implies the remaining dependencies. Examples like this are
3307 not treated as errors. Note that dependencies appear only in class
3308 declarations, and not in any other part of the language. In particular, the
3309 syntax for instance declarations, class constraints, and types is completely
3313 By including dependencies in a class declaration, we provide a mechanism for
3314 the programmer to specify each multiple parameter class more precisely. The
3315 compiler, on the other hand, is responsible for ensuring that the set of
3316 instances that are in scope at any given point in the program is consistent
3317 with any declared dependencies. For example, the following pair of instance
3318 declarations cannot appear together in the same scope because they violate the
3319 dependency for D, even though either one on its own would be acceptable:
3321 instance D Bool Int where ...
3322 instance D Bool Char where ...
3324 Note also that the following declaration is not allowed, even by itself:
3326 instance D [a] b where ...
3328 The problem here is that this instance would allow one particular choice of [a]
3329 to be associated with more than one choice for b, which contradicts the
3330 dependency specified in the definition of D. More generally, this means that,
3331 in any instance of the form:
3333 instance D t s where ...
3335 for some particular types t and s, the only variables that can appear in s are
3336 the ones that appear in t, and hence, if the type t is known, then s will be
3337 uniquely determined.
3340 The benefit of including dependency information is that it allows us to define
3341 more general multiple parameter classes, without ambiguity problems, and with
3342 the benefit of more accurate types. To illustrate this, we return to the
3343 collection class example, and annotate the original definition of <literal>Collects</literal>
3344 with a simple dependency:
3346 class Collects e ce | ce -> e where
3348 insert :: e -> ce -> ce
3349 member :: e -> ce -> Bool
3351 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3352 determined by the type of the collection ce. Note that both parameters of
3353 Collects are of kind *; there are no constructor classes here. Note too that
3354 all of the instances of Collects that we gave earlier can be used
3355 together with this new definition.
3358 What about the ambiguity problems that we encountered with the original
3359 definition? The empty function still has type Collects e ce => ce, but it is no
3360 longer necessary to regard that as an ambiguous type: Although the variable e
3361 does not appear on the right of the => symbol, the dependency for class
3362 Collects tells us that it is uniquely determined by ce, which does appear on
3363 the right of the => symbol. Hence the context in which empty is used can still
3364 give enough information to determine types for both ce and e, without
3365 ambiguity. More generally, we need only regard a type as ambiguous if it
3366 contains a variable on the left of the => that is not uniquely determined
3367 (either directly or indirectly) by the variables on the right.
3370 Dependencies also help to produce more accurate types for user defined
3371 functions, and hence to provide earlier detection of errors, and less cluttered
3372 types for programmers to work with. Recall the previous definition for a
3375 f x y = insert x y = insert x . insert y
3377 for which we originally obtained a type:
3379 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3381 Given the dependency information that we have for Collects, however, we can
3382 deduce that a and b must be equal because they both appear as the second
3383 parameter in a Collects constraint with the same first parameter c. Hence we
3384 can infer a shorter and more accurate type for f:
3386 f :: (Collects a c) => a -> a -> c -> c
3388 In a similar way, the earlier definition of g will now be flagged as a type error.
3391 Although we have given only a few examples here, it should be clear that the
3392 addition of dependency information can help to make multiple parameter classes
3393 more useful in practice, avoiding ambiguity problems, and allowing more general
3394 sets of instance declarations.
3400 <sect2 id="instance-decls">
3401 <title>Instance declarations</title>
3403 <para>An instance declaration has the form
3405 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 ...
3407 The part before the "<literal>=></literal>" is the
3408 <emphasis>context</emphasis>, while the part after the
3409 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3412 <sect3 id="flexible-instance-head">
3413 <title>Relaxed rules for the instance head</title>
3416 In Haskell 98 the head of an instance declaration
3417 must be of the form <literal>C (T a1 ... an)</literal>, where
3418 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3419 and the <literal>a1 ... an</literal> are distinct type variables.
3420 GHC relaxes these rules in two ways.
3424 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3425 declaration to mention arbitrary nested types.
3426 For example, this becomes a legal instance declaration
3428 instance C (Maybe Int) where ...
3430 See also the <link linkend="instance-overlap">rules on overlap</link>.
3433 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3434 synonyms. As always, using a type synonym is just shorthand for
3435 writing the RHS of the type synonym definition. For example:
3439 type Point = (Int,Int)
3440 instance C Point where ...
3441 instance C [Point] where ...
3445 is legal. However, if you added
3449 instance C (Int,Int) where ...
3453 as well, then the compiler will complain about the overlapping
3454 (actually, identical) instance declarations. As always, type synonyms
3455 must be fully applied. You cannot, for example, write:
3459 instance Monad P where ...
3467 <sect3 id="instance-rules">
3468 <title>Relaxed rules for instance contexts</title>
3470 <para>In Haskell 98, the assertions in the context of the instance declaration
3471 must be of the form <literal>C a</literal> where <literal>a</literal>
3472 is a type variable that occurs in the head.
3476 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3477 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3478 With this flag the context of the instance declaration can each consist of arbitrary
3479 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3483 The Paterson Conditions: for each assertion in the context
3485 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3486 <listitem><para>The assertion has fewer constructors and variables (taken together
3487 and counting repetitions) than the head</para></listitem>
3491 <listitem><para>The Coverage Condition. For each functional dependency,
3492 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3493 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3494 every type variable in
3495 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3496 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3497 substitution mapping each type variable in the class declaration to the
3498 corresponding type in the instance declaration.
3501 These restrictions ensure that context reduction terminates: each reduction
3502 step makes the problem smaller by at least one
3503 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3504 if you give the <option>-XUndecidableInstances</option>
3505 flag (<xref linkend="undecidable-instances"/>).
3506 You can find lots of background material about the reason for these
3507 restrictions in the paper <ulink
3508 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3509 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3512 For example, these are OK:
3514 instance C Int [a] -- Multiple parameters
3515 instance Eq (S [a]) -- Structured type in head
3517 -- Repeated type variable in head
3518 instance C4 a a => C4 [a] [a]
3519 instance Stateful (ST s) (MutVar s)
3521 -- Head can consist of type variables only
3523 instance (Eq a, Show b) => C2 a b
3525 -- Non-type variables in context
3526 instance Show (s a) => Show (Sized s a)
3527 instance C2 Int a => C3 Bool [a]
3528 instance C2 Int a => C3 [a] b
3532 -- Context assertion no smaller than head
3533 instance C a => C a where ...
3534 -- (C b b) has more more occurrences of b than the head
3535 instance C b b => Foo [b] where ...
3540 The same restrictions apply to instances generated by
3541 <literal>deriving</literal> clauses. Thus the following is accepted:
3543 data MinHeap h a = H a (h a)
3546 because the derived instance
3548 instance (Show a, Show (h a)) => Show (MinHeap h a)
3550 conforms to the above rules.
3554 A useful idiom permitted by the above rules is as follows.
3555 If one allows overlapping instance declarations then it's quite
3556 convenient to have a "default instance" declaration that applies if
3557 something more specific does not:
3565 <sect3 id="undecidable-instances">
3566 <title>Undecidable instances</title>
3569 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3570 For example, sometimes you might want to use the following to get the
3571 effect of a "class synonym":
3573 class (C1 a, C2 a, C3 a) => C a where { }
3575 instance (C1 a, C2 a, C3 a) => C a where { }
3577 This allows you to write shorter signatures:
3583 f :: (C1 a, C2 a, C3 a) => ...
3585 The restrictions on functional dependencies (<xref
3586 linkend="functional-dependencies"/>) are particularly troublesome.
3587 It is tempting to introduce type variables in the context that do not appear in
3588 the head, something that is excluded by the normal rules. For example:
3590 class HasConverter a b | a -> b where
3593 data Foo a = MkFoo a
3595 instance (HasConverter a b,Show b) => Show (Foo a) where
3596 show (MkFoo value) = show (convert value)
3598 This is dangerous territory, however. Here, for example, is a program that would make the
3603 instance F [a] [[a]]
3604 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3606 Similarly, it can be tempting to lift the coverage condition:
3608 class Mul a b c | a b -> c where
3609 (.*.) :: a -> b -> c
3611 instance Mul Int Int Int where (.*.) = (*)
3612 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3613 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3615 The third instance declaration does not obey the coverage condition;
3616 and indeed the (somewhat strange) definition:
3618 f = \ b x y -> if b then x .*. [y] else y
3620 makes instance inference go into a loop, because it requires the constraint
3621 <literal>(Mul a [b] b)</literal>.
3624 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3625 the experimental flag <option>-XUndecidableInstances</option>
3626 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3627 both the Paterson Conditions and the Coverage Condition
3628 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3629 fixed-depth recursion stack. If you exceed the stack depth you get a
3630 sort of backtrace, and the opportunity to increase the stack depth
3631 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3637 <sect3 id="instance-overlap">
3638 <title>Overlapping instances</title>
3640 In general, <emphasis>GHC requires that that it be unambiguous which instance
3642 should be used to resolve a type-class constraint</emphasis>. This behaviour
3643 can be modified by two flags: <option>-XOverlappingInstances</option>
3644 <indexterm><primary>-XOverlappingInstances
3645 </primary></indexterm>
3646 and <option>-XIncoherentInstances</option>
3647 <indexterm><primary>-XIncoherentInstances
3648 </primary></indexterm>, as this section discusses. Both these
3649 flags are dynamic flags, and can be set on a per-module basis, using
3650 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3652 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3653 it tries to match every instance declaration against the
3655 by instantiating the head of the instance declaration. For example, consider
3658 instance context1 => C Int a where ... -- (A)
3659 instance context2 => C a Bool where ... -- (B)
3660 instance context3 => C Int [a] where ... -- (C)
3661 instance context4 => C Int [Int] where ... -- (D)
3663 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3664 but (C) and (D) do not. When matching, GHC takes
3665 no account of the context of the instance declaration
3666 (<literal>context1</literal> etc).
3667 GHC's default behaviour is that <emphasis>exactly one instance must match the
3668 constraint it is trying to resolve</emphasis>.
3669 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3670 including both declarations (A) and (B), say); an error is only reported if a
3671 particular constraint matches more than one.
3675 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3676 more than one instance to match, provided there is a most specific one. For
3677 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3678 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3679 most-specific match, the program is rejected.
3682 However, GHC is conservative about committing to an overlapping instance. For example:
3687 Suppose that from the RHS of <literal>f</literal> we get the constraint
3688 <literal>C Int [b]</literal>. But
3689 GHC does not commit to instance (C), because in a particular
3690 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3691 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3692 So GHC rejects the program.
3693 (If you add the flag <option>-XIncoherentInstances</option>,
3694 GHC will instead pick (C), without complaining about
3695 the problem of subsequent instantiations.)
3698 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3699 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3700 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3701 it instead. In this case, GHC will refrain from
3702 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3703 as before) but, rather than rejecting the program, it will infer the type
3705 f :: C Int [b] => [b] -> [b]
3707 That postpones the question of which instance to pick to the
3708 call site for <literal>f</literal>
3709 by which time more is known about the type <literal>b</literal>.
3710 You can write this type signature yourself if you use the
3711 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3715 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3719 instance Foo [b] where
3722 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3723 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3724 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3725 declaration. The solution is to postpone the choice by adding the constraint to the context
3726 of the instance declaration, thus:
3728 instance C Int [b] => Foo [b] where
3731 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3734 The willingness to be overlapped or incoherent is a property of
3735 the <emphasis>instance declaration</emphasis> itself, controlled by the
3736 presence or otherwise of the <option>-XOverlappingInstances</option>
3737 and <option>-XIncoherentInstances</option> flags when that module is
3738 being defined. Neither flag is required in a module that imports and uses the
3739 instance declaration. Specifically, during the lookup process:
3742 An instance declaration is ignored during the lookup process if (a) a more specific
3743 match is found, and (b) the instance declaration was compiled with
3744 <option>-XOverlappingInstances</option>. The flag setting for the
3745 more-specific instance does not matter.
3748 Suppose an instance declaration does not match the constraint being looked up, but
3749 does unify with it, so that it might match when the constraint is further
3750 instantiated. Usually GHC will regard this as a reason for not committing to
3751 some other constraint. But if the instance declaration was compiled with
3752 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3753 check for that declaration.
3756 These rules make it possible for a library author to design a library that relies on
3757 overlapping instances without the library client having to know.
3760 If an instance declaration is compiled without
3761 <option>-XOverlappingInstances</option>,
3762 then that instance can never be overlapped. This could perhaps be
3763 inconvenient. Perhaps the rule should instead say that the
3764 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3765 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3766 at a usage site should be permitted regardless of how the instance declarations
3767 are compiled, if the <option>-XOverlappingInstances</option> flag is
3768 used at the usage site. (Mind you, the exact usage site can occasionally be
3769 hard to pin down.) We are interested to receive feedback on these points.
3771 <para>The <option>-XIncoherentInstances</option> flag implies the
3772 <option>-XOverlappingInstances</option> flag, but not vice versa.
3780 <sect2 id="overloaded-strings">
3781 <title>Overloaded string literals
3785 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3786 string literal has type <literal>String</literal>, but with overloaded string
3787 literals enabled (with <literal>-XOverloadedStrings</literal>)
3788 a string literal has type <literal>(IsString a) => a</literal>.
3791 This means that the usual string syntax can be used, e.g., for packed strings
3792 and other variations of string like types. String literals behave very much
3793 like integer literals, i.e., they can be used in both expressions and patterns.
3794 If used in a pattern the literal with be replaced by an equality test, in the same
3795 way as an integer literal is.
3798 The class <literal>IsString</literal> is defined as:
3800 class IsString a where
3801 fromString :: String -> a
3803 The only predefined instance is the obvious one to make strings work as usual:
3805 instance IsString [Char] where
3808 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3809 it explicitly (for example, to give an instance declaration for it), you can import it
3810 from module <literal>GHC.Exts</literal>.
3813 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3817 Each type in a default declaration must be an
3818 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3822 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3823 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3824 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3825 <emphasis>or</emphasis> <literal>IsString</literal>.
3834 import GHC.Exts( IsString(..) )
3836 newtype MyString = MyString String deriving (Eq, Show)
3837 instance IsString MyString where
3838 fromString = MyString
3840 greet :: MyString -> MyString
3841 greet "hello" = "world"
3845 print $ greet "hello"
3846 print $ greet "fool"
3850 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3851 to work since it gets translated into an equality comparison.
3857 <sect1 id="type-families">
3858 <title>Type families</title>
3861 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3862 facilitate type-level
3863 programming. Type families are a generalisation of <firstterm>associated
3864 data types</firstterm>
3865 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3866 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3867 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3868 Symposium on Principles of Programming Languages (POPL'05)”, pages
3869 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3870 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3871 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3873 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3874 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3875 themselves are described in the paper “<ulink
3876 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3877 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3879 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3880 13th ACM SIGPLAN International Conference on Functional
3881 Programming”, ACM Press, pages 51-62, 2008. Type families
3882 essentially provide type-indexed data types and named functions on types,
3883 which are useful for generic programming and highly parameterised library
3884 interfaces as well as interfaces with enhanced static information, much like
3885 dependent types. They might also be regarded as an alternative to functional
3886 dependencies, but provide a more functional style of type-level programming
3887 than the relational style of functional dependencies.
3890 Indexed type families, or type families for short, are type constructors that
3891 represent sets of types. Set members are denoted by supplying the type family
3892 constructor with type parameters, which are called <firstterm>type
3893 indices</firstterm>. The
3894 difference between vanilla parametrised type constructors and family
3895 constructors is much like between parametrically polymorphic functions and
3896 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3897 behave the same at all type instances, whereas class methods can change their
3898 behaviour in dependence on the class type parameters. Similarly, vanilla type
3899 constructors imply the same data representation for all type instances, but
3900 family constructors can have varying representation types for varying type
3904 Indexed type families come in two flavours: <firstterm>data
3905 families</firstterm> and <firstterm>type synonym
3906 families</firstterm>. They are the indexed family variants of algebraic
3907 data types and type synonyms, respectively. The instances of data families
3908 can be data types and newtypes.
3911 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3912 Additional information on the use of type families in GHC is available on
3913 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3914 Haskell wiki page on type families</ulink>.
3917 <sect2 id="data-families">
3918 <title>Data families</title>
3921 Data families appear in two flavours: (1) they can be defined on the
3923 or (2) they can appear inside type classes (in which case they are known as
3924 associated types). The former is the more general variant, as it lacks the
3925 requirement for the type-indexes to coincide with the class
3926 parameters. However, the latter can lead to more clearly structured code and
3927 compiler warnings if some type instances were - possibly accidentally -
3928 omitted. In the following, we always discuss the general toplevel form first
3929 and then cover the additional constraints placed on associated types.
3932 <sect3 id="data-family-declarations">
3933 <title>Data family declarations</title>
3936 Indexed data families are introduced by a signature, such as
3938 data family GMap k :: * -> *
3940 The special <literal>family</literal> distinguishes family from standard
3941 data declarations. The result kind annotation is optional and, as
3942 usual, defaults to <literal>*</literal> if omitted. An example is
3946 Named arguments can also be given explicit kind signatures if needed.
3948 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3949 declarations] named arguments are entirely optional, so that we can
3950 declare <literal>Array</literal> alternatively with
3952 data family Array :: * -> *
3956 <sect4 id="assoc-data-family-decl">
3957 <title>Associated data family declarations</title>
3959 When a data family is declared as part of a type class, we drop
3960 the <literal>family</literal> special. The <literal>GMap</literal>
3961 declaration takes the following form
3963 class GMapKey k where
3964 data GMap k :: * -> *
3967 In contrast to toplevel declarations, named arguments must be used for
3968 all type parameters that are to be used as type-indexes. Moreover,
3969 the argument names must be class parameters. Each class parameter may
3970 only be used at most once per associated type, but some may be omitted
3971 and they may be in an order other than in the class head. Hence, the
3972 following contrived example is admissible:
3981 <sect3 id="data-instance-declarations">
3982 <title>Data instance declarations</title>
3985 Instance declarations of data and newtype families are very similar to
3986 standard data and newtype declarations. The only two differences are
3987 that the keyword <literal>data</literal> or <literal>newtype</literal>
3988 is followed by <literal>instance</literal> and that some or all of the
3989 type arguments can be non-variable types, but may not contain forall
3990 types or type synonym families. However, data families are generally
3991 allowed in type parameters, and type synonyms are allowed as long as
3992 they are fully applied and expand to a type that is itself admissible -
3993 exactly as this is required for occurrences of type synonyms in class
3994 instance parameters. For example, the <literal>Either</literal>
3995 instance for <literal>GMap</literal> is
3997 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3999 In this example, the declaration has only one variant. In general, it
4003 Data and newtype instance declarations are only permitted when an
4004 appropriate family declaration is in scope - just as a class instance declaratoin
4005 requires the class declaration to be visible. Moreover, each instance
4006 declaration has to conform to the kind determined by its family
4007 declaration. This implies that the number of parameters of an instance
4008 declaration matches the arity determined by the kind of the family.
4011 A data family instance declaration can use the full exprssiveness of
4012 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4014 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4015 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4016 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4019 data instance T Int = T1 Int | T2 Bool
4020 newtype instance T Char = TC Bool
4023 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4024 and indeed can define a GADT. For example:
4027 data instance G [a] b where
4028 G1 :: c -> G [Int] b
4032 <listitem><para> You can use a <literal>deriving</literal> clause on a
4033 <literal>data instance</literal> or <literal>newtype instance</literal>
4040 Even if type families are defined as toplevel declarations, functions
4041 that perform different computations for different family instances may still
4042 need to be defined as methods of type classes. In particular, the
4043 following is not possible:
4046 data instance T Int = A
4047 data instance T Char = B
4049 foo A = 1 -- WRONG: These two equations together...
4050 foo B = 2 -- ...will produce a type error.
4052 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4056 instance Foo Int where
4058 instance Foo Char where
4061 (Given the functionality provided by GADTs (Generalised Algebraic Data
4062 Types), it might seem as if a definition, such as the above, should be
4063 feasible. However, type families are - in contrast to GADTs - are
4064 <emphasis>open;</emphasis> i.e., new instances can always be added,
4066 modules. Supporting pattern matching across different data instances
4067 would require a form of extensible case construct.)
4070 <sect4 id="assoc-data-inst">
4071 <title>Associated data instances</title>
4073 When an associated data family instance is declared within a type
4074 class instance, we drop the <literal>instance</literal> keyword in the
4075 family instance. So, the <literal>Either</literal> instance
4076 for <literal>GMap</literal> becomes:
4078 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4079 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4082 The most important point about associated family instances is that the
4083 type indexes corresponding to class parameters must be identical to
4084 the type given in the instance head; here this is the first argument
4085 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4086 which coincides with the only class parameter. Any parameters to the
4087 family constructor that do not correspond to class parameters, need to
4088 be variables in every instance; here this is the
4089 variable <literal>v</literal>.
4092 Instances for an associated family can only appear as part of
4093 instances declarations of the class in which the family was declared -
4094 just as with the equations of the methods of a class. Also in
4095 correspondence to how methods are handled, declarations of associated
4096 types can be omitted in class instances. If an associated family
4097 instance is omitted, the corresponding instance type is not inhabited;
4098 i.e., only diverging expressions, such
4099 as <literal>undefined</literal>, can assume the type.
4103 <sect4 id="scoping-class-params">
4104 <title>Scoping of class parameters</title>
4106 In the case of multi-parameter type classes, the visibility of class
4107 parameters in the right-hand side of associated family instances
4108 depends <emphasis>solely</emphasis> on the parameters of the data
4109 family. As an example, consider the simple class declaration
4114 Only one of the two class parameters is a parameter to the data
4115 family. Hence, the following instance declaration is invalid:
4117 instance C [c] d where
4118 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4120 Here, the right-hand side of the data instance mentions the type
4121 variable <literal>d</literal> that does not occur in its left-hand
4122 side. We cannot admit such data instances as they would compromise
4127 <sect4 id="family-class-inst">
4128 <title>Type class instances of family instances</title>
4130 Type class instances of instances of data families can be defined as
4131 usual, and in particular data instance declarations can
4132 have <literal>deriving</literal> clauses. For example, we can write
4134 data GMap () v = GMapUnit (Maybe v)
4137 which implicitly defines an instance of the form
4139 instance Show v => Show (GMap () v) where ...
4143 Note that class instances are always for
4144 particular <emphasis>instances</emphasis> of a data family and never
4145 for an entire family as a whole. This is for essentially the same
4146 reasons that we cannot define a toplevel function that performs
4147 pattern matching on the data constructors
4148 of <emphasis>different</emphasis> instances of a single type family.
4149 It would require a form of extensible case construct.
4153 <sect4 id="data-family-overlap">
4154 <title>Overlap of data instances</title>
4156 The instance declarations of a data family used in a single program
4157 may not overlap at all, independent of whether they are associated or
4158 not. In contrast to type class instances, this is not only a matter
4159 of consistency, but one of type safety.
4165 <sect3 id="data-family-import-export">
4166 <title>Import and export</title>
4169 The association of data constructors with type families is more dynamic
4170 than that is the case with standard data and newtype declarations. In
4171 the standard case, the notation <literal>T(..)</literal> in an import or
4172 export list denotes the type constructor and all the data constructors
4173 introduced in its declaration. However, a family declaration never
4174 introduces any data constructors; instead, data constructors are
4175 introduced by family instances. As a result, which data constructors
4176 are associated with a type family depends on the currently visible
4177 instance declarations for that family. Consequently, an import or
4178 export item of the form <literal>T(..)</literal> denotes the family
4179 constructor and all currently visible data constructors - in the case of
4180 an export item, these may be either imported or defined in the current
4181 module. The treatment of import and export items that explicitly list
4182 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4186 <sect4 id="data-family-impexp-assoc">
4187 <title>Associated families</title>
4189 As expected, an import or export item of the
4190 form <literal>C(..)</literal> denotes all of the class' methods and
4191 associated types. However, when associated types are explicitly
4192 listed as subitems of a class, we need some new syntax, as uppercase
4193 identifiers as subitems are usually data constructors, not type
4194 constructors. To clarify that we denote types here, each associated
4195 type name needs to be prefixed by the keyword <literal>type</literal>.
4196 So for example, when explicitly listing the components of
4197 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4198 GMap, empty, lookup, insert)</literal>.
4202 <sect4 id="data-family-impexp-examples">
4203 <title>Examples</title>
4205 Assuming our running <literal>GMapKey</literal> class example, let us
4206 look at some export lists and their meaning:
4209 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4210 just the class name.</para>
4213 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4214 Exports the class, the associated type <literal>GMap</literal>
4216 functions <literal>empty</literal>, <literal>lookup</literal>,
4217 and <literal>insert</literal>. None of the data constructors is
4221 <para><literal>module GMap (GMapKey(..), GMap(..))
4222 where...</literal>: As before, but also exports all the data
4223 constructors <literal>GMapInt</literal>,
4224 <literal>GMapChar</literal>,
4225 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4226 and <literal>GMapUnit</literal>.</para>
4229 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4230 GMap(..)) where...</literal>: As before.</para>
4233 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4234 where...</literal>: As before.</para>
4239 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4240 both the class <literal>GMapKey</literal> as well as its associated
4241 type <literal>GMap</literal>. However, you cannot
4242 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4243 sub-component specifications cannot be nested. To
4244 specify <literal>GMap</literal>'s data constructors, you have to list
4249 <sect4 id="data-family-impexp-instances">
4250 <title>Instances</title>
4252 Family instances are implicitly exported, just like class instances.
4253 However, this applies only to the heads of instances, not to the data
4254 constructors an instance defines.
4262 <sect2 id="synonym-families">
4263 <title>Synonym families</title>
4266 Type families appear in two flavours: (1) they can be defined on the
4267 toplevel or (2) they can appear inside type classes (in which case they
4268 are known as associated type synonyms). The former is the more general
4269 variant, as it lacks the requirement for the type-indexes to coincide with
4270 the class parameters. However, the latter can lead to more clearly
4271 structured code and compiler warnings if some type instances were -
4272 possibly accidentally - omitted. In the following, we always discuss the
4273 general toplevel form first and then cover the additional constraints
4274 placed on associated types.
4277 <sect3 id="type-family-declarations">
4278 <title>Type family declarations</title>
4281 Indexed type families are introduced by a signature, such as
4283 type family Elem c :: *
4285 The special <literal>family</literal> distinguishes family from standard
4286 type declarations. The result kind annotation is optional and, as
4287 usual, defaults to <literal>*</literal> if omitted. An example is
4291 Parameters can also be given explicit kind signatures if needed. We
4292 call the number of parameters in a type family declaration, the family's
4293 arity, and all applications of a type family must be fully saturated
4294 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4295 and it implies that the kind of a type family is not sufficient to
4296 determine a family's arity, and hence in general, also insufficient to
4297 determine whether a type family application is well formed. As an
4298 example, consider the following declaration:
4300 type family F a b :: * -> * -- F's arity is 2,
4301 -- although it's overall kind is * -> * -> * -> *
4303 Given this declaration the following are examples of well-formed and
4306 F Char [Int] -- OK! Kind: * -> *
4307 F Char [Int] Bool -- OK! Kind: *
4308 F IO Bool -- WRONG: kind mismatch in the first argument
4309 F Bool -- WRONG: unsaturated application
4313 <sect4 id="assoc-type-family-decl">
4314 <title>Associated type family declarations</title>
4316 When a type family is declared as part of a type class, we drop
4317 the <literal>family</literal> special. The <literal>Elem</literal>
4318 declaration takes the following form
4320 class Collects ce where
4324 The argument names of the type family must be class parameters. Each
4325 class parameter may only be used at most once per associated type, but
4326 some may be omitted and they may be in an order other than in the
4327 class head. Hence, the following contrived example is admissible:
4332 These rules are exactly as for associated data families.
4337 <sect3 id="type-instance-declarations">
4338 <title>Type instance declarations</title>
4340 Instance declarations of type families are very similar to standard type
4341 synonym declarations. The only two differences are that the
4342 keyword <literal>type</literal> is followed
4343 by <literal>instance</literal> and that some or all of the type
4344 arguments can be non-variable types, but may not contain forall types or
4345 type synonym families. However, data families are generally allowed, and
4346 type synonyms are allowed as long as they are fully applied and expand
4347 to a type that is admissible - these are the exact same requirements as
4348 for data instances. For example, the <literal>[e]</literal> instance
4349 for <literal>Elem</literal> is
4351 type instance Elem [e] = e
4355 Type family instance declarations are only legitimate when an
4356 appropriate family declaration is in scope - just like class instances
4357 require the class declaration to be visible. Moreover, each instance
4358 declaration has to conform to the kind determined by its family
4359 declaration, and the number of type parameters in an instance
4360 declaration must match the number of type parameters in the family
4361 declaration. Finally, the right-hand side of a type instance must be a
4362 monotype (i.e., it may not include foralls) and after the expansion of
4363 all saturated vanilla type synonyms, no synonyms, except family synonyms
4364 may remain. Here are some examples of admissible and illegal type
4367 type family F a :: *
4368 type instance F [Int] = Int -- OK!
4369 type instance F String = Char -- OK!
4370 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4371 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4372 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4374 type family G a b :: * -> *
4375 type instance G Int = (,) -- WRONG: must be two type parameters
4376 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4380 <sect4 id="assoc-type-instance">
4381 <title>Associated type instance declarations</title>
4383 When an associated family instance is declared within a type class
4384 instance, we drop the <literal>instance</literal> keyword in the family
4385 instance. So, the <literal>[e]</literal> instance
4386 for <literal>Elem</literal> becomes:
4388 instance (Eq (Elem [e])) => Collects ([e]) where
4392 The most important point about associated family instances is that the
4393 type indexes corresponding to class parameters must be identical to the
4394 type given in the instance head; here this is <literal>[e]</literal>,
4395 which coincides with the only class parameter.
4398 Instances for an associated family can only appear as part of instances
4399 declarations of the class in which the family was declared - just as
4400 with the equations of the methods of a class. Also in correspondence to
4401 how methods are handled, declarations of associated types can be omitted
4402 in class instances. If an associated family instance is omitted, the
4403 corresponding instance type is not inhabited; i.e., only diverging
4404 expressions, such as <literal>undefined</literal>, can assume the type.
4408 <sect4 id="type-family-overlap">
4409 <title>Overlap of type synonym instances</title>
4411 The instance declarations of a type family used in a single program
4412 may only overlap if the right-hand sides of the overlapping instances
4413 coincide for the overlapping types. More formally, two instance
4414 declarations overlap if there is a substitution that makes the
4415 left-hand sides of the instances syntactically the same. Whenever
4416 that is the case, the right-hand sides of the instances must also be
4417 syntactically equal under the same substitution. This condition is
4418 independent of whether the type family is associated or not, and it is
4419 not only a matter of consistency, but one of type safety.
4422 Here are two example to illustrate the condition under which overlap
4425 type instance F (a, Int) = [a]
4426 type instance F (Int, b) = [b] -- overlap permitted
4428 type instance G (a, Int) = [a]
4429 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4434 <sect4 id="type-family-decidability">
4435 <title>Decidability of type synonym instances</title>
4437 In order to guarantee that type inference in the presence of type
4438 families decidable, we need to place a number of additional
4439 restrictions on the formation of type instance declarations (c.f.,
4440 Definition 5 (Relaxed Conditions) of “<ulink
4441 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4442 Checking with Open Type Functions</ulink>”). Instance
4443 declarations have the general form
4445 type instance F t1 .. tn = t
4447 where we require that for every type family application <literal>(G s1
4448 .. sm)</literal> in <literal>t</literal>,
4451 <para><literal>s1 .. sm</literal> do not contain any type family
4452 constructors,</para>
4455 <para>the total number of symbols (data type constructors and type
4456 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4457 in <literal>t1 .. tn</literal>, and</para>
4460 <para>for every type
4461 variable <literal>a</literal>, <literal>a</literal> occurs
4462 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4463 .. tn</literal>.</para>
4466 These restrictions are easily verified and ensure termination of type
4467 inference. However, they are not sufficient to guarantee completeness
4468 of type inference in the presence of, so called, ''loopy equalities'',
4469 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4470 a type variable is underneath a family application and data
4471 constructor application - see the above mentioned paper for details.
4474 If the option <option>-XUndecidableInstances</option> is passed to the
4475 compiler, the above restrictions are not enforced and it is on the
4476 programmer to ensure termination of the normalisation of type families
4477 during type inference.
4482 <sect3 id-="equality-constraints">
4483 <title>Equality constraints</title>
4485 Type context can include equality constraints of the form <literal>t1 ~
4486 t2</literal>, which denote that the types <literal>t1</literal>
4487 and <literal>t2</literal> need to be the same. In the presence of type
4488 families, whether two types are equal cannot generally be decided
4489 locally. Hence, the contexts of function signatures may include
4490 equality constraints, as in the following example:
4492 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4494 where we require that the element type of <literal>c1</literal>
4495 and <literal>c2</literal> are the same. In general, the
4496 types <literal>t1</literal> and <literal>t2</literal> of an equality
4497 constraint may be arbitrary monotypes; i.e., they may not contain any
4498 quantifiers, independent of whether higher-rank types are otherwise
4502 Equality constraints can also appear in class and instance contexts.
4503 The former enable a simple translation of programs using functional
4504 dependencies into programs using family synonyms instead. The general
4505 idea is to rewrite a class declaration of the form
4507 class C a b | a -> b
4511 class (F a ~ b) => C a b where
4514 That is, we represent every functional dependency (FD) <literal>a1 .. an
4515 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4516 superclass context equality <literal>F a1 .. an ~ b</literal>,
4517 essentially giving a name to the functional dependency. In class
4518 instances, we define the type instances of FD families in accordance
4519 with the class head. Method signatures are not affected by that
4523 NB: Equalities in superclass contexts are not fully implemented in
4528 <sect3 id-="ty-fams-in-instances">
4529 <title>Type families and instance declarations</title>
4530 <para>Type families require us to extend the rules for
4531 the form of instance heads, which are given
4532 in <xref linkend="flexible-instance-head"/>.
4535 <listitem><para>Data type families may appear in an instance head</para></listitem>
4536 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4538 The reason for the latter restriction is that there is no way to check for. Consider
4541 type instance F Bool = Int
4548 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4549 The situation is especially bad because the type instance for <literal>F Bool</literal>
4550 might be in another module, or even in a module that is not yet written.
4557 <sect1 id="other-type-extensions">
4558 <title>Other type system extensions</title>
4560 <sect2 id="type-restrictions">
4561 <title>Type signatures</title>
4563 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4565 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4566 that the type-class constraints in a type signature must have the
4567 form <emphasis>(class type-variable)</emphasis> or
4568 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4569 With <option>-XFlexibleContexts</option>
4570 these type signatures are perfectly OK
4573 g :: Ord (T a ()) => ...
4577 GHC imposes the following restrictions on the constraints in a type signature.
4581 forall tv1..tvn (c1, ...,cn) => type
4584 (Here, we write the "foralls" explicitly, although the Haskell source
4585 language omits them; in Haskell 98, all the free type variables of an
4586 explicit source-language type signature are universally quantified,
4587 except for the class type variables in a class declaration. However,
4588 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4597 <emphasis>Each universally quantified type variable
4598 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4600 A type variable <literal>a</literal> is "reachable" if it appears
4601 in the same constraint as either a type variable free in
4602 <literal>type</literal>, or another reachable type variable.
4603 A value with a type that does not obey
4604 this reachability restriction cannot be used without introducing
4605 ambiguity; that is why the type is rejected.
4606 Here, for example, is an illegal type:
4610 forall a. Eq a => Int
4614 When a value with this type was used, the constraint <literal>Eq tv</literal>
4615 would be introduced where <literal>tv</literal> is a fresh type variable, and
4616 (in the dictionary-translation implementation) the value would be
4617 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4618 can never know which instance of <literal>Eq</literal> to use because we never
4619 get any more information about <literal>tv</literal>.
4623 that the reachability condition is weaker than saying that <literal>a</literal> is
4624 functionally dependent on a type variable free in
4625 <literal>type</literal> (see <xref
4626 linkend="functional-dependencies"/>). The reason for this is there
4627 might be a "hidden" dependency, in a superclass perhaps. So
4628 "reachable" is a conservative approximation to "functionally dependent".
4629 For example, consider:
4631 class C a b | a -> b where ...
4632 class C a b => D a b where ...
4633 f :: forall a b. D a b => a -> a
4635 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4636 but that is not immediately apparent from <literal>f</literal>'s type.
4642 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4643 universally quantified type variables <literal>tvi</literal></emphasis>.
4645 For example, this type is OK because <literal>C a b</literal> mentions the
4646 universally quantified type variable <literal>b</literal>:
4650 forall a. C a b => burble
4654 The next type is illegal because the constraint <literal>Eq b</literal> does not
4655 mention <literal>a</literal>:
4659 forall a. Eq b => burble
4663 The reason for this restriction is milder than the other one. The
4664 excluded types are never useful or necessary (because the offending
4665 context doesn't need to be witnessed at this point; it can be floated
4666 out). Furthermore, floating them out increases sharing. Lastly,
4667 excluding them is a conservative choice; it leaves a patch of
4668 territory free in case we need it later.
4682 <sect2 id="implicit-parameters">
4683 <title>Implicit parameters</title>
4685 <para> Implicit parameters are implemented as described in
4686 "Implicit parameters: dynamic scoping with static types",
4687 J Lewis, MB Shields, E Meijer, J Launchbury,
4688 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4692 <para>(Most of the following, still rather incomplete, documentation is
4693 due to Jeff Lewis.)</para>
4695 <para>Implicit parameter support is enabled with the option
4696 <option>-XImplicitParams</option>.</para>
4699 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4700 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4701 context. In Haskell, all variables are statically bound. Dynamic
4702 binding of variables is a notion that goes back to Lisp, but was later
4703 discarded in more modern incarnations, such as Scheme. Dynamic binding
4704 can be very confusing in an untyped language, and unfortunately, typed
4705 languages, in particular Hindley-Milner typed languages like Haskell,
4706 only support static scoping of variables.
4709 However, by a simple extension to the type class system of Haskell, we
4710 can support dynamic binding. Basically, we express the use of a
4711 dynamically bound variable as a constraint on the type. These
4712 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4713 function uses a dynamically-bound variable <literal>?x</literal>
4714 of type <literal>t'</literal>". For
4715 example, the following expresses the type of a sort function,
4716 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4718 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4720 The dynamic binding constraints are just a new form of predicate in the type class system.
4723 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4724 where <literal>x</literal> is
4725 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4726 Use of this construct also introduces a new
4727 dynamic-binding constraint in the type of the expression.
4728 For example, the following definition
4729 shows how we can define an implicitly parameterized sort function in
4730 terms of an explicitly parameterized <literal>sortBy</literal> function:
4732 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4734 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4740 <title>Implicit-parameter type constraints</title>
4742 Dynamic binding constraints behave just like other type class
4743 constraints in that they are automatically propagated. Thus, when a
4744 function is used, its implicit parameters are inherited by the
4745 function that called it. For example, our <literal>sort</literal> function might be used
4746 to pick out the least value in a list:
4748 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4749 least xs = head (sort xs)
4751 Without lifting a finger, the <literal>?cmp</literal> parameter is
4752 propagated to become a parameter of <literal>least</literal> as well. With explicit
4753 parameters, the default is that parameters must always be explicit
4754 propagated. With implicit parameters, the default is to always
4758 An implicit-parameter type constraint differs from other type class constraints in the
4759 following way: All uses of a particular implicit parameter must have
4760 the same type. This means that the type of <literal>(?x, ?x)</literal>
4761 is <literal>(?x::a) => (a,a)</literal>, and not
4762 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4766 <para> You can't have an implicit parameter in the context of a class or instance
4767 declaration. For example, both these declarations are illegal:
4769 class (?x::Int) => C a where ...
4770 instance (?x::a) => Foo [a] where ...
4772 Reason: exactly which implicit parameter you pick up depends on exactly where
4773 you invoke a function. But the ``invocation'' of instance declarations is done
4774 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4775 Easiest thing is to outlaw the offending types.</para>
4777 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4779 f :: (?x :: [a]) => Int -> Int
4782 g :: (Read a, Show a) => String -> String
4785 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4786 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4787 quite unambiguous, and fixes the type <literal>a</literal>.
4792 <title>Implicit-parameter bindings</title>
4795 An implicit parameter is <emphasis>bound</emphasis> using the standard
4796 <literal>let</literal> or <literal>where</literal> binding forms.
4797 For example, we define the <literal>min</literal> function by binding
4798 <literal>cmp</literal>.
4801 min = let ?cmp = (<=) in least
4805 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4806 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4807 (including in a list comprehension, or do-notation, or pattern guards),
4808 or a <literal>where</literal> clause.
4809 Note the following points:
4812 An implicit-parameter binding group must be a
4813 collection of simple bindings to implicit-style variables (no
4814 function-style bindings, and no type signatures); these bindings are
4815 neither polymorphic or recursive.
4818 You may not mix implicit-parameter bindings with ordinary bindings in a
4819 single <literal>let</literal>
4820 expression; use two nested <literal>let</literal>s instead.
4821 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4825 You may put multiple implicit-parameter bindings in a
4826 single binding group; but they are <emphasis>not</emphasis> treated
4827 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4828 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4829 parameter. The bindings are not nested, and may be re-ordered without changing
4830 the meaning of the program.
4831 For example, consider:
4833 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4835 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4836 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4838 f :: (?x::Int) => Int -> Int
4846 <sect3><title>Implicit parameters and polymorphic recursion</title>
4849 Consider these two definitions:
4852 len1 xs = let ?acc = 0 in len_acc1 xs
4855 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4860 len2 xs = let ?acc = 0 in len_acc2 xs
4862 len_acc2 :: (?acc :: Int) => [a] -> Int
4864 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4866 The only difference between the two groups is that in the second group
4867 <literal>len_acc</literal> is given a type signature.
4868 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4869 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4870 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4871 has a type signature, the recursive call is made to the
4872 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4873 as an implicit parameter. So we get the following results in GHCi:
4880 Adding a type signature dramatically changes the result! This is a rather
4881 counter-intuitive phenomenon, worth watching out for.
4885 <sect3><title>Implicit parameters and monomorphism</title>
4887 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4888 Haskell Report) to implicit parameters. For example, consider:
4896 Since the binding for <literal>y</literal> falls under the Monomorphism
4897 Restriction it is not generalised, so the type of <literal>y</literal> is
4898 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4899 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4900 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4901 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4902 <literal>y</literal> in the body of the <literal>let</literal> will see the
4903 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4904 <literal>14</literal>.
4909 <!-- ======================= COMMENTED OUT ========================
4911 We intend to remove linear implicit parameters, so I'm at least removing
4912 them from the 6.6 user manual
4914 <sect2 id="linear-implicit-parameters">
4915 <title>Linear implicit parameters</title>
4917 Linear implicit parameters are an idea developed by Koen Claessen,
4918 Mark Shields, and Simon PJ. They address the long-standing
4919 problem that monads seem over-kill for certain sorts of problem, notably:
4922 <listitem> <para> distributing a supply of unique names </para> </listitem>
4923 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4924 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4928 Linear implicit parameters are just like ordinary implicit parameters,
4929 except that they are "linear"; that is, they cannot be copied, and
4930 must be explicitly "split" instead. Linear implicit parameters are
4931 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4932 (The '/' in the '%' suggests the split!)
4937 import GHC.Exts( Splittable )
4939 data NameSupply = ...
4941 splitNS :: NameSupply -> (NameSupply, NameSupply)
4942 newName :: NameSupply -> Name
4944 instance Splittable NameSupply where
4948 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4949 f env (Lam x e) = Lam x' (f env e)
4952 env' = extend env x x'
4953 ...more equations for f...
4955 Notice that the implicit parameter %ns is consumed
4957 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4958 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4962 So the translation done by the type checker makes
4963 the parameter explicit:
4965 f :: NameSupply -> Env -> Expr -> Expr
4966 f ns env (Lam x e) = Lam x' (f ns1 env e)
4968 (ns1,ns2) = splitNS ns
4970 env = extend env x x'
4972 Notice the call to 'split' introduced by the type checker.
4973 How did it know to use 'splitNS'? Because what it really did
4974 was to introduce a call to the overloaded function 'split',
4975 defined by the class <literal>Splittable</literal>:
4977 class Splittable a where
4980 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4981 split for name supplies. But we can simply write
4987 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4989 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4990 <literal>GHC.Exts</literal>.
4995 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4996 are entirely distinct implicit parameters: you
4997 can use them together and they won't interfere with each other. </para>
5000 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5002 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5003 in the context of a class or instance declaration. </para></listitem>
5007 <sect3><title>Warnings</title>
5010 The monomorphism restriction is even more important than usual.
5011 Consider the example above:
5013 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5014 f env (Lam x e) = Lam x' (f env e)
5017 env' = extend env x x'
5019 If we replaced the two occurrences of x' by (newName %ns), which is
5020 usually a harmless thing to do, we get:
5022 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5023 f env (Lam x e) = Lam (newName %ns) (f env e)
5025 env' = extend env x (newName %ns)
5027 But now the name supply is consumed in <emphasis>three</emphasis> places
5028 (the two calls to newName,and the recursive call to f), so
5029 the result is utterly different. Urk! We don't even have
5033 Well, this is an experimental change. With implicit
5034 parameters we have already lost beta reduction anyway, and
5035 (as John Launchbury puts it) we can't sensibly reason about
5036 Haskell programs without knowing their typing.
5041 <sect3><title>Recursive functions</title>
5042 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5045 foo :: %x::T => Int -> [Int]
5047 foo n = %x : foo (n-1)
5049 where T is some type in class Splittable.</para>
5051 Do you get a list of all the same T's or all different T's
5052 (assuming that split gives two distinct T's back)?
5054 If you supply the type signature, taking advantage of polymorphic
5055 recursion, you get what you'd probably expect. Here's the
5056 translated term, where the implicit param is made explicit:
5059 foo x n = let (x1,x2) = split x
5060 in x1 : foo x2 (n-1)
5062 But if you don't supply a type signature, GHC uses the Hindley
5063 Milner trick of using a single monomorphic instance of the function
5064 for the recursive calls. That is what makes Hindley Milner type inference
5065 work. So the translation becomes
5069 foom n = x : foom (n-1)
5073 Result: 'x' is not split, and you get a list of identical T's. So the
5074 semantics of the program depends on whether or not foo has a type signature.
5077 You may say that this is a good reason to dislike linear implicit parameters
5078 and you'd be right. That is why they are an experimental feature.
5084 ================ END OF Linear Implicit Parameters commented out -->
5086 <sect2 id="kinding">
5087 <title>Explicitly-kinded quantification</title>
5090 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5091 to give the kind explicitly as (machine-checked) documentation,
5092 just as it is nice to give a type signature for a function. On some occasions,
5093 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5094 John Hughes had to define the data type:
5096 data Set cxt a = Set [a]
5097 | Unused (cxt a -> ())
5099 The only use for the <literal>Unused</literal> constructor was to force the correct
5100 kind for the type variable <literal>cxt</literal>.
5103 GHC now instead allows you to specify the kind of a type variable directly, wherever
5104 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5107 This flag enables kind signatures in the following places:
5109 <listitem><para><literal>data</literal> declarations:
5111 data Set (cxt :: * -> *) a = Set [a]
5112 </screen></para></listitem>
5113 <listitem><para><literal>type</literal> declarations:
5115 type T (f :: * -> *) = f Int
5116 </screen></para></listitem>
5117 <listitem><para><literal>class</literal> declarations:
5119 class (Eq a) => C (f :: * -> *) a where ...
5120 </screen></para></listitem>
5121 <listitem><para><literal>forall</literal>'s in type signatures:
5123 f :: forall (cxt :: * -> *). Set cxt Int
5124 </screen></para></listitem>
5129 The parentheses are required. Some of the spaces are required too, to
5130 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5131 will get a parse error, because "<literal>::*->*</literal>" is a
5132 single lexeme in Haskell.
5136 As part of the same extension, you can put kind annotations in types
5139 f :: (Int :: *) -> Int
5140 g :: forall a. a -> (a :: *)
5144 atype ::= '(' ctype '::' kind ')
5146 The parentheses are required.
5151 <sect2 id="universal-quantification">
5152 <title>Arbitrary-rank polymorphism
5156 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5157 allows us to say exactly what this means. For example:
5165 g :: forall b. (b -> b)
5167 The two are treated identically.
5171 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5172 explicit universal quantification in
5174 For example, all the following types are legal:
5176 f1 :: forall a b. a -> b -> a
5177 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5179 f2 :: (forall a. a->a) -> Int -> Int
5180 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5182 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5184 f4 :: Int -> (forall a. a -> a)
5186 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5187 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5188 The <literal>forall</literal> makes explicit the universal quantification that
5189 is implicitly added by Haskell.
5192 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5193 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5194 shows, the polymorphic type on the left of the function arrow can be overloaded.
5197 The function <literal>f3</literal> has a rank-3 type;
5198 it has rank-2 types on the left of a function arrow.
5201 GHC has three flags to control higher-rank types:
5204 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5207 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5210 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5211 That is, you can nest <literal>forall</literal>s
5212 arbitrarily deep in function arrows.
5213 In particular, a forall-type (also called a "type scheme"),
5214 including an operational type class context, is legal:
5216 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5217 of a function arrow </para> </listitem>
5218 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5219 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5220 field type signatures.</para> </listitem>
5221 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5222 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5226 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5227 a type variable any more!
5236 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5237 the types of the constructor arguments. Here are several examples:
5243 data T a = T1 (forall b. b -> b -> b) a
5245 data MonadT m = MkMonad { return :: forall a. a -> m a,
5246 bind :: forall a b. m a -> (a -> m b) -> m b
5249 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5255 The constructors have rank-2 types:
5261 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5262 MkMonad :: forall m. (forall a. a -> m a)
5263 -> (forall a b. m a -> (a -> m b) -> m b)
5265 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5271 Notice that you don't need to use a <literal>forall</literal> if there's an
5272 explicit context. For example in the first argument of the
5273 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5274 prefixed to the argument type. The implicit <literal>forall</literal>
5275 quantifies all type variables that are not already in scope, and are
5276 mentioned in the type quantified over.
5280 As for type signatures, implicit quantification happens for non-overloaded
5281 types too. So if you write this:
5284 data T a = MkT (Either a b) (b -> b)
5287 it's just as if you had written this:
5290 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5293 That is, since the type variable <literal>b</literal> isn't in scope, it's
5294 implicitly universally quantified. (Arguably, it would be better
5295 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5296 where that is what is wanted. Feedback welcomed.)
5300 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5301 the constructor to suitable values, just as usual. For example,
5312 a3 = MkSwizzle reverse
5315 a4 = let r x = Just x
5322 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5323 mkTs f x y = [T1 f x, T1 f y]
5329 The type of the argument can, as usual, be more general than the type
5330 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5331 does not need the <literal>Ord</literal> constraint.)
5335 When you use pattern matching, the bound variables may now have
5336 polymorphic types. For example:
5342 f :: T a -> a -> (a, Char)
5343 f (T1 w k) x = (w k x, w 'c' 'd')
5345 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5346 g (MkSwizzle s) xs f = s (map f (s xs))
5348 h :: MonadT m -> [m a] -> m [a]
5349 h m [] = return m []
5350 h m (x:xs) = bind m x $ \y ->
5351 bind m (h m xs) $ \ys ->
5358 In the function <function>h</function> we use the record selectors <literal>return</literal>
5359 and <literal>bind</literal> to extract the polymorphic bind and return functions
5360 from the <literal>MonadT</literal> data structure, rather than using pattern
5366 <title>Type inference</title>
5369 In general, type inference for arbitrary-rank types is undecidable.
5370 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5371 to get a decidable algorithm by requiring some help from the programmer.
5372 We do not yet have a formal specification of "some help" but the rule is this:
5375 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5376 provides an explicit polymorphic type for x, or GHC's type inference will assume
5377 that x's type has no foralls in it</emphasis>.
5380 What does it mean to "provide" an explicit type for x? You can do that by
5381 giving a type signature for x directly, using a pattern type signature
5382 (<xref linkend="scoped-type-variables"/>), thus:
5384 \ f :: (forall a. a->a) -> (f True, f 'c')
5386 Alternatively, you can give a type signature to the enclosing
5387 context, which GHC can "push down" to find the type for the variable:
5389 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5391 Here the type signature on the expression can be pushed inwards
5392 to give a type signature for f. Similarly, and more commonly,
5393 one can give a type signature for the function itself:
5395 h :: (forall a. a->a) -> (Bool,Char)
5396 h f = (f True, f 'c')
5398 You don't need to give a type signature if the lambda bound variable
5399 is a constructor argument. Here is an example we saw earlier:
5401 f :: T a -> a -> (a, Char)
5402 f (T1 w k) x = (w k x, w 'c' 'd')
5404 Here we do not need to give a type signature to <literal>w</literal>, because
5405 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5412 <sect3 id="implicit-quant">
5413 <title>Implicit quantification</title>
5416 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5417 user-written types, if and only if there is no explicit <literal>forall</literal>,
5418 GHC finds all the type variables mentioned in the type that are not already
5419 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5423 f :: forall a. a -> a
5430 h :: forall b. a -> b -> b
5436 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5439 f :: (a -> a) -> Int
5441 f :: forall a. (a -> a) -> Int
5443 f :: (forall a. a -> a) -> Int
5446 g :: (Ord a => a -> a) -> Int
5447 -- MEANS the illegal type
5448 g :: forall a. (Ord a => a -> a) -> Int
5450 g :: (forall a. Ord a => a -> a) -> Int
5452 The latter produces an illegal type, which you might think is silly,
5453 but at least the rule is simple. If you want the latter type, you
5454 can write your for-alls explicitly. Indeed, doing so is strongly advised
5461 <sect2 id="impredicative-polymorphism">
5462 <title>Impredicative polymorphism
5464 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5465 enabled with <option>-XImpredicativeTypes</option>.
5467 that you can call a polymorphic function at a polymorphic type, and
5468 parameterise data structures over polymorphic types. For example:
5470 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5471 f (Just g) = Just (g [3], g "hello")
5474 Notice here that the <literal>Maybe</literal> type is parameterised by the
5475 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5478 <para>The technical details of this extension are described in the paper
5479 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5480 type inference for higher-rank types and impredicativity</ulink>,
5481 which appeared at ICFP 2006.
5485 <sect2 id="scoped-type-variables">
5486 <title>Lexically scoped type variables
5490 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5491 which some type signatures are simply impossible to write. For example:
5493 f :: forall a. [a] -> [a]
5499 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5500 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5501 The type variables bound by a <literal>forall</literal> scope over
5502 the entire definition of the accompanying value declaration.
5503 In this example, the type variable <literal>a</literal> scopes over the whole
5504 definition of <literal>f</literal>, including over
5505 the type signature for <varname>ys</varname>.
5506 In Haskell 98 it is not possible to declare
5507 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5508 it becomes possible to do so.
5510 <para>Lexically-scoped type variables are enabled by
5511 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5513 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5514 variables work, compared to earlier releases. Read this section
5518 <title>Overview</title>
5520 <para>The design follows the following principles
5522 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5523 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5524 design.)</para></listitem>
5525 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5526 type variables. This means that every programmer-written type signature
5527 (including one that contains free scoped type variables) denotes a
5528 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5529 checker, and no inference is involved.</para></listitem>
5530 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5531 changing the program.</para></listitem>
5535 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5537 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5538 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5539 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5540 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5544 In Haskell, a programmer-written type signature is implicitly quantified over
5545 its free type variables (<ulink
5546 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5548 of the Haskell Report).
5549 Lexically scoped type variables affect this implicit quantification rules
5550 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5551 quantified. For example, if type variable <literal>a</literal> is in scope,
5554 (e :: a -> a) means (e :: a -> a)
5555 (e :: b -> b) means (e :: forall b. b->b)
5556 (e :: a -> b) means (e :: forall b. a->b)
5564 <sect3 id="decl-type-sigs">
5565 <title>Declaration type signatures</title>
5566 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5567 quantification (using <literal>forall</literal>) brings into scope the
5568 explicitly-quantified
5569 type variables, in the definition of the named function. For example:
5571 f :: forall a. [a] -> [a]
5572 f (x:xs) = xs ++ [ x :: a ]
5574 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5575 the definition of "<literal>f</literal>".
5577 <para>This only happens if:
5579 <listitem><para> The quantification in <literal>f</literal>'s type
5580 signature is explicit. For example:
5583 g (x:xs) = xs ++ [ x :: a ]
5585 This program will be rejected, because "<literal>a</literal>" does not scope
5586 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5587 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5588 quantification rules.
5590 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5591 not a pattern binding.
5594 f1 :: forall a. [a] -> [a]
5595 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5597 f2 :: forall a. [a] -> [a]
5598 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5600 f3 :: forall a. [a] -> [a]
5601 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5603 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5604 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5605 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5606 the type signature brings <literal>a</literal> into scope.
5612 <sect3 id="exp-type-sigs">
5613 <title>Expression type signatures</title>
5615 <para>An expression type signature that has <emphasis>explicit</emphasis>
5616 quantification (using <literal>forall</literal>) brings into scope the
5617 explicitly-quantified
5618 type variables, in the annotated expression. For example:
5620 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5622 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5623 type variable <literal>s</literal> into scope, in the annotated expression
5624 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5629 <sect3 id="pattern-type-sigs">
5630 <title>Pattern type signatures</title>
5632 A type signature may occur in any pattern; this is a <emphasis>pattern type
5633 signature</emphasis>.
5636 -- f and g assume that 'a' is already in scope
5637 f = \(x::Int, y::a) -> x
5639 h ((x,y) :: (Int,Bool)) = (y,x)
5641 In the case where all the type variables in the pattern type signature are
5642 already in scope (i.e. bound by the enclosing context), matters are simple: the
5643 signature simply constrains the type of the pattern in the obvious way.
5646 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5647 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5648 that are already in scope. For example:
5650 f :: forall a. [a] -> (Int, [a])
5653 (ys::[a], n) = (reverse xs, length xs) -- OK
5654 zs::[a] = xs ++ ys -- OK
5656 Just (v::b) = ... -- Not OK; b is not in scope
5658 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5659 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5663 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5664 type signature may mention a type variable that is not in scope; in this case,
5665 <emphasis>the signature brings that type variable into scope</emphasis>.
5666 This is particularly important for existential data constructors. For example:
5668 data T = forall a. MkT [a]
5671 k (MkT [t::a]) = MkT t3
5675 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5676 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5677 because it is bound by the pattern match. GHC's rule is that in this situation
5678 (and only then), a pattern type signature can mention a type variable that is
5679 not already in scope; the effect is to bring it into scope, standing for the
5680 existentially-bound type variable.
5683 When a pattern type signature binds a type variable in this way, GHC insists that the
5684 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5685 This means that any user-written type signature always stands for a completely known type.
5688 If all this seems a little odd, we think so too. But we must have
5689 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5690 could not name existentially-bound type variables in subsequent type signatures.
5693 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5694 signature is allowed to mention a lexical variable that is not already in
5696 For example, both <literal>f</literal> and <literal>g</literal> would be
5697 illegal if <literal>a</literal> was not already in scope.
5703 <!-- ==================== Commented out part about result type signatures
5705 <sect3 id="result-type-sigs">
5706 <title>Result type signatures</title>
5709 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5712 {- f assumes that 'a' is already in scope -}
5713 f x y :: [a] = [x,y,x]
5715 g = \ x :: [Int] -> [3,4]
5717 h :: forall a. [a] -> a
5721 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5722 the result of the function. Similarly, the body of the lambda in the RHS of
5723 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5724 alternative in <literal>h</literal> is <literal>a</literal>.
5726 <para> A result type signature never brings new type variables into scope.</para>
5728 There are a couple of syntactic wrinkles. First, notice that all three
5729 examples would parse quite differently with parentheses:
5731 {- f assumes that 'a' is already in scope -}
5732 f x (y :: [a]) = [x,y,x]
5734 g = \ (x :: [Int]) -> [3,4]
5736 h :: forall a. [a] -> a
5740 Now the signature is on the <emphasis>pattern</emphasis>; and
5741 <literal>h</literal> would certainly be ill-typed (since the pattern
5742 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5744 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5745 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5746 token or a parenthesised type of some sort). To see why,
5747 consider how one would parse this:
5756 <sect3 id="cls-inst-scoped-tyvars">
5757 <title>Class and instance declarations</title>
5760 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5761 scope over the methods defined in the <literal>where</literal> part. For example:
5779 <sect2 id="typing-binds">
5780 <title>Generalised typing of mutually recursive bindings</title>
5783 The Haskell Report specifies that a group of bindings (at top level, or in a
5784 <literal>let</literal> or <literal>where</literal>) should be sorted into
5785 strongly-connected components, and then type-checked in dependency order
5786 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5787 Report, Section 4.5.1</ulink>).
5788 As each group is type-checked, any binders of the group that
5790 an explicit type signature are put in the type environment with the specified
5792 and all others are monomorphic until the group is generalised
5793 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5796 <para>Following a suggestion of Mark Jones, in his paper
5797 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5799 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5801 <emphasis>the dependency analysis ignores references to variables that have an explicit
5802 type signature</emphasis>.
5803 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5804 typecheck. For example, consider:
5806 f :: Eq a => a -> Bool
5807 f x = (x == x) || g True || g "Yes"
5809 g y = (y <= y) || f True
5811 This is rejected by Haskell 98, but under Jones's scheme the definition for
5812 <literal>g</literal> is typechecked first, separately from that for
5813 <literal>f</literal>,
5814 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5815 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5816 type is generalised, to get
5818 g :: Ord a => a -> Bool
5820 Now, the definition for <literal>f</literal> is typechecked, with this type for
5821 <literal>g</literal> in the type environment.
5825 The same refined dependency analysis also allows the type signatures of
5826 mutually-recursive functions to have different contexts, something that is illegal in
5827 Haskell 98 (Section 4.5.2, last sentence). With
5828 <option>-XRelaxedPolyRec</option>
5829 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5830 type signatures; in practice this means that only variables bound by the same
5831 pattern binding must have the same context. For example, this is fine:
5833 f :: Eq a => a -> Bool
5834 f x = (x == x) || g True
5836 g :: Ord a => a -> Bool
5837 g y = (y <= y) || f True
5843 <!-- ==================== End of type system extensions ================= -->
5845 <!-- ====================== TEMPLATE HASKELL ======================= -->
5847 <sect1 id="template-haskell">
5848 <title>Template Haskell</title>
5850 <para>Template Haskell allows you to do compile-time meta-programming in
5853 the main technical innovations is discussed in "<ulink
5854 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5855 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5858 There is a Wiki page about
5859 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5860 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5864 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5865 Haskell library reference material</ulink>
5866 (look for module <literal>Language.Haskell.TH</literal>).
5867 Many changes to the original design are described in
5868 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5869 Notes on Template Haskell version 2</ulink>.
5870 Not all of these changes are in GHC, however.
5873 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5874 as a worked example to help get you started.
5878 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5879 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5884 <title>Syntax</title>
5886 <para> Template Haskell has the following new syntactic
5887 constructions. You need to use the flag
5888 <option>-XTemplateHaskell</option>
5889 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5890 </indexterm>to switch these syntactic extensions on
5891 (<option>-XTemplateHaskell</option> is no longer implied by
5892 <option>-fglasgow-exts</option>).</para>
5896 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5897 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5898 There must be no space between the "$" and the identifier or parenthesis. This use
5899 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5900 of "." as an infix operator. If you want the infix operator, put spaces around it.
5902 <para> A splice can occur in place of
5904 <listitem><para> an expression; the spliced expression must
5905 have type <literal>Q Exp</literal></para></listitem>
5906 <listitem><para> an type; the spliced expression must
5907 have type <literal>Q Typ</literal></para></listitem>
5908 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5911 Inside a splice you can can only call functions defined in imported modules,
5912 not functions defined elsewhere in the same module.</listitem>
5916 A expression quotation is written in Oxford brackets, thus:
5918 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5919 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5920 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5921 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5922 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5923 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5924 </itemizedlist></para></listitem>
5927 A quasi-quotation can appear in either a pattern context or an
5928 expression context and is also written in Oxford brackets:
5930 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5931 where the "..." is an arbitrary string; a full description of the
5932 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5933 </itemizedlist></para></listitem>
5936 A name can be quoted with either one or two prefix single quotes:
5938 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5939 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5940 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5942 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5943 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5946 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5947 may also be given as an argument to the <literal>reify</literal> function.
5953 (Compared to the original paper, there are many differences of detail.
5954 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5955 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5956 Pattern splices and quotations are not implemented.)
5960 <sect2> <title> Using Template Haskell </title>
5964 The data types and monadic constructor functions for Template Haskell are in the library
5965 <literal>Language.Haskell.THSyntax</literal>.
5969 You can only run a function at compile time if it is imported from another module. That is,
5970 you can't define a function in a module, and call it from within a splice in the same module.
5971 (It would make sense to do so, but it's hard to implement.)
5975 You can only run a function at compile time if it is imported
5976 from another module <emphasis>that is not part of a mutually-recursive group of modules
5977 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5978 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5979 splice is to be run.</para>
5981 For example, when compiling module A,
5982 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5983 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5987 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5990 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5991 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5992 compiles and runs a program, and then looks at the result. So it's important that
5993 the program it compiles produces results whose representations are identical to
5994 those of the compiler itself.
5998 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5999 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6004 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6005 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6006 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6013 -- Import our template "pr"
6014 import Printf ( pr )
6016 -- The splice operator $ takes the Haskell source code
6017 -- generated at compile time by "pr" and splices it into
6018 -- the argument of "putStrLn".
6019 main = putStrLn ( $(pr "Hello") )
6025 -- Skeletal printf from the paper.
6026 -- It needs to be in a separate module to the one where
6027 -- you intend to use it.
6029 -- Import some Template Haskell syntax
6030 import Language.Haskell.TH
6032 -- Describe a format string
6033 data Format = D | S | L String
6035 -- Parse a format string. This is left largely to you
6036 -- as we are here interested in building our first ever
6037 -- Template Haskell program and not in building printf.
6038 parse :: String -> [Format]
6041 -- Generate Haskell source code from a parsed representation
6042 -- of the format string. This code will be spliced into
6043 -- the module which calls "pr", at compile time.
6044 gen :: [Format] -> Q Exp
6045 gen [D] = [| \n -> show n |]
6046 gen [S] = [| \s -> s |]
6047 gen [L s] = stringE s
6049 -- Here we generate the Haskell code for the splice
6050 -- from an input format string.
6051 pr :: String -> Q Exp
6052 pr s = gen (parse s)
6055 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6058 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6061 <para>Run "main.exe" and here is your output:</para>
6071 <title>Using Template Haskell with Profiling</title>
6072 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6074 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6075 interpreter to run the splice expressions. The bytecode interpreter
6076 runs the compiled expression on top of the same runtime on which GHC
6077 itself is running; this means that the compiled code referred to by
6078 the interpreted expression must be compatible with this runtime, and
6079 in particular this means that object code that is compiled for
6080 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6081 expression, because profiled object code is only compatible with the
6082 profiling version of the runtime.</para>
6084 <para>This causes difficulties if you have a multi-module program
6085 containing Template Haskell code and you need to compile it for
6086 profiling, because GHC cannot load the profiled object code and use it
6087 when executing the splices. Fortunately GHC provides a workaround.
6088 The basic idea is to compile the program twice:</para>
6092 <para>Compile the program or library first the normal way, without
6093 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6096 <para>Then compile it again with <option>-prof</option>, and
6097 additionally use <option>-osuf
6098 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6099 to name the object files differently (you can choose any suffix
6100 that isn't the normal object suffix here). GHC will automatically
6101 load the object files built in the first step when executing splice
6102 expressions. If you omit the <option>-osuf</option> flag when
6103 building with <option>-prof</option> and Template Haskell is used,
6104 GHC will emit an error message. </para>
6109 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6110 <para>Quasi-quotation allows patterns and expressions to be written using
6111 programmer-defined concrete syntax; the motivation behind the extension and
6112 several examples are documented in
6113 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6114 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6115 2007). The example below shows how to write a quasiquoter for a simple
6116 expression language.</para>
6119 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6120 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6121 functions for quoting expressions and patterns, respectively. The first argument
6122 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6123 context of the quasi-quotation statement determines which of the two parsers is
6124 called: if the quasi-quotation occurs in an expression context, the expression
6125 parser is called, and if it occurs in a pattern context, the pattern parser is
6129 Note that in the example we make use of an antiquoted
6130 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6131 (this syntax for anti-quotation was defined by the parser's
6132 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6133 integer value argument of the constructor <literal>IntExpr</literal> when
6134 pattern matching. Please see the referenced paper for further details regarding
6135 anti-quotation as well as the description of a technique that uses SYB to
6136 leverage a single parser of type <literal>String -> a</literal> to generate both
6137 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6138 pattern parser that returns a value of type <literal>Q Pat</literal>.
6141 <para>In general, a quasi-quote has the form
6142 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6143 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6144 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6145 can be arbitrary, and may contain newlines.
6148 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6149 the example, <literal>expr</literal> cannot be defined
6150 in <literal>Main.hs</literal> where it is used, but must be imported.
6161 main = do { print $ eval [$expr|1 + 2|]
6163 { [$expr|'int:n|] -> print n
6172 import qualified Language.Haskell.TH as TH
6173 import Language.Haskell.TH.Quote
6175 data Expr = IntExpr Integer
6176 | AntiIntExpr String
6177 | BinopExpr BinOp Expr Expr
6179 deriving(Show, Typeable, Data)
6185 deriving(Show, Typeable, Data)
6187 eval :: Expr -> Integer
6188 eval (IntExpr n) = n
6189 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6196 expr = QuasiQuoter parseExprExp parseExprPat
6198 -- Parse an Expr, returning its representation as
6199 -- either a Q Exp or a Q Pat. See the referenced paper
6200 -- for how to use SYB to do this by writing a single
6201 -- parser of type String -> Expr instead of two
6202 -- separate parsers.
6204 parseExprExp :: String -> Q Exp
6207 parseExprPat :: String -> Q Pat
6211 <para>Now run the compiler:
6214 $ ghc --make -XQuasiQuotes Main.hs -o main
6217 <para>Run "main" and here is your output:</para>
6229 <!-- ===================== Arrow notation =================== -->
6231 <sect1 id="arrow-notation">
6232 <title>Arrow notation
6235 <para>Arrows are a generalization of monads introduced by John Hughes.
6236 For more details, see
6241 “Generalising Monads to Arrows”,
6242 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6243 pp67–111, May 2000.
6244 The paper that introduced arrows: a friendly introduction, motivated with
6245 programming examples.
6251 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6252 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6253 Introduced the notation described here.
6259 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6260 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6267 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6268 John Hughes, in <citetitle>5th International Summer School on
6269 Advanced Functional Programming</citetitle>,
6270 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6272 This paper includes another introduction to the notation,
6273 with practical examples.
6279 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6280 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6281 A terse enumeration of the formal rules used
6282 (extracted from comments in the source code).
6288 The arrows web page at
6289 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6294 With the <option>-XArrows</option> flag, GHC supports the arrow
6295 notation described in the second of these papers,
6296 translating it using combinators from the
6297 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6299 What follows is a brief introduction to the notation;
6300 it won't make much sense unless you've read Hughes's paper.
6303 <para>The extension adds a new kind of expression for defining arrows:
6305 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6306 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6308 where <literal>proc</literal> is a new keyword.
6309 The variables of the pattern are bound in the body of the
6310 <literal>proc</literal>-expression,
6311 which is a new sort of thing called a <firstterm>command</firstterm>.
6312 The syntax of commands is as follows:
6314 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6315 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6316 | <replaceable>cmd</replaceable><superscript>0</superscript>
6318 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6319 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6320 infix operators as for expressions, and
6322 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6323 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6324 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6325 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6326 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6327 | <replaceable>fcmd</replaceable>
6329 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6330 | ( <replaceable>cmd</replaceable> )
6331 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6333 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6334 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6335 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6336 | <replaceable>cmd</replaceable>
6338 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6339 except that the bodies are commands instead of expressions.
6343 Commands produce values, but (like monadic computations)
6344 may yield more than one value,
6345 or none, and may do other things as well.
6346 For the most part, familiarity with monadic notation is a good guide to
6348 However the values of expressions, even monadic ones,
6349 are determined by the values of the variables they contain;
6350 this is not necessarily the case for commands.
6354 A simple example of the new notation is the expression
6356 proc x -> f -< x+1
6358 We call this a <firstterm>procedure</firstterm> or
6359 <firstterm>arrow abstraction</firstterm>.
6360 As with a lambda expression, the variable <literal>x</literal>
6361 is a new variable bound within the <literal>proc</literal>-expression.
6362 It refers to the input to the arrow.
6363 In the above example, <literal>-<</literal> is not an identifier but an
6364 new reserved symbol used for building commands from an expression of arrow
6365 type and an expression to be fed as input to that arrow.
6366 (The weird look will make more sense later.)
6367 It may be read as analogue of application for arrows.
6368 The above example is equivalent to the Haskell expression
6370 arr (\ x -> x+1) >>> f
6372 That would make no sense if the expression to the left of
6373 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6374 More generally, the expression to the left of <literal>-<</literal>
6375 may not involve any <firstterm>local variable</firstterm>,
6376 i.e. a variable bound in the current arrow abstraction.
6377 For such a situation there is a variant <literal>-<<</literal>, as in
6379 proc x -> f x -<< x+1
6381 which is equivalent to
6383 arr (\ x -> (f x, x+1)) >>> app
6385 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6387 Such an arrow is equivalent to a monad, so if you're using this form
6388 you may find a monadic formulation more convenient.
6392 <title>do-notation for commands</title>
6395 Another form of command is a form of <literal>do</literal>-notation.
6396 For example, you can write
6405 You can read this much like ordinary <literal>do</literal>-notation,
6406 but with commands in place of monadic expressions.
6407 The first line sends the value of <literal>x+1</literal> as an input to
6408 the arrow <literal>f</literal>, and matches its output against
6409 <literal>y</literal>.
6410 In the next line, the output is discarded.
6411 The arrow <function>returnA</function> is defined in the
6412 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6413 module as <literal>arr id</literal>.
6414 The above example is treated as an abbreviation for
6416 arr (\ x -> (x, x)) >>>
6417 first (arr (\ x -> x+1) >>> f) >>>
6418 arr (\ (y, x) -> (y, (x, y))) >>>
6419 first (arr (\ y -> 2*y) >>> g) >>>
6421 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6422 first (arr (\ (x, z) -> x*z) >>> h) >>>
6423 arr (\ (t, z) -> t+z) >>>
6426 Note that variables not used later in the composition are projected out.
6427 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6429 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6430 module, this reduces to
6432 arr (\ x -> (x+1, x)) >>>
6434 arr (\ (y, x) -> (2*y, (x, y))) >>>
6436 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6438 arr (\ (t, z) -> t+z)
6440 which is what you might have written by hand.
6441 With arrow notation, GHC keeps track of all those tuples of variables for you.
6445 Note that although the above translation suggests that
6446 <literal>let</literal>-bound variables like <literal>z</literal> must be
6447 monomorphic, the actual translation produces Core,
6448 so polymorphic variables are allowed.
6452 It's also possible to have mutually recursive bindings,
6453 using the new <literal>rec</literal> keyword, as in the following example:
6455 counter :: ArrowCircuit a => a Bool Int
6456 counter = proc reset -> do
6457 rec output <- returnA -< if reset then 0 else next
6458 next <- delay 0 -< output+1
6459 returnA -< output
6461 The translation of such forms uses the <function>loop</function> combinator,
6462 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6468 <title>Conditional commands</title>
6471 In the previous example, we used a conditional expression to construct the
6473 Sometimes we want to conditionally execute different commands, as in
6480 which is translated to
6482 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6483 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6485 Since the translation uses <function>|||</function>,
6486 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6490 There are also <literal>case</literal> commands, like
6496 y <- h -< (x1, x2)
6500 The syntax is the same as for <literal>case</literal> expressions,
6501 except that the bodies of the alternatives are commands rather than expressions.
6502 The translation is similar to that of <literal>if</literal> commands.
6508 <title>Defining your own control structures</title>
6511 As we're seen, arrow notation provides constructs,
6512 modelled on those for expressions,
6513 for sequencing, value recursion and conditionals.
6514 But suitable combinators,
6515 which you can define in ordinary Haskell,
6516 may also be used to build new commands out of existing ones.
6517 The basic idea is that a command defines an arrow from environments to values.
6518 These environments assign values to the free local variables of the command.
6519 Thus combinators that produce arrows from arrows
6520 may also be used to build commands from commands.
6521 For example, the <literal>ArrowChoice</literal> class includes a combinator
6523 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6525 so we can use it to build commands:
6527 expr' = proc x -> do
6530 symbol Plus -< ()
6531 y <- term -< ()
6534 symbol Minus -< ()
6535 y <- term -< ()
6538 (The <literal>do</literal> on the first line is needed to prevent the first
6539 <literal><+> ...</literal> from being interpreted as part of the
6540 expression on the previous line.)
6541 This is equivalent to
6543 expr' = (proc x -> returnA -< x)
6544 <+> (proc x -> do
6545 symbol Plus -< ()
6546 y <- term -< ()
6548 <+> (proc x -> do
6549 symbol Minus -< ()
6550 y <- term -< ()
6553 It is essential that this operator be polymorphic in <literal>e</literal>
6554 (representing the environment input to the command
6555 and thence to its subcommands)
6556 and satisfy the corresponding naturality property
6558 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6560 at least for strict <literal>k</literal>.
6561 (This should be automatic if you're not using <function>seq</function>.)
6562 This ensures that environments seen by the subcommands are environments
6563 of the whole command,
6564 and also allows the translation to safely trim these environments.
6565 The operator must also not use any variable defined within the current
6570 We could define our own operator
6572 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6573 untilA body cond = proc x ->
6574 b <- cond -< x
6575 if b then returnA -< ()
6578 untilA body cond -< x
6580 and use it in the same way.
6581 Of course this infix syntax only makes sense for binary operators;
6582 there is also a more general syntax involving special brackets:
6586 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6593 <title>Primitive constructs</title>
6596 Some operators will need to pass additional inputs to their subcommands.
6597 For example, in an arrow type supporting exceptions,
6598 the operator that attaches an exception handler will wish to pass the
6599 exception that occurred to the handler.
6600 Such an operator might have a type
6602 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6604 where <literal>Ex</literal> is the type of exceptions handled.
6605 You could then use this with arrow notation by writing a command
6607 body `handleA` \ ex -> handler
6609 so that if an exception is raised in the command <literal>body</literal>,
6610 the variable <literal>ex</literal> is bound to the value of the exception
6611 and the command <literal>handler</literal>,
6612 which typically refers to <literal>ex</literal>, is entered.
6613 Though the syntax here looks like a functional lambda,
6614 we are talking about commands, and something different is going on.
6615 The input to the arrow represented by a command consists of values for
6616 the free local variables in the command, plus a stack of anonymous values.
6617 In all the prior examples, this stack was empty.
6618 In the second argument to <function>handleA</function>,
6619 this stack consists of one value, the value of the exception.
6620 The command form of lambda merely gives this value a name.
6625 the values on the stack are paired to the right of the environment.
6626 So operators like <function>handleA</function> that pass
6627 extra inputs to their subcommands can be designed for use with the notation
6628 by pairing the values with the environment in this way.
6629 More precisely, the type of each argument of the operator (and its result)
6630 should have the form
6632 a (...(e,t1), ... tn) t
6634 where <replaceable>e</replaceable> is a polymorphic variable
6635 (representing the environment)
6636 and <replaceable>ti</replaceable> are the types of the values on the stack,
6637 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6638 The polymorphic variable <replaceable>e</replaceable> must not occur in
6639 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6640 <replaceable>t</replaceable>.
6641 However the arrows involved need not be the same.
6642 Here are some more examples of suitable operators:
6644 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6645 runReader :: ... => a e c -> a' (e,State) c
6646 runState :: ... => a e c -> a' (e,State) (c,State)
6648 We can supply the extra input required by commands built with the last two
6649 by applying them to ordinary expressions, as in
6653 (|runReader (do { ... })|) s
6655 which adds <literal>s</literal> to the stack of inputs to the command
6656 built using <function>runReader</function>.
6660 The command versions of lambda abstraction and application are analogous to
6661 the expression versions.
6662 In particular, the beta and eta rules describe equivalences of commands.
6663 These three features (operators, lambda abstraction and application)
6664 are the core of the notation; everything else can be built using them,
6665 though the results would be somewhat clumsy.
6666 For example, we could simulate <literal>do</literal>-notation by defining
6668 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6669 u `bind` f = returnA &&& u >>> f
6671 bind_ :: Arrow a => a e b -> a e c -> a e c
6672 u `bind_` f = u `bind` (arr fst >>> f)
6674 We could simulate <literal>if</literal> by defining
6676 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6677 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6684 <title>Differences with the paper</title>
6689 <para>Instead of a single form of arrow application (arrow tail) with two
6690 translations, the implementation provides two forms
6691 <quote><literal>-<</literal></quote> (first-order)
6692 and <quote><literal>-<<</literal></quote> (higher-order).
6697 <para>User-defined operators are flagged with banana brackets instead of
6698 a new <literal>form</literal> keyword.
6707 <title>Portability</title>
6710 Although only GHC implements arrow notation directly,
6711 there is also a preprocessor
6713 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6714 that translates arrow notation into Haskell 98
6715 for use with other Haskell systems.
6716 You would still want to check arrow programs with GHC;
6717 tracing type errors in the preprocessor output is not easy.
6718 Modules intended for both GHC and the preprocessor must observe some
6719 additional restrictions:
6724 The module must import
6725 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6731 The preprocessor cannot cope with other Haskell extensions.
6732 These would have to go in separate modules.
6738 Because the preprocessor targets Haskell (rather than Core),
6739 <literal>let</literal>-bound variables are monomorphic.
6750 <!-- ==================== BANG PATTERNS ================= -->
6752 <sect1 id="bang-patterns">
6753 <title>Bang patterns
6754 <indexterm><primary>Bang patterns</primary></indexterm>
6756 <para>GHC supports an extension of pattern matching called <emphasis>bang
6757 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6758 Bang patterns are under consideration for Haskell Prime.
6760 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6761 prime feature description</ulink> contains more discussion and examples
6762 than the material below.
6765 The key change is the addition of a new rule to the
6766 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6767 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6768 against a value <replaceable>v</replaceable> behaves as follows:
6770 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6771 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6775 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6778 <sect2 id="bang-patterns-informal">
6779 <title>Informal description of bang patterns
6782 The main idea is to add a single new production to the syntax of patterns:
6786 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6787 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6792 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6793 whereas without the bang it would be lazy.
6794 Bang patterns can be nested of course:
6798 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6799 <literal>y</literal>.
6800 A bang only really has an effect if it precedes a variable or wild-card pattern:
6805 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6806 putting a bang before a pattern that
6807 forces evaluation anyway does nothing.
6810 There is one (apparent) exception to this general rule that a bang only
6811 makes a difference when it precedes a variable or wild-card: a bang at the
6812 top level of a <literal>let</literal> or <literal>where</literal>
6813 binding makes the binding strict, regardless of the pattern. For example:
6817 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6818 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6819 (We say "apparent" exception because the Right Way to think of it is that the bang
6820 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6821 is part of the syntax of the <emphasis>binding</emphasis>.)
6822 Nested bangs in a pattern binding behave uniformly with all other forms of
6823 pattern matching. For example
6825 let (!x,[y]) = e in b
6827 is equivalent to this:
6829 let { t = case e of (x,[y]) -> x `seq` (x,y)
6834 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6835 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6836 evaluation of <literal>x</literal>.
6839 Bang patterns work in <literal>case</literal> expressions too, of course:
6841 g5 x = let y = f x in body
6842 g6 x = case f x of { y -> body }
6843 g7 x = case f x of { !y -> body }
6845 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6846 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6847 result, and then evaluates <literal>body</literal>.
6852 <sect2 id="bang-patterns-sem">
6853 <title>Syntax and semantics
6857 We add a single new production to the syntax of patterns:
6861 There is one problem with syntactic ambiguity. Consider:
6865 Is this a definition of the infix function "<literal>(!)</literal>",
6866 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6867 ambiguity in favour of the latter. If you want to define
6868 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6873 The semantics of Haskell pattern matching is described in <ulink
6874 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6875 Section 3.17.2</ulink> of the Haskell Report. To this description add
6876 one extra item 10, saying:
6877 <itemizedlist><listitem><para>Matching
6878 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6879 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6880 <listitem><para>otherwise, <literal>pat</literal> is matched against
6881 <literal>v</literal></para></listitem>
6883 </para></listitem></itemizedlist>
6884 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6885 Section 3.17.3</ulink>, add a new case (t):
6887 case v of { !pat -> e; _ -> e' }
6888 = v `seq` case v of { pat -> e; _ -> e' }
6891 That leaves let expressions, whose translation is given in
6892 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6894 of the Haskell Report.
6895 In the translation box, first apply
6896 the following transformation: for each pattern <literal>pi</literal> that is of
6897 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6898 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6899 have a bang at the top, apply the rules in the existing box.
6901 <para>The effect of the let rule is to force complete matching of the pattern
6902 <literal>qi</literal> before evaluation of the body is begun. The bang is
6903 retained in the translated form in case <literal>qi</literal> is a variable,
6911 The let-binding can be recursive. However, it is much more common for
6912 the let-binding to be non-recursive, in which case the following law holds:
6913 <literal>(let !p = rhs in body)</literal>
6915 <literal>(case rhs of !p -> body)</literal>
6918 A pattern with a bang at the outermost level is not allowed at the top level of
6924 <!-- ==================== ASSERTIONS ================= -->
6926 <sect1 id="assertions">
6928 <indexterm><primary>Assertions</primary></indexterm>
6932 If you want to make use of assertions in your standard Haskell code, you
6933 could define a function like the following:
6939 assert :: Bool -> a -> a
6940 assert False x = error "assertion failed!"
6947 which works, but gives you back a less than useful error message --
6948 an assertion failed, but which and where?
6952 One way out is to define an extended <function>assert</function> function which also
6953 takes a descriptive string to include in the error message and
6954 perhaps combine this with the use of a pre-processor which inserts
6955 the source location where <function>assert</function> was used.
6959 Ghc offers a helping hand here, doing all of this for you. For every
6960 use of <function>assert</function> in the user's source:
6966 kelvinToC :: Double -> Double
6967 kelvinToC k = assert (k >= 0.0) (k+273.15)
6973 Ghc will rewrite this to also include the source location where the
6980 assert pred val ==> assertError "Main.hs|15" pred val
6986 The rewrite is only performed by the compiler when it spots
6987 applications of <function>Control.Exception.assert</function>, so you
6988 can still define and use your own versions of
6989 <function>assert</function>, should you so wish. If not, import
6990 <literal>Control.Exception</literal> to make use
6991 <function>assert</function> in your code.
6995 GHC ignores assertions when optimisation is turned on with the
6996 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6997 <literal>assert pred e</literal> will be rewritten to
6998 <literal>e</literal>. You can also disable assertions using the
6999 <option>-fignore-asserts</option>
7000 option<indexterm><primary><option>-fignore-asserts</option></primary>
7001 </indexterm>.</para>
7004 Assertion failures can be caught, see the documentation for the
7005 <literal>Control.Exception</literal> library for the details.
7011 <!-- =============================== PRAGMAS =========================== -->
7013 <sect1 id="pragmas">
7014 <title>Pragmas</title>
7016 <indexterm><primary>pragma</primary></indexterm>
7018 <para>GHC supports several pragmas, or instructions to the
7019 compiler placed in the source code. Pragmas don't normally affect
7020 the meaning of the program, but they might affect the efficiency
7021 of the generated code.</para>
7023 <para>Pragmas all take the form
7025 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7027 where <replaceable>word</replaceable> indicates the type of
7028 pragma, and is followed optionally by information specific to that
7029 type of pragma. Case is ignored in
7030 <replaceable>word</replaceable>. The various values for
7031 <replaceable>word</replaceable> that GHC understands are described
7032 in the following sections; any pragma encountered with an
7033 unrecognised <replaceable>word</replaceable> is
7034 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7035 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7037 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7041 pragma must precede the <literal>module</literal> keyword in the file.
7044 There can be as many file-header pragmas as you please, and they can be
7045 preceded or followed by comments.
7048 File-header pragmas are read once only, before
7049 pre-processing the file (e.g. with cpp).
7052 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7053 <literal>{-# OPTIONS_GHC #-}</literal>, and
7054 <literal>{-# INCLUDE #-}</literal>.
7059 <sect2 id="language-pragma">
7060 <title>LANGUAGE pragma</title>
7062 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7063 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7065 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7067 It is the intention that all Haskell compilers support the
7068 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7069 all extensions are supported by all compilers, of
7070 course. The <literal>LANGUAGE</literal> pragma should be used instead
7071 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7073 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7075 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7077 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7079 <para>Every language extension can also be turned into a command-line flag
7080 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7081 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7084 <para>A list of all supported language extensions can be obtained by invoking
7085 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7087 <para>Any extension from the <literal>Extension</literal> type defined in
7089 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7090 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7094 <sect2 id="options-pragma">
7095 <title>OPTIONS_GHC pragma</title>
7096 <indexterm><primary>OPTIONS_GHC</primary>
7098 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7101 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7102 additional options that are given to the compiler when compiling
7103 this source file. See <xref linkend="source-file-options"/> for
7106 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7107 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7110 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7112 <sect2 id="include-pragma">
7113 <title>INCLUDE pragma</title>
7115 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
7116 of C header files that should be <literal>#include</literal>'d into
7117 the C source code generated by the compiler for the current module (if
7118 compiling via C). For example:</para>
7121 {-# INCLUDE "foo.h" #-}
7122 {-# INCLUDE <stdio.h> #-}</programlisting>
7124 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7126 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
7127 to the <option>-#include</option> option (<xref
7128 linkend="options-C-compiler" />), because the
7129 <literal>INCLUDE</literal> pragma is understood by other
7130 compilers. Yet another alternative is to add the include file to each
7131 <literal>foreign import</literal> declaration in your code, but we
7132 don't recommend using this approach with GHC.</para>
7135 <sect2 id="warning-deprecated-pragma">
7136 <title>WARNING and DEPRECATED pragmas</title>
7137 <indexterm><primary>WARNING</primary></indexterm>
7138 <indexterm><primary>DEPRECATED</primary></indexterm>
7140 <para>The WARNING pragma allows you to attach an arbitrary warning
7141 to a particular function, class, or type.
7142 A DEPRECATED pragma lets you specify that
7143 a particular function, class, or type is deprecated.
7144 There are two ways of using these pragmas.
7148 <para>You can work on an entire module thus:</para>
7150 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7155 module Wibble {-# WARNING "This is an unstable interface." #-} where
7158 <para>When you compile any module that import
7159 <literal>Wibble</literal>, GHC will print the specified
7164 <para>You can attach a warning to a function, class, type, or data constructor, with the
7165 following top-level declarations:</para>
7167 {-# DEPRECATED f, C, T "Don't use these" #-}
7168 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7170 <para>When you compile any module that imports and uses any
7171 of the specified entities, GHC will print the specified
7173 <para> You can only attach to entities declared at top level in the module
7174 being compiled, and you can only use unqualified names in the list of
7175 entities. A capitalised name, such as <literal>T</literal>
7176 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7177 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7178 both are in scope. If both are in scope, there is currently no way to
7179 specify one without the other (c.f. fixities
7180 <xref linkend="infix-tycons"/>).</para>
7183 Warnings and deprecations are not reported for
7184 (a) uses within the defining module, and
7185 (b) uses in an export list.
7186 The latter reduces spurious complaints within a library
7187 in which one module gathers together and re-exports
7188 the exports of several others.
7190 <para>You can suppress the warnings with the flag
7191 <option>-fno-warn-warnings-deprecations</option>.</para>
7194 <sect2 id="inline-noinline-pragma">
7195 <title>INLINE and NOINLINE pragmas</title>
7197 <para>These pragmas control the inlining of function
7200 <sect3 id="inline-pragma">
7201 <title>INLINE pragma</title>
7202 <indexterm><primary>INLINE</primary></indexterm>
7204 <para>GHC (with <option>-O</option>, as always) tries to
7205 inline (or “unfold”) functions/values that are
7206 “small enough,” thus avoiding the call overhead
7207 and possibly exposing other more-wonderful optimisations.
7208 Normally, if GHC decides a function is “too
7209 expensive” to inline, it will not do so, nor will it
7210 export that unfolding for other modules to use.</para>
7212 <para>The sledgehammer you can bring to bear is the
7213 <literal>INLINE</literal><indexterm><primary>INLINE
7214 pragma</primary></indexterm> pragma, used thusly:</para>
7217 key_function :: Int -> String -> (Bool, Double)
7218 {-# INLINE key_function #-}
7221 <para>The major effect of an <literal>INLINE</literal> pragma
7222 is to declare a function's “cost” to be very low.
7223 The normal unfolding machinery will then be very keen to
7224 inline it. However, an <literal>INLINE</literal> pragma for a
7225 function "<literal>f</literal>" has a number of other effects:
7228 No functions are inlined into <literal>f</literal>. Otherwise
7229 GHC might inline a big function into <literal>f</literal>'s right hand side,
7230 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7233 The float-in, float-out, and common-sub-expression transformations are not
7234 applied to the body of <literal>f</literal>.
7237 An INLINE function is not worker/wrappered by strictness analysis.
7238 It's going to be inlined wholesale instead.
7241 All of these effects are aimed at ensuring that what gets inlined is
7242 exactly what you asked for, no more and no less.
7244 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7245 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7246 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7247 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7248 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7249 when there is no choice even an INLINE function can be selected, in which case
7250 the INLINE pragma is ignored.
7251 For example, for a self-recursive function, the loop breaker can only be the function
7252 itself, so an INLINE pragma is always ignored.</para>
7254 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7255 function can be put anywhere its type signature could be
7258 <para><literal>INLINE</literal> pragmas are a particularly
7260 <literal>then</literal>/<literal>return</literal> (or
7261 <literal>bind</literal>/<literal>unit</literal>) functions in
7262 a monad. For example, in GHC's own
7263 <literal>UniqueSupply</literal> monad code, we have:</para>
7266 {-# INLINE thenUs #-}
7267 {-# INLINE returnUs #-}
7270 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7271 linkend="noinline-pragma"/>).</para>
7273 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7274 so if you want your code to be HBC-compatible you'll have to surround
7275 the pragma with C pre-processor directives
7276 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7280 <sect3 id="noinline-pragma">
7281 <title>NOINLINE pragma</title>
7283 <indexterm><primary>NOINLINE</primary></indexterm>
7284 <indexterm><primary>NOTINLINE</primary></indexterm>
7286 <para>The <literal>NOINLINE</literal> pragma does exactly what
7287 you'd expect: it stops the named function from being inlined
7288 by the compiler. You shouldn't ever need to do this, unless
7289 you're very cautious about code size.</para>
7291 <para><literal>NOTINLINE</literal> is a synonym for
7292 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7293 specified by Haskell 98 as the standard way to disable
7294 inlining, so it should be used if you want your code to be
7298 <sect3 id="phase-control">
7299 <title>Phase control</title>
7301 <para> Sometimes you want to control exactly when in GHC's
7302 pipeline the INLINE pragma is switched on. Inlining happens
7303 only during runs of the <emphasis>simplifier</emphasis>. Each
7304 run of the simplifier has a different <emphasis>phase
7305 number</emphasis>; the phase number decreases towards zero.
7306 If you use <option>-dverbose-core2core</option> you'll see the
7307 sequence of phase numbers for successive runs of the
7308 simplifier. In an INLINE pragma you can optionally specify a
7312 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7313 <literal>f</literal>
7314 until phase <literal>k</literal>, but from phase
7315 <literal>k</literal> onwards be very keen to inline it.
7318 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7319 <literal>f</literal>
7320 until phase <literal>k</literal>, but from phase
7321 <literal>k</literal> onwards do not inline it.
7324 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7325 <literal>f</literal>
7326 until phase <literal>k</literal>, but from phase
7327 <literal>k</literal> onwards be willing to inline it (as if
7328 there was no pragma).
7331 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7332 <literal>f</literal>
7333 until phase <literal>k</literal>, but from phase
7334 <literal>k</literal> onwards do not inline it.
7337 The same information is summarised here:
7339 -- Before phase 2 Phase 2 and later
7340 {-# INLINE [2] f #-} -- No Yes
7341 {-# INLINE [~2] f #-} -- Yes No
7342 {-# NOINLINE [2] f #-} -- No Maybe
7343 {-# NOINLINE [~2] f #-} -- Maybe No
7345 {-# INLINE f #-} -- Yes Yes
7346 {-# NOINLINE f #-} -- No No
7348 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7349 function body is small, or it is applied to interesting-looking arguments etc).
7350 Another way to understand the semantics is this:
7352 <listitem><para>For both INLINE and NOINLINE, the phase number says
7353 when inlining is allowed at all.</para></listitem>
7354 <listitem><para>The INLINE pragma has the additional effect of making the
7355 function body look small, so that when inlining is allowed it is very likely to
7360 <para>The same phase-numbering control is available for RULES
7361 (<xref linkend="rewrite-rules"/>).</para>
7365 <sect2 id="annotation-pragmas">
7366 <title>ANN pragmas</title>
7368 <para>GHC offers the ability to annotate various code constructs with additional
7369 data by using three pragmas. This data can then be inspected at a later date by
7370 using GHC-as-a-library.</para>
7372 <sect3 id="ann-pragma">
7373 <title>Annotating values</title>
7375 <indexterm><primary>ANN</primary></indexterm>
7377 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7378 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7379 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7380 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7381 you would do this:</para>
7384 {-# ANN foo (Just "Hello") #-}
7389 A number of restrictions apply to use of annotations:
7391 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7392 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7393 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7394 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7395 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7397 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7398 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7401 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7402 please give the GHC team a shout</ulink>.
7405 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7406 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7409 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7414 <sect3 id="typeann-pragma">
7415 <title>Annotating types</title>
7417 <indexterm><primary>ANN type</primary></indexterm>
7418 <indexterm><primary>ANN</primary></indexterm>
7420 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7423 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7428 <sect3 id="modann-pragma">
7429 <title>Annotating modules</title>
7431 <indexterm><primary>ANN module</primary></indexterm>
7432 <indexterm><primary>ANN</primary></indexterm>
7434 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7437 {-# ANN module (Just "A `Maybe String' annotation") #-}
7442 <sect2 id="line-pragma">
7443 <title>LINE pragma</title>
7445 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7446 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7447 <para>This pragma is similar to C's <literal>#line</literal>
7448 pragma, and is mainly for use in automatically generated Haskell
7449 code. It lets you specify the line number and filename of the
7450 original code; for example</para>
7452 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7454 <para>if you'd generated the current file from something called
7455 <filename>Foo.vhs</filename> and this line corresponds to line
7456 42 in the original. GHC will adjust its error messages to refer
7457 to the line/file named in the <literal>LINE</literal>
7462 <title>RULES pragma</title>
7464 <para>The RULES pragma lets you specify rewrite rules. It is
7465 described in <xref linkend="rewrite-rules"/>.</para>
7468 <sect2 id="specialize-pragma">
7469 <title>SPECIALIZE pragma</title>
7471 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7472 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7473 <indexterm><primary>overloading, death to</primary></indexterm>
7475 <para>(UK spelling also accepted.) For key overloaded
7476 functions, you can create extra versions (NB: more code space)
7477 specialised to particular types. Thus, if you have an
7478 overloaded function:</para>
7481 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7484 <para>If it is heavily used on lists with
7485 <literal>Widget</literal> keys, you could specialise it as
7489 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7492 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7493 be put anywhere its type signature could be put.</para>
7495 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7496 (a) a specialised version of the function and (b) a rewrite rule
7497 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7498 un-specialised function into a call to the specialised one.</para>
7500 <para>The type in a SPECIALIZE pragma can be any type that is less
7501 polymorphic than the type of the original function. In concrete terms,
7502 if the original function is <literal>f</literal> then the pragma
7504 {-# SPECIALIZE f :: <type> #-}
7506 is valid if and only if the definition
7508 f_spec :: <type>
7511 is valid. Here are some examples (where we only give the type signature
7512 for the original function, not its code):
7514 f :: Eq a => a -> b -> b
7515 {-# SPECIALISE f :: Int -> b -> b #-}
7517 g :: (Eq a, Ix b) => a -> b -> b
7518 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7520 h :: Eq a => a -> a -> a
7521 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7523 The last of these examples will generate a
7524 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7525 well. If you use this kind of specialisation, let us know how well it works.
7528 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7529 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7530 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7531 The <literal>INLINE</literal> pragma affects the specialised version of the
7532 function (only), and applies even if the function is recursive. The motivating
7535 -- A GADT for arrays with type-indexed representation
7537 ArrInt :: !Int -> ByteArray# -> Arr Int
7538 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7540 (!:) :: Arr e -> Int -> e
7541 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7542 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7543 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7544 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7546 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7547 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7548 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7549 the specialised function will be inlined. It has two calls to
7550 <literal>(!:)</literal>,
7551 both at type <literal>Int</literal>. Both these calls fire the first
7552 specialisation, whose body is also inlined. The result is a type-based
7553 unrolling of the indexing function.</para>
7554 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7555 on an ordinarily-recursive function.</para>
7557 <para>Note: In earlier versions of GHC, it was possible to provide your own
7558 specialised function for a given type:
7561 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7564 This feature has been removed, as it is now subsumed by the
7565 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7569 <sect2 id="specialize-instance-pragma">
7570 <title>SPECIALIZE instance pragma
7574 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7575 <indexterm><primary>overloading, death to</primary></indexterm>
7576 Same idea, except for instance declarations. For example:
7579 instance (Eq a) => Eq (Foo a) where {
7580 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7584 The pragma must occur inside the <literal>where</literal> part
7585 of the instance declaration.
7588 Compatible with HBC, by the way, except perhaps in the placement
7594 <sect2 id="unpack-pragma">
7595 <title>UNPACK pragma</title>
7597 <indexterm><primary>UNPACK</primary></indexterm>
7599 <para>The <literal>UNPACK</literal> indicates to the compiler
7600 that it should unpack the contents of a constructor field into
7601 the constructor itself, removing a level of indirection. For
7605 data T = T {-# UNPACK #-} !Float
7606 {-# UNPACK #-} !Float
7609 <para>will create a constructor <literal>T</literal> containing
7610 two unboxed floats. This may not always be an optimisation: if
7611 the <function>T</function> constructor is scrutinised and the
7612 floats passed to a non-strict function for example, they will
7613 have to be reboxed (this is done automatically by the
7616 <para>Unpacking constructor fields should only be used in
7617 conjunction with <option>-O</option>, in order to expose
7618 unfoldings to the compiler so the reboxing can be removed as
7619 often as possible. For example:</para>
7623 f (T f1 f2) = f1 + f2
7626 <para>The compiler will avoid reboxing <function>f1</function>
7627 and <function>f2</function> by inlining <function>+</function>
7628 on floats, but only when <option>-O</option> is on.</para>
7630 <para>Any single-constructor data is eligible for unpacking; for
7634 data T = T {-# UNPACK #-} !(Int,Int)
7637 <para>will store the two <literal>Int</literal>s directly in the
7638 <function>T</function> constructor, by flattening the pair.
7639 Multi-level unpacking is also supported:
7642 data T = T {-# UNPACK #-} !S
7643 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7646 will store two unboxed <literal>Int#</literal>s
7647 directly in the <function>T</function> constructor. The
7648 unpacker can see through newtypes, too.</para>
7650 <para>If a field cannot be unpacked, you will not get a warning,
7651 so it might be an idea to check the generated code with
7652 <option>-ddump-simpl</option>.</para>
7654 <para>See also the <option>-funbox-strict-fields</option> flag,
7655 which essentially has the effect of adding
7656 <literal>{-# UNPACK #-}</literal> to every strict
7657 constructor field.</para>
7660 <sect2 id="source-pragma">
7661 <title>SOURCE pragma</title>
7663 <indexterm><primary>SOURCE</primary></indexterm>
7664 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7665 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7671 <!-- ======================= REWRITE RULES ======================== -->
7673 <sect1 id="rewrite-rules">
7674 <title>Rewrite rules
7676 <indexterm><primary>RULES pragma</primary></indexterm>
7677 <indexterm><primary>pragma, RULES</primary></indexterm>
7678 <indexterm><primary>rewrite rules</primary></indexterm></title>
7681 The programmer can specify rewrite rules as part of the source program
7687 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7692 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7693 If you need more information, then <option>-ddump-rule-firings</option> shows you
7694 each individual rule firing in detail.
7698 <title>Syntax</title>
7701 From a syntactic point of view:
7707 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7708 may be generated by the layout rule).
7714 The layout rule applies in a pragma.
7715 Currently no new indentation level
7716 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7717 you must lay out the starting in the same column as the enclosing definitions.
7720 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7721 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7724 Furthermore, the closing <literal>#-}</literal>
7725 should start in a column to the right of the opening <literal>{-#</literal>.
7731 Each rule has a name, enclosed in double quotes. The name itself has
7732 no significance at all. It is only used when reporting how many times the rule fired.
7738 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7739 immediately after the name of the rule. Thus:
7742 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7745 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7746 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7755 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7756 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7757 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7758 by spaces, just like in a type <literal>forall</literal>.
7764 A pattern variable may optionally have a type signature.
7765 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7766 For example, here is the <literal>foldr/build</literal> rule:
7769 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7770 foldr k z (build g) = g k z
7773 Since <function>g</function> has a polymorphic type, it must have a type signature.
7780 The left hand side of a rule must consist of a top-level variable applied
7781 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7784 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7785 "wrong2" forall f. f True = True
7788 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7795 A rule does not need to be in the same module as (any of) the
7796 variables it mentions, though of course they need to be in scope.
7802 All rules are implicitly exported from the module, and are therefore
7803 in force in any module that imports the module that defined the rule, directly
7804 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7805 in force when compiling A.) The situation is very similar to that for instance
7813 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7814 any other flag settings. Furthermore, inside a RULE, the language extension
7815 <option>-XScopedTypeVariables</option> is automatically enabled; see
7816 <xref linkend="scoped-type-variables"/>.
7822 Like other pragmas, RULE pragmas are always checked for scope errors, and
7823 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7824 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7825 if the <option>-fenable-rewrite-rules</option> flag is
7826 on (see <xref linkend="rule-semantics"/>).
7835 <sect2 id="rule-semantics">
7836 <title>Semantics</title>
7839 From a semantic point of view:
7844 Rules are enabled (that is, used during optimisation)
7845 by the <option>-fenable-rewrite-rules</option> flag.
7846 This flag is implied by <option>-O</option>, and may be switched
7847 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7848 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7849 may not do what you expect, though, because without <option>-O</option> GHC
7850 ignores all optimisation information in interface files;
7851 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7852 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7853 has no effect on parsing or typechecking.
7859 Rules are regarded as left-to-right rewrite rules.
7860 When GHC finds an expression that is a substitution instance of the LHS
7861 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7862 By "a substitution instance" we mean that the LHS can be made equal to the
7863 expression by substituting for the pattern variables.
7870 GHC makes absolutely no attempt to verify that the LHS and RHS
7871 of a rule have the same meaning. That is undecidable in general, and
7872 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7879 GHC makes no attempt to make sure that the rules are confluent or
7880 terminating. For example:
7883 "loop" forall x y. f x y = f y x
7886 This rule will cause the compiler to go into an infinite loop.
7893 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7899 GHC currently uses a very simple, syntactic, matching algorithm
7900 for matching a rule LHS with an expression. It seeks a substitution
7901 which makes the LHS and expression syntactically equal modulo alpha
7902 conversion. The pattern (rule), but not the expression, is eta-expanded if
7903 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7904 But not beta conversion (that's called higher-order matching).
7908 Matching is carried out on GHC's intermediate language, which includes
7909 type abstractions and applications. So a rule only matches if the
7910 types match too. See <xref linkend="rule-spec"/> below.
7916 GHC keeps trying to apply the rules as it optimises the program.
7917 For example, consider:
7926 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7927 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7928 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7929 not be substituted, and the rule would not fire.
7936 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7937 results. Consider this (artificial) example
7940 {-# RULES "f" f True = False #-}
7946 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7951 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7953 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7954 would have been a better chance that <literal>f</literal>'s RULE might fire.
7957 The way to get predictable behaviour is to use a NOINLINE
7958 pragma on <literal>f</literal>, to ensure
7959 that it is not inlined until its RULEs have had a chance to fire.
7969 <title>List fusion</title>
7972 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7973 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7974 intermediate list should be eliminated entirely.
7978 The following are good producers:
7990 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7996 Explicit lists (e.g. <literal>[True, False]</literal>)
8002 The cons constructor (e.g <literal>3:4:[]</literal>)
8008 <function>++</function>
8014 <function>map</function>
8020 <function>take</function>, <function>filter</function>
8026 <function>iterate</function>, <function>repeat</function>
8032 <function>zip</function>, <function>zipWith</function>
8041 The following are good consumers:
8053 <function>array</function> (on its second argument)
8059 <function>++</function> (on its first argument)
8065 <function>foldr</function>
8071 <function>map</function>
8077 <function>take</function>, <function>filter</function>
8083 <function>concat</function>
8089 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8095 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8096 will fuse with one but not the other)
8102 <function>partition</function>
8108 <function>head</function>
8114 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8120 <function>sequence_</function>
8126 <function>msum</function>
8132 <function>sortBy</function>
8141 So, for example, the following should generate no intermediate lists:
8144 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8150 This list could readily be extended; if there are Prelude functions that you use
8151 a lot which are not included, please tell us.
8155 If you want to write your own good consumers or producers, look at the
8156 Prelude definitions of the above functions to see how to do so.
8161 <sect2 id="rule-spec">
8162 <title>Specialisation
8166 Rewrite rules can be used to get the same effect as a feature
8167 present in earlier versions of GHC.
8168 For example, suppose that:
8171 genericLookup :: Ord a => Table a b -> a -> b
8172 intLookup :: Table Int b -> Int -> b
8175 where <function>intLookup</function> is an implementation of
8176 <function>genericLookup</function> that works very fast for
8177 keys of type <literal>Int</literal>. You might wish
8178 to tell GHC to use <function>intLookup</function> instead of
8179 <function>genericLookup</function> whenever the latter was called with
8180 type <literal>Table Int b -> Int -> b</literal>.
8181 It used to be possible to write
8184 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8187 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8190 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8193 This slightly odd-looking rule instructs GHC to replace
8194 <function>genericLookup</function> by <function>intLookup</function>
8195 <emphasis>whenever the types match</emphasis>.
8196 What is more, this rule does not need to be in the same
8197 file as <function>genericLookup</function>, unlike the
8198 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8199 have an original definition available to specialise).
8202 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8203 <function>intLookup</function> really behaves as a specialised version
8204 of <function>genericLookup</function>!!!</para>
8206 <para>An example in which using <literal>RULES</literal> for
8207 specialisation will Win Big:
8210 toDouble :: Real a => a -> Double
8211 toDouble = fromRational . toRational
8213 {-# RULES "toDouble/Int" toDouble = i2d #-}
8214 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8217 The <function>i2d</function> function is virtually one machine
8218 instruction; the default conversion—via an intermediate
8219 <literal>Rational</literal>—is obscenely expensive by
8226 <title>Controlling what's going on</title>
8234 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8240 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8241 If you add <option>-dppr-debug</option> you get a more detailed listing.
8247 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8250 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8251 {-# INLINE build #-}
8255 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8256 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8257 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8258 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8265 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8266 see how to write rules that will do fusion and yet give an efficient
8267 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8277 <sect2 id="core-pragma">
8278 <title>CORE pragma</title>
8280 <indexterm><primary>CORE pragma</primary></indexterm>
8281 <indexterm><primary>pragma, CORE</primary></indexterm>
8282 <indexterm><primary>core, annotation</primary></indexterm>
8285 The external core format supports <quote>Note</quote> annotations;
8286 the <literal>CORE</literal> pragma gives a way to specify what these
8287 should be in your Haskell source code. Syntactically, core
8288 annotations are attached to expressions and take a Haskell string
8289 literal as an argument. The following function definition shows an
8293 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8296 Semantically, this is equivalent to:
8304 However, when external core is generated (via
8305 <option>-fext-core</option>), there will be Notes attached to the
8306 expressions <function>show</function> and <varname>x</varname>.
8307 The core function declaration for <function>f</function> is:
8311 f :: %forall a . GHCziShow.ZCTShow a ->
8312 a -> GHCziBase.ZMZN GHCziBase.Char =
8313 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8315 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8317 (tpl1::GHCziBase.Int ->
8319 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8321 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8322 (tpl3::GHCziBase.ZMZN a ->
8323 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8331 Here, we can see that the function <function>show</function> (which
8332 has been expanded out to a case expression over the Show dictionary)
8333 has a <literal>%note</literal> attached to it, as does the
8334 expression <varname>eta</varname> (which used to be called
8335 <varname>x</varname>).
8342 <sect1 id="special-ids">
8343 <title>Special built-in functions</title>
8344 <para>GHC has a few built-in functions with special behaviour. These
8345 are now described in the module <ulink
8346 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8347 in the library documentation.</para>
8351 <sect1 id="generic-classes">
8352 <title>Generic classes</title>
8355 The ideas behind this extension are described in detail in "Derivable type classes",
8356 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8357 An example will give the idea:
8365 fromBin :: [Int] -> (a, [Int])
8367 toBin {| Unit |} Unit = []
8368 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8369 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8370 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8372 fromBin {| Unit |} bs = (Unit, bs)
8373 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8374 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8375 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8376 (y,bs'') = fromBin bs'
8379 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8380 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8381 which are defined thus in the library module <literal>Generics</literal>:
8385 data a :+: b = Inl a | Inr b
8386 data a :*: b = a :*: b
8389 Now you can make a data type into an instance of Bin like this:
8391 instance (Bin a, Bin b) => Bin (a,b)
8392 instance Bin a => Bin [a]
8394 That is, just leave off the "where" clause. Of course, you can put in the
8395 where clause and over-ride whichever methods you please.
8399 <title> Using generics </title>
8400 <para>To use generics you need to</para>
8403 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8404 <option>-XGenerics</option> (to generate extra per-data-type code),
8405 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8409 <para>Import the module <literal>Generics</literal> from the
8410 <literal>lang</literal> package. This import brings into
8411 scope the data types <literal>Unit</literal>,
8412 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8413 don't need this import if you don't mention these types
8414 explicitly; for example, if you are simply giving instance
8415 declarations.)</para>
8420 <sect2> <title> Changes wrt the paper </title>
8422 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8423 can be written infix (indeed, you can now use
8424 any operator starting in a colon as an infix type constructor). Also note that
8425 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8426 Finally, note that the syntax of the type patterns in the class declaration
8427 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8428 alone would ambiguous when they appear on right hand sides (an extension we
8429 anticipate wanting).
8433 <sect2> <title>Terminology and restrictions</title>
8435 Terminology. A "generic default method" in a class declaration
8436 is one that is defined using type patterns as above.
8437 A "polymorphic default method" is a default method defined as in Haskell 98.
8438 A "generic class declaration" is a class declaration with at least one
8439 generic default method.
8447 Alas, we do not yet implement the stuff about constructor names and
8454 A generic class can have only one parameter; you can't have a generic
8455 multi-parameter class.
8461 A default method must be defined entirely using type patterns, or entirely
8462 without. So this is illegal:
8465 op :: a -> (a, Bool)
8466 op {| Unit |} Unit = (Unit, True)
8469 However it is perfectly OK for some methods of a generic class to have
8470 generic default methods and others to have polymorphic default methods.
8476 The type variable(s) in the type pattern for a generic method declaration
8477 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:
8481 op {| p :*: q |} (x :*: y) = op (x :: p)
8489 The type patterns in a generic default method must take one of the forms:
8495 where "a" and "b" are type variables. Furthermore, all the type patterns for
8496 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8497 must use the same type variables. So this is illegal:
8501 op {| a :+: b |} (Inl x) = True
8502 op {| p :+: q |} (Inr y) = False
8504 The type patterns must be identical, even in equations for different methods of the class.
8505 So this too is illegal:
8509 op1 {| a :*: b |} (x :*: y) = True
8512 op2 {| p :*: q |} (x :*: y) = False
8514 (The reason for this restriction is that we gather all the equations for a particular type constructor
8515 into a single generic instance declaration.)
8521 A generic method declaration must give a case for each of the three type constructors.
8527 The type for a generic method can be built only from:
8529 <listitem> <para> Function arrows </para> </listitem>
8530 <listitem> <para> Type variables </para> </listitem>
8531 <listitem> <para> Tuples </para> </listitem>
8532 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8534 Here are some example type signatures for generic methods:
8537 op2 :: Bool -> (a,Bool)
8538 op3 :: [Int] -> a -> a
8541 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8545 This restriction is an implementation restriction: we just haven't got around to
8546 implementing the necessary bidirectional maps over arbitrary type constructors.
8547 It would be relatively easy to add specific type constructors, such as Maybe and list,
8548 to the ones that are allowed.</para>
8553 In an instance declaration for a generic class, the idea is that the compiler
8554 will fill in the methods for you, based on the generic templates. However it can only
8559 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8564 No constructor of the instance type has unboxed fields.
8568 (Of course, these things can only arise if you are already using GHC extensions.)
8569 However, you can still give an instance declarations for types which break these rules,
8570 provided you give explicit code to override any generic default methods.
8578 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8579 what the compiler does with generic declarations.
8584 <sect2> <title> Another example </title>
8586 Just to finish with, here's another example I rather like:
8590 nCons {| Unit |} _ = 1
8591 nCons {| a :*: b |} _ = 1
8592 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8595 tag {| Unit |} _ = 1
8596 tag {| a :*: b |} _ = 1
8597 tag {| a :+: b |} (Inl x) = tag x
8598 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8604 <sect1 id="monomorphism">
8605 <title>Control over monomorphism</title>
8607 <para>GHC supports two flags that control the way in which generalisation is
8608 carried out at let and where bindings.
8612 <title>Switching off the dreaded Monomorphism Restriction</title>
8613 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8615 <para>Haskell's monomorphism restriction (see
8616 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8618 of the Haskell Report)
8619 can be completely switched off by
8620 <option>-XNoMonomorphismRestriction</option>.
8625 <title>Monomorphic pattern bindings</title>
8626 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8627 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8629 <para> As an experimental change, we are exploring the possibility of
8630 making pattern bindings monomorphic; that is, not generalised at all.
8631 A pattern binding is a binding whose LHS has no function arguments,
8632 and is not a simple variable. For example:
8634 f x = x -- Not a pattern binding
8635 f = \x -> x -- Not a pattern binding
8636 f :: Int -> Int = \x -> x -- Not a pattern binding
8638 (g,h) = e -- A pattern binding
8639 (f) = e -- A pattern binding
8640 [x] = e -- A pattern binding
8642 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8643 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8652 ;;; Local Variables: ***
8654 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8655 ;;; ispell-local-dictionary: "british" ***
projects / ghc-hetmet.git / blob