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/ghc-prim/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. Its 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 syntactic 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 its 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="tuple-sections">
1273 <title>Tuple sections</title>
1276 The <option>-XTupleSections</option> flag enables Python-style partially applied
1277 tuple constructors. For example, the following program
1281 is considered to be an alternative notation for the more unwieldy alternative
1285 You can omit any combination of arguments to the tuple, as in the following
1287 (, "I", , , "Love", , 1337)
1291 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1296 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1297 will also be available for them, like so
1301 Because there is no unboxed unit tuple, the following expression
1305 continues to stand for the unboxed singleton tuple data constructor.
1310 <sect2 id="disambiguate-fields">
1311 <title>Record field disambiguation</title>
1313 In record construction and record pattern matching
1314 it is entirely unambiguous which field is referred to, even if there are two different
1315 data types in scope with a common field name. For example:
1318 data S = MkS { x :: Int, y :: Bool }
1323 data T = MkT { x :: Int }
1325 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1327 ok2 n = MkT { x = n+1 } -- Unambiguous
1329 bad1 k = k { x = 3 } -- Ambiguous
1330 bad2 k = x k -- Ambiguous
1332 Even though there are two <literal>x</literal>'s in scope,
1333 it is clear that the <literal>x</literal> in the pattern in the
1334 definition of <literal>ok1</literal> can only mean the field
1335 <literal>x</literal> from type <literal>S</literal>. Similarly for
1336 the function <literal>ok2</literal>. However, in the record update
1337 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1338 it is not clear which of the two types is intended.
1341 Haskell 98 regards all four as ambiguous, but with the
1342 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1343 the former two. The rules are precisely the same as those for instance
1344 declarations in Haskell 98, where the method names on the left-hand side
1345 of the method bindings in an instance declaration refer unambiguously
1346 to the method of that class (provided they are in scope at all), even
1347 if there are other variables in scope with the same name.
1348 This reduces the clutter of qualified names when you import two
1349 records from different modules that use the same field name.
1353 <!-- ===================== Record puns =================== -->
1355 <sect2 id="record-puns">
1360 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1364 When using records, it is common to write a pattern that binds a
1365 variable with the same name as a record field, such as:
1368 data C = C {a :: Int}
1374 Record punning permits the variable name to be elided, so one can simply
1381 to mean the same pattern as above. That is, in a record pattern, the
1382 pattern <literal>a</literal> expands into the pattern <literal>a =
1383 a</literal> for the same name <literal>a</literal>.
1387 Note that puns and other patterns can be mixed in the same record:
1389 data C = C {a :: Int, b :: Int}
1390 f (C {a, b = 4}) = a
1392 and that puns can be used wherever record patterns occur (e.g. in
1393 <literal>let</literal> bindings or at the top-level).
1397 Record punning can also be used in an expression, writing, for example,
1403 let a = 1 in C {a = a}
1406 Note that this expansion is purely syntactic, so the record pun
1407 expression refers to the nearest enclosing variable that is spelled the
1408 same as the field name.
1413 <!-- ===================== Record wildcards =================== -->
1415 <sect2 id="record-wildcards">
1416 <title>Record wildcards
1420 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1424 For records with many fields, it can be tiresome to write out each field
1425 individually in a record pattern, as in
1427 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1428 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1433 Record wildcard syntax permits a (<literal>..</literal>) in a record
1434 pattern, where each elided field <literal>f</literal> is replaced by the
1435 pattern <literal>f = f</literal>. For example, the above pattern can be
1438 f (C {a = 1, ..}) = b + c + d
1443 Note that wildcards can be mixed with other patterns, including puns
1444 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1445 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1446 wherever record patterns occur, including in <literal>let</literal>
1447 bindings and at the top-level. For example, the top-level binding
1451 defines <literal>b</literal>, <literal>c</literal>, and
1452 <literal>d</literal>.
1456 Record wildcards can also be used in expressions, writing, for example,
1459 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1465 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1468 Note that this expansion is purely syntactic, so the record wildcard
1469 expression refers to the nearest enclosing variables that are spelled
1470 the same as the omitted field names.
1475 <!-- ===================== Local fixity declarations =================== -->
1477 <sect2 id="local-fixity-declarations">
1478 <title>Local Fixity Declarations
1481 <para>A careful reading of the Haskell 98 Report reveals that fixity
1482 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1483 <literal>infixr</literal>) are permitted to appear inside local bindings
1484 such those introduced by <literal>let</literal> and
1485 <literal>where</literal>. However, the Haskell Report does not specify
1486 the semantics of such bindings very precisely.
1489 <para>In GHC, a fixity declaration may accompany a local binding:
1496 and the fixity declaration applies wherever the binding is in scope.
1497 For example, in a <literal>let</literal>, it applies in the right-hand
1498 sides of other <literal>let</literal>-bindings and the body of the
1499 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1500 expressions (<xref linkend="mdo-notation"/>), the local fixity
1501 declarations of a <literal>let</literal> statement scope over other
1502 statements in the group, just as the bound name does.
1506 Moreover, a local fixity declaration *must* accompany a local binding of
1507 that name: it is not possible to revise the fixity of name bound
1510 let infixr 9 $ in ...
1513 Because local fixity declarations are technically Haskell 98, no flag is
1514 necessary to enable them.
1518 <sect2 id="package-imports">
1519 <title>Package-qualified imports</title>
1521 <para>With the <option>-XPackageImports</option> flag, GHC allows
1522 import declarations to be qualified by the package name that the
1523 module is intended to be imported from. For example:</para>
1526 import "network" Network.Socket
1529 <para>would import the module <literal>Network.Socket</literal> from
1530 the package <literal>network</literal> (any version). This may
1531 be used to disambiguate an import when the same module is
1532 available from multiple packages, or is present in both the
1533 current package being built and an external package.</para>
1535 <para>Note: you probably don't need to use this feature, it was
1536 added mainly so that we can build backwards-compatible versions of
1537 packages when APIs change. It can lead to fragile dependencies in
1538 the common case: modules occasionally move from one package to
1539 another, rendering any package-qualified imports broken.</para>
1542 <sect2 id="syntax-stolen">
1543 <title>Summary of stolen syntax</title>
1545 <para>Turning on an option that enables special syntax
1546 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1547 to compile, perhaps because it uses a variable name which has
1548 become a reserved word. This section lists the syntax that is
1549 "stolen" by language extensions.
1551 notation and nonterminal names from the Haskell 98 lexical syntax
1552 (see the Haskell 98 Report).
1553 We only list syntax changes here that might affect
1554 existing working programs (i.e. "stolen" syntax). Many of these
1555 extensions will also enable new context-free syntax, but in all
1556 cases programs written to use the new syntax would not be
1557 compilable without the option enabled.</para>
1559 <para>There are two classes of special
1564 <para>New reserved words and symbols: character sequences
1565 which are no longer available for use as identifiers in the
1569 <para>Other special syntax: sequences of characters that have
1570 a different meaning when this particular option is turned
1575 The following syntax is stolen:
1580 <literal>forall</literal>
1581 <indexterm><primary><literal>forall</literal></primary></indexterm>
1584 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1585 <option>-XLiberalTypeSynonyms</option>,
1586 <option>-XRank2Types</option>,
1587 <option>-XRankNTypes</option>,
1588 <option>-XPolymorphicComponents</option>,
1589 <option>-XExistentialQuantification</option>
1595 <literal>mdo</literal>
1596 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1599 Stolen by: <option>-XRecursiveDo</option>,
1605 <literal>foreign</literal>
1606 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1609 Stolen by: <option>-XForeignFunctionInterface</option>,
1615 <literal>rec</literal>,
1616 <literal>proc</literal>, <literal>-<</literal>,
1617 <literal>>-</literal>, <literal>-<<</literal>,
1618 <literal>>>-</literal>, and <literal>(|</literal>,
1619 <literal>|)</literal> brackets
1620 <indexterm><primary><literal>proc</literal></primary></indexterm>
1623 Stolen by: <option>-XArrows</option>,
1629 <literal>?<replaceable>varid</replaceable></literal>,
1630 <literal>%<replaceable>varid</replaceable></literal>
1631 <indexterm><primary>implicit parameters</primary></indexterm>
1634 Stolen by: <option>-XImplicitParams</option>,
1640 <literal>[|</literal>,
1641 <literal>[e|</literal>, <literal>[p|</literal>,
1642 <literal>[d|</literal>, <literal>[t|</literal>,
1643 <literal>$(</literal>,
1644 <literal>$<replaceable>varid</replaceable></literal>
1645 <indexterm><primary>Template Haskell</primary></indexterm>
1648 Stolen by: <option>-XTemplateHaskell</option>,
1654 <literal>[:<replaceable>varid</replaceable>|</literal>
1655 <indexterm><primary>quasi-quotation</primary></indexterm>
1658 Stolen by: <option>-XQuasiQuotes</option>,
1664 <replaceable>varid</replaceable>{<literal>#</literal>},
1665 <replaceable>char</replaceable><literal>#</literal>,
1666 <replaceable>string</replaceable><literal>#</literal>,
1667 <replaceable>integer</replaceable><literal>#</literal>,
1668 <replaceable>float</replaceable><literal>#</literal>,
1669 <replaceable>float</replaceable><literal>##</literal>,
1670 <literal>(#</literal>, <literal>#)</literal>,
1673 Stolen by: <option>-XMagicHash</option>,
1682 <!-- TYPE SYSTEM EXTENSIONS -->
1683 <sect1 id="data-type-extensions">
1684 <title>Extensions to data types and type synonyms</title>
1686 <sect2 id="nullary-types">
1687 <title>Data types with no constructors</title>
1689 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1690 a data type with no constructors. For example:</para>
1694 data T a -- T :: * -> *
1697 <para>Syntactically, the declaration lacks the "= constrs" part. The
1698 type can be parameterised over types of any kind, but if the kind is
1699 not <literal>*</literal> then an explicit kind annotation must be used
1700 (see <xref linkend="kinding"/>).</para>
1702 <para>Such data types have only one value, namely bottom.
1703 Nevertheless, they can be useful when defining "phantom types".</para>
1706 <sect2 id="infix-tycons">
1707 <title>Infix type constructors, classes, and type variables</title>
1710 GHC allows type constructors, classes, and type variables to be operators, and
1711 to be written infix, very much like expressions. More specifically:
1714 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1715 The lexical syntax is the same as that for data constructors.
1718 Data type and type-synonym declarations can be written infix, parenthesised
1719 if you want further arguments. E.g.
1721 data a :*: b = Foo a b
1722 type a :+: b = Either a b
1723 class a :=: b where ...
1725 data (a :**: b) x = Baz a b x
1726 type (a :++: b) y = Either (a,b) y
1730 Types, and class constraints, can be written infix. For example
1733 f :: (a :=: b) => a -> b
1737 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1738 The lexical syntax is the same as that for variable operators, excluding "(.)",
1739 "(!)", and "(*)". In a binding position, the operator must be
1740 parenthesised. For example:
1742 type T (+) = Int + Int
1746 liftA2 :: Arrow (~>)
1747 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1753 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1754 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1757 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1758 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1759 sets the fixity for a data constructor and the corresponding type constructor. For example:
1763 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1764 and similarly for <literal>:*:</literal>.
1765 <literal>Int `a` Bool</literal>.
1768 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1775 <sect2 id="type-synonyms">
1776 <title>Liberalised type synonyms</title>
1779 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1780 on individual synonym declarations.
1781 With the <option>-XLiberalTypeSynonyms</option> extension,
1782 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1783 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1786 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1787 in a type synonym, thus:
1789 type Discard a = forall b. Show b => a -> b -> (a, String)
1794 g :: Discard Int -> (Int,String) -- A rank-2 type
1801 If you also use <option>-XUnboxedTuples</option>,
1802 you can write an unboxed tuple in a type synonym:
1804 type Pr = (# Int, Int #)
1812 You can apply a type synonym to a forall type:
1814 type Foo a = a -> a -> Bool
1816 f :: Foo (forall b. b->b)
1818 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1820 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1825 You can apply a type synonym to a partially applied type synonym:
1827 type Generic i o = forall x. i x -> o x
1830 foo :: Generic Id []
1832 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1834 foo :: forall x. x -> [x]
1842 GHC currently does kind checking before expanding synonyms (though even that
1846 After expanding type synonyms, GHC does validity checking on types, looking for
1847 the following mal-formedness which isn't detected simply by kind checking:
1850 Type constructor applied to a type involving for-alls.
1853 Unboxed tuple on left of an arrow.
1856 Partially-applied type synonym.
1860 this will be rejected:
1862 type Pr = (# Int, Int #)
1867 because GHC does not allow unboxed tuples on the left of a function arrow.
1872 <sect2 id="existential-quantification">
1873 <title>Existentially quantified data constructors
1877 The idea of using existential quantification in data type declarations
1878 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1879 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1880 London, 1991). It was later formalised by Laufer and Odersky
1881 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1882 TOPLAS, 16(5), pp1411-1430, 1994).
1883 It's been in Lennart
1884 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1885 proved very useful. Here's the idea. Consider the declaration:
1891 data Foo = forall a. MkFoo a (a -> Bool)
1898 The data type <literal>Foo</literal> has two constructors with types:
1904 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1911 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1912 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1913 For example, the following expression is fine:
1919 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1925 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1926 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1927 isUpper</function> packages a character with a compatible function. These
1928 two things are each of type <literal>Foo</literal> and can be put in a list.
1932 What can we do with a value of type <literal>Foo</literal>?. In particular,
1933 what happens when we pattern-match on <function>MkFoo</function>?
1939 f (MkFoo val fn) = ???
1945 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1946 are compatible, the only (useful) thing we can do with them is to
1947 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1954 f (MkFoo val fn) = fn val
1960 What this allows us to do is to package heterogeneous values
1961 together with a bunch of functions that manipulate them, and then treat
1962 that collection of packages in a uniform manner. You can express
1963 quite a bit of object-oriented-like programming this way.
1966 <sect3 id="existential">
1967 <title>Why existential?
1971 What has this to do with <emphasis>existential</emphasis> quantification?
1972 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1978 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1984 But Haskell programmers can safely think of the ordinary
1985 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1986 adding a new existential quantification construct.
1991 <sect3 id="existential-with-context">
1992 <title>Existentials and type classes</title>
1995 An easy extension is to allow
1996 arbitrary contexts before the constructor. For example:
2002 data Baz = forall a. Eq a => Baz1 a a
2003 | forall b. Show b => Baz2 b (b -> b)
2009 The two constructors have the types you'd expect:
2015 Baz1 :: forall a. Eq a => a -> a -> Baz
2016 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2022 But when pattern matching on <function>Baz1</function> the matched values can be compared
2023 for equality, and when pattern matching on <function>Baz2</function> the first matched
2024 value can be converted to a string (as well as applying the function to it).
2025 So this program is legal:
2032 f (Baz1 p q) | p == q = "Yes"
2034 f (Baz2 v fn) = show (fn v)
2040 Operationally, in a dictionary-passing implementation, the
2041 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2042 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2043 extract it on pattern matching.
2048 <sect3 id="existential-records">
2049 <title>Record Constructors</title>
2052 GHC allows existentials to be used with records syntax as well. For example:
2055 data Counter a = forall self. NewCounter
2057 , _inc :: self -> self
2058 , _display :: self -> IO ()
2062 Here <literal>tag</literal> is a public field, with a well-typed selector
2063 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2064 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2065 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2066 compile-time error. In other words, <emphasis>GHC defines a record selector function
2067 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2068 (This example used an underscore in the fields for which record selectors
2069 will not be defined, but that is only programming style; GHC ignores them.)
2073 To make use of these hidden fields, we need to create some helper functions:
2076 inc :: Counter a -> Counter a
2077 inc (NewCounter x i d t) = NewCounter
2078 { _this = i x, _inc = i, _display = d, tag = t }
2080 display :: Counter a -> IO ()
2081 display NewCounter{ _this = x, _display = d } = d x
2084 Now we can define counters with different underlying implementations:
2087 counterA :: Counter String
2088 counterA = NewCounter
2089 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2091 counterB :: Counter String
2092 counterB = NewCounter
2093 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2096 display (inc counterA) -- prints "1"
2097 display (inc (inc counterB)) -- prints "##"
2100 Record update syntax is supported for existentials (and GADTs):
2102 setTag :: Counter a -> a -> Counter a
2103 setTag obj t = obj{ tag = t }
2105 The rule for record update is this: <emphasis>
2106 the types of the updated fields may
2107 mention only the universally-quantified type variables
2108 of the data constructor. For GADTs, the field may mention only types
2109 that appear as a simple type-variable argument in the constructor's result
2110 type</emphasis>. For example:
2112 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2113 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2114 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2115 -- existentially quantified)
2117 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2118 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2119 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2120 -- type-variable argument in G1's result type)
2128 <title>Restrictions</title>
2131 There are several restrictions on the ways in which existentially-quantified
2132 constructors can be use.
2141 When pattern matching, each pattern match introduces a new,
2142 distinct, type for each existential type variable. These types cannot
2143 be unified with any other type, nor can they escape from the scope of
2144 the pattern match. For example, these fragments are incorrect:
2152 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2153 is the result of <function>f1</function>. One way to see why this is wrong is to
2154 ask what type <function>f1</function> has:
2158 f1 :: Foo -> a -- Weird!
2162 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2167 f1 :: forall a. Foo -> a -- Wrong!
2171 The original program is just plain wrong. Here's another sort of error
2175 f2 (Baz1 a b) (Baz1 p q) = a==q
2179 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2180 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2181 from the two <function>Baz1</function> constructors.
2189 You can't pattern-match on an existentially quantified
2190 constructor in a <literal>let</literal> or <literal>where</literal> group of
2191 bindings. So this is illegal:
2195 f3 x = a==b where { Baz1 a b = x }
2198 Instead, use a <literal>case</literal> expression:
2201 f3 x = case x of Baz1 a b -> a==b
2204 In general, you can only pattern-match
2205 on an existentially-quantified constructor in a <literal>case</literal> expression or
2206 in the patterns of a function definition.
2208 The reason for this restriction is really an implementation one.
2209 Type-checking binding groups is already a nightmare without
2210 existentials complicating the picture. Also an existential pattern
2211 binding at the top level of a module doesn't make sense, because it's
2212 not clear how to prevent the existentially-quantified type "escaping".
2213 So for now, there's a simple-to-state restriction. We'll see how
2221 You can't use existential quantification for <literal>newtype</literal>
2222 declarations. So this is illegal:
2226 newtype T = forall a. Ord a => MkT a
2230 Reason: a value of type <literal>T</literal> must be represented as a
2231 pair of a dictionary for <literal>Ord t</literal> and a value of type
2232 <literal>t</literal>. That contradicts the idea that
2233 <literal>newtype</literal> should have no concrete representation.
2234 You can get just the same efficiency and effect by using
2235 <literal>data</literal> instead of <literal>newtype</literal>. If
2236 there is no overloading involved, then there is more of a case for
2237 allowing an existentially-quantified <literal>newtype</literal>,
2238 because the <literal>data</literal> version does carry an
2239 implementation cost, but single-field existentially quantified
2240 constructors aren't much use. So the simple restriction (no
2241 existential stuff on <literal>newtype</literal>) stands, unless there
2242 are convincing reasons to change it.
2250 You can't use <literal>deriving</literal> to define instances of a
2251 data type with existentially quantified data constructors.
2253 Reason: in most cases it would not make sense. For example:;
2256 data T = forall a. MkT [a] deriving( Eq )
2259 To derive <literal>Eq</literal> in the standard way we would need to have equality
2260 between the single component of two <function>MkT</function> constructors:
2264 (MkT a) == (MkT b) = ???
2267 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2268 It's just about possible to imagine examples in which the derived instance
2269 would make sense, but it seems altogether simpler simply to prohibit such
2270 declarations. Define your own instances!
2281 <!-- ====================== Generalised algebraic data types ======================= -->
2283 <sect2 id="gadt-style">
2284 <title>Declaring data types with explicit constructor signatures</title>
2286 <para>GHC allows you to declare an algebraic data type by
2287 giving the type signatures of constructors explicitly. For example:
2291 Just :: a -> Maybe a
2293 The form is called a "GADT-style declaration"
2294 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2295 can only be declared using this form.</para>
2296 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2297 For example, these two declarations are equivalent:
2299 data Foo = forall a. MkFoo a (a -> Bool)
2300 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2303 <para>Any data type that can be declared in standard Haskell-98 syntax
2304 can also be declared using GADT-style syntax.
2305 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2306 they treat class constraints on the data constructors differently.
2307 Specifically, if the constructor is given a type-class context, that
2308 context is made available by pattern matching. For example:
2311 MkSet :: Eq a => [a] -> Set a
2313 makeSet :: Eq a => [a] -> Set a
2314 makeSet xs = MkSet (nub xs)
2316 insert :: a -> Set a -> Set a
2317 insert a (MkSet as) | a `elem` as = MkSet as
2318 | otherwise = MkSet (a:as)
2320 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2321 gives rise to a <literal>(Eq a)</literal>
2322 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2323 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2324 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2325 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2326 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2327 In the example, the equality dictionary is used to satisfy the equality constraint
2328 generated by the call to <literal>elem</literal>, so that the type of
2329 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2332 For example, one possible application is to reify dictionaries:
2334 data NumInst a where
2335 MkNumInst :: Num a => NumInst a
2337 intInst :: NumInst Int
2340 plus :: NumInst a -> a -> a -> a
2341 plus MkNumInst p q = p + q
2343 Here, a value of type <literal>NumInst a</literal> is equivalent
2344 to an explicit <literal>(Num a)</literal> dictionary.
2347 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2348 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2352 = Num a => MkNumInst (NumInst a)
2354 Notice that, unlike the situation when declaring an existential, there is
2355 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2356 data type's universally quantified type variable <literal>a</literal>.
2357 A constructor may have both universal and existential type variables: for example,
2358 the following two declarations are equivalent:
2361 = forall b. (Num a, Eq b) => MkT1 a b
2363 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2366 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2367 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2368 In Haskell 98 the definition
2370 data Eq a => Set' a = MkSet' [a]
2372 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2373 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2374 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2375 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2376 GHC's behaviour is much more useful, as well as much more intuitive.
2380 The rest of this section gives further details about GADT-style data
2385 The result type of each data constructor must begin with the type constructor being defined.
2386 If the result type of all constructors
2387 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2388 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2389 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2393 As with other type signatures, you can give a single signature for several data constructors.
2394 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2403 The type signature of
2404 each constructor is independent, and is implicitly universally quantified as usual.
2405 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2406 have no scope, and different constructors may have different universally-quantified type variables:
2408 data T a where -- The 'a' has no scope
2409 T1,T2 :: b -> T b -- Means forall b. b -> T b
2410 T3 :: T a -- Means forall a. T a
2415 A constructor signature may mention type class constraints, which can differ for
2416 different constructors. For example, this is fine:
2419 T1 :: Eq b => b -> b -> T b
2420 T2 :: (Show c, Ix c) => c -> [c] -> T c
2422 When patten matching, these constraints are made available to discharge constraints
2423 in the body of the match. For example:
2426 f (T1 x y) | x==y = "yes"
2430 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2431 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2432 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2436 Unlike a Haskell-98-style
2437 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2438 have no scope. Indeed, one can write a kind signature instead:
2440 data Set :: * -> * where ...
2442 or even a mixture of the two:
2444 data Bar a :: (* -> *) -> * where ...
2446 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2449 data Bar a (b :: * -> *) where ...
2455 You can use strictness annotations, in the obvious places
2456 in the constructor type:
2459 Lit :: !Int -> Term Int
2460 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2461 Pair :: Term a -> Term b -> Term (a,b)
2466 You can use a <literal>deriving</literal> clause on a GADT-style data type
2467 declaration. For example, these two declarations are equivalent
2469 data Maybe1 a where {
2470 Nothing1 :: Maybe1 a ;
2471 Just1 :: a -> Maybe1 a
2472 } deriving( Eq, Ord )
2474 data Maybe2 a = Nothing2 | Just2 a
2480 The type signature may have quantified type variables that do not appear
2484 MkFoo :: a -> (a->Bool) -> Foo
2487 Here the type variable <literal>a</literal> does not appear in the result type
2488 of either constructor.
2489 Although it is universally quantified in the type of the constructor, such
2490 a type variable is often called "existential".
2491 Indeed, the above declaration declares precisely the same type as
2492 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2494 The type may contain a class context too, of course:
2497 MkShowable :: Show a => a -> Showable
2502 You can use record syntax on a GADT-style data type declaration:
2506 Adult :: { name :: String, children :: [Person] } -> Person
2507 Child :: Show a => { name :: !String, funny :: a } -> Person
2509 As usual, for every constructor that has a field <literal>f</literal>, the type of
2510 field <literal>f</literal> must be the same (modulo alpha conversion).
2511 The <literal>Child</literal> constructor above shows that the signature
2512 may have a context, existentially-quantified variables, and strictness annotations,
2513 just as in the non-record case. (NB: the "type" that follows the double-colon
2514 is not really a type, because of the record syntax and strictness annotations.
2515 A "type" of this form can appear only in a constructor signature.)
2519 Record updates are allowed with GADT-style declarations,
2520 only fields that have the following property: the type of the field
2521 mentions no existential type variables.
2525 As in the case of existentials declared using the Haskell-98-like record syntax
2526 (<xref linkend="existential-records"/>),
2527 record-selector functions are generated only for those fields that have well-typed
2529 Here is the example of that section, in GADT-style syntax:
2531 data Counter a where
2532 NewCounter { _this :: self
2533 , _inc :: self -> self
2534 , _display :: self -> IO ()
2539 As before, only one selector function is generated here, that for <literal>tag</literal>.
2540 Nevertheless, you can still use all the field names in pattern matching and record construction.
2542 </itemizedlist></para>
2546 <title>Generalised Algebraic Data Types (GADTs)</title>
2548 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2549 by allowing constructors to have richer return types. Here is an example:
2552 Lit :: Int -> Term Int
2553 Succ :: Term Int -> Term Int
2554 IsZero :: Term Int -> Term Bool
2555 If :: Term Bool -> Term a -> Term a -> Term a
2556 Pair :: Term a -> Term b -> Term (a,b)
2558 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2559 case with ordinary data types. This generality allows us to
2560 write a well-typed <literal>eval</literal> function
2561 for these <literal>Terms</literal>:
2565 eval (Succ t) = 1 + eval t
2566 eval (IsZero t) = eval t == 0
2567 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2568 eval (Pair e1 e2) = (eval e1, eval e2)
2570 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2571 For example, in the right hand side of the equation
2576 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2577 A precise specification of the type rules is beyond what this user manual aspires to,
2578 but the design closely follows that described in
2580 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2581 unification-based type inference for GADTs</ulink>,
2583 The general principle is this: <emphasis>type refinement is only carried out
2584 based on user-supplied type annotations</emphasis>.
2585 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2586 and lots of obscure error messages will
2587 occur. However, the refinement is quite general. For example, if we had:
2589 eval :: Term a -> a -> a
2590 eval (Lit i) j = i+j
2592 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2593 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2594 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2597 These and many other examples are given in papers by Hongwei Xi, and
2598 Tim Sheard. There is a longer introduction
2599 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2601 <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
2602 may use different notation to that implemented in GHC.
2605 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2606 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2609 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2610 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2611 The result type of each constructor must begin with the type constructor being defined,
2612 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2613 For example, in the <literal>Term</literal> data
2614 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2615 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2620 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2621 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2622 whose result type is not just <literal>T a b</literal>.
2626 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2627 an ordinary data type.
2631 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2635 Lit { val :: Int } :: Term Int
2636 Succ { num :: Term Int } :: Term Int
2637 Pred { num :: Term Int } :: Term Int
2638 IsZero { arg :: Term Int } :: Term Bool
2639 Pair { arg1 :: Term a
2642 If { cnd :: Term Bool
2647 However, for GADTs there is the following additional constraint:
2648 every constructor that has a field <literal>f</literal> must have
2649 the same result type (modulo alpha conversion)
2650 Hence, in the above example, we cannot merge the <literal>num</literal>
2651 and <literal>arg</literal> fields above into a
2652 single name. Although their field types are both <literal>Term Int</literal>,
2653 their selector functions actually have different types:
2656 num :: Term Int -> Term Int
2657 arg :: Term Bool -> Term Int
2662 When pattern-matching against data constructors drawn from a GADT,
2663 for example in a <literal>case</literal> expression, the following rules apply:
2665 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2666 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2667 <listitem><para>The type of any free variable mentioned in any of
2668 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2670 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2671 way to ensure that a variable a rigid type is to give it a type signature.
2672 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2673 Simple unification-based type inference for GADTs
2674 </ulink>. The criteria implemented by GHC are given in the Appendix.
2684 <!-- ====================== End of Generalised algebraic data types ======================= -->
2686 <sect1 id="deriving">
2687 <title>Extensions to the "deriving" mechanism</title>
2689 <sect2 id="deriving-inferred">
2690 <title>Inferred context for deriving clauses</title>
2693 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2696 data T0 f a = MkT0 a deriving( Eq )
2697 data T1 f a = MkT1 (f a) deriving( Eq )
2698 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2700 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2702 instance Eq a => Eq (T0 f a) where ...
2703 instance Eq (f a) => Eq (T1 f a) where ...
2704 instance Eq (f (f a)) => Eq (T2 f a) where ...
2706 The first of these is obviously fine. The second is still fine, although less obviously.
2707 The third is not Haskell 98, and risks losing termination of instances.
2710 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2711 each constraint in the inferred instance context must consist only of type variables,
2712 with no repetitions.
2715 This rule is applied regardless of flags. If you want a more exotic context, you can write
2716 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2720 <sect2 id="stand-alone-deriving">
2721 <title>Stand-alone deriving declarations</title>
2724 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2726 data Foo a = Bar a | Baz String
2728 deriving instance Eq a => Eq (Foo a)
2730 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2731 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2732 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2733 exactly as you would in an ordinary instance declaration.
2734 (In contrast the context is inferred in a <literal>deriving</literal> clause
2735 attached to a data type declaration.)
2737 A <literal>deriving instance</literal> declaration
2738 must obey the same rules concerning form and termination as ordinary instance declarations,
2739 controlled by the same flags; see <xref linkend="instance-decls"/>.
2742 Unlike a <literal>deriving</literal>
2743 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2744 than the data type (assuming you also use
2745 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2748 data Foo a = Bar a | Baz String
2750 deriving instance Eq a => Eq (Foo [a])
2751 deriving instance Eq a => Eq (Foo (Maybe a))
2753 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2754 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2757 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2758 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2761 newtype Foo a = MkFoo (State Int a)
2763 deriving instance MonadState Int Foo
2765 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2766 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2772 <sect2 id="deriving-typeable">
2773 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2776 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2777 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2778 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2779 classes <literal>Eq</literal>, <literal>Ord</literal>,
2780 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2783 GHC extends this list with several more classes that may be automatically derived:
2785 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2786 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2787 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2789 <para>An instance of <literal>Typeable</literal> can only be derived if the
2790 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2791 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2793 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2794 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2796 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2797 are used, and only <literal>Typeable1</literal> up to
2798 <literal>Typeable7</literal> are provided in the library.)
2799 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2800 class, whose kind suits that of the data type constructor, and
2801 then writing the data type instance by hand.
2805 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2806 the class <literal>Functor</literal>,
2807 defined in <literal>GHC.Base</literal>.
2810 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2811 the class <literal>Foldable</literal>,
2812 defined in <literal>Data.Foldable</literal>.
2815 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2816 the class <literal>Traversable</literal>,
2817 defined in <literal>Data.Traversable</literal>.
2820 In each case the appropriate class must be in scope before it
2821 can be mentioned in the <literal>deriving</literal> clause.
2825 <sect2 id="newtype-deriving">
2826 <title>Generalised derived instances for newtypes</title>
2829 When you define an abstract type using <literal>newtype</literal>, you may want
2830 the new type to inherit some instances from its representation. In
2831 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2832 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2833 other classes you have to write an explicit instance declaration. For
2834 example, if you define
2837 newtype Dollars = Dollars Int
2840 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2841 explicitly define an instance of <literal>Num</literal>:
2844 instance Num Dollars where
2845 Dollars a + Dollars b = Dollars (a+b)
2848 All the instance does is apply and remove the <literal>newtype</literal>
2849 constructor. It is particularly galling that, since the constructor
2850 doesn't appear at run-time, this instance declaration defines a
2851 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2852 dictionary, only slower!
2856 <sect3> <title> Generalising the deriving clause </title>
2858 GHC now permits such instances to be derived instead,
2859 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2862 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2865 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2866 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2867 derives an instance declaration of the form
2870 instance Num Int => Num Dollars
2873 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2877 We can also derive instances of constructor classes in a similar
2878 way. For example, suppose we have implemented state and failure monad
2879 transformers, such that
2882 instance Monad m => Monad (State s m)
2883 instance Monad m => Monad (Failure m)
2885 In Haskell 98, we can define a parsing monad by
2887 type Parser tok m a = State [tok] (Failure m) a
2890 which is automatically a monad thanks to the instance declarations
2891 above. With the extension, we can make the parser type abstract,
2892 without needing to write an instance of class <literal>Monad</literal>, via
2895 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2898 In this case the derived instance declaration is of the form
2900 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2903 Notice that, since <literal>Monad</literal> is a constructor class, the
2904 instance is a <emphasis>partial application</emphasis> of the new type, not the
2905 entire left hand side. We can imagine that the type declaration is
2906 "eta-converted" to generate the context of the instance
2911 We can even derive instances of multi-parameter classes, provided the
2912 newtype is the last class parameter. In this case, a ``partial
2913 application'' of the class appears in the <literal>deriving</literal>
2914 clause. For example, given the class
2917 class StateMonad s m | m -> s where ...
2918 instance Monad m => StateMonad s (State s m) where ...
2920 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2922 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2923 deriving (Monad, StateMonad [tok])
2926 The derived instance is obtained by completing the application of the
2927 class to the new type:
2930 instance StateMonad [tok] (State [tok] (Failure m)) =>
2931 StateMonad [tok] (Parser tok m)
2936 As a result of this extension, all derived instances in newtype
2937 declarations are treated uniformly (and implemented just by reusing
2938 the dictionary for the representation type), <emphasis>except</emphasis>
2939 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2940 the newtype and its representation.
2944 <sect3> <title> A more precise specification </title>
2946 Derived instance declarations are constructed as follows. Consider the
2947 declaration (after expansion of any type synonyms)
2950 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2956 The <literal>ci</literal> are partial applications of
2957 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2958 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2961 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2964 The type <literal>t</literal> is an arbitrary type.
2967 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2968 nor in the <literal>ci</literal>, and
2971 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2972 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2973 should not "look through" the type or its constructor. You can still
2974 derive these classes for a newtype, but it happens in the usual way, not
2975 via this new mechanism.
2978 Then, for each <literal>ci</literal>, the derived instance
2981 instance ci t => ci (T v1...vk)
2983 As an example which does <emphasis>not</emphasis> work, consider
2985 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2987 Here we cannot derive the instance
2989 instance Monad (State s m) => Monad (NonMonad m)
2992 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2993 and so cannot be "eta-converted" away. It is a good thing that this
2994 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2995 not, in fact, a monad --- for the same reason. Try defining
2996 <literal>>>=</literal> with the correct type: you won't be able to.
3000 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3001 important, since we can only derive instances for the last one. If the
3002 <literal>StateMonad</literal> class above were instead defined as
3005 class StateMonad m s | m -> s where ...
3008 then we would not have been able to derive an instance for the
3009 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3010 classes usually have one "main" parameter for which deriving new
3011 instances is most interesting.
3013 <para>Lastly, all of this applies only for classes other than
3014 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3015 and <literal>Data</literal>, for which the built-in derivation applies (section
3016 4.3.3. of the Haskell Report).
3017 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3018 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3019 the standard method is used or the one described here.)
3026 <!-- TYPE SYSTEM EXTENSIONS -->
3027 <sect1 id="type-class-extensions">
3028 <title>Class and instances declarations</title>
3030 <sect2 id="multi-param-type-classes">
3031 <title>Class declarations</title>
3034 This section, and the next one, documents GHC's type-class extensions.
3035 There's lots of background in the paper <ulink
3036 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3037 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3038 Jones, Erik Meijer).
3041 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3045 <title>Multi-parameter type classes</title>
3047 Multi-parameter type classes are permitted. For example:
3051 class Collection c a where
3052 union :: c a -> c a -> c a
3060 <title>The superclasses of a class declaration</title>
3063 There are no restrictions on the context in a class declaration
3064 (which introduces superclasses), except that the class hierarchy must
3065 be acyclic. So these class declarations are OK:
3069 class Functor (m k) => FiniteMap m k where
3072 class (Monad m, Monad (t m)) => Transform t m where
3073 lift :: m a -> (t m) a
3079 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3080 of "acyclic" involves only the superclass relationships. For example,
3086 op :: D b => a -> b -> b
3089 class C a => D a where { ... }
3093 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3094 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3095 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3102 <sect3 id="class-method-types">
3103 <title>Class method types</title>
3106 Haskell 98 prohibits class method types to mention constraints on the
3107 class type variable, thus:
3110 fromList :: [a] -> s a
3111 elem :: Eq a => a -> s a -> Bool
3113 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3114 contains the constraint <literal>Eq a</literal>, constrains only the
3115 class type variable (in this case <literal>a</literal>).
3116 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3123 <sect2 id="functional-dependencies">
3124 <title>Functional dependencies
3127 <para> Functional dependencies are implemented as described by Mark Jones
3128 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3129 In Proceedings of the 9th European Symposium on Programming,
3130 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3134 Functional dependencies are introduced by a vertical bar in the syntax of a
3135 class declaration; e.g.
3137 class (Monad m) => MonadState s m | m -> s where ...
3139 class Foo a b c | a b -> c where ...
3141 There should be more documentation, but there isn't (yet). Yell if you need it.
3144 <sect3><title>Rules for functional dependencies </title>
3146 In a class declaration, all of the class type variables must be reachable (in the sense
3147 mentioned in <xref linkend="type-restrictions"/>)
3148 from the free variables of each method type.
3152 class Coll s a where
3154 insert :: s -> a -> s
3157 is not OK, because the type of <literal>empty</literal> doesn't mention
3158 <literal>a</literal>. Functional dependencies can make the type variable
3161 class Coll s a | s -> a where
3163 insert :: s -> a -> s
3166 Alternatively <literal>Coll</literal> might be rewritten
3169 class Coll s a where
3171 insert :: s a -> a -> s a
3175 which makes the connection between the type of a collection of
3176 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3177 Occasionally this really doesn't work, in which case you can split the
3185 class CollE s => Coll s a where
3186 insert :: s -> a -> s
3193 <title>Background on functional dependencies</title>
3195 <para>The following description of the motivation and use of functional dependencies is taken
3196 from the Hugs user manual, reproduced here (with minor changes) by kind
3197 permission of Mark Jones.
3200 Consider the following class, intended as part of a
3201 library for collection types:
3203 class Collects e ce where
3205 insert :: e -> ce -> ce
3206 member :: e -> ce -> Bool
3208 The type variable e used here represents the element type, while ce is the type
3209 of the container itself. Within this framework, we might want to define
3210 instances of this class for lists or characteristic functions (both of which
3211 can be used to represent collections of any equality type), bit sets (which can
3212 be used to represent collections of characters), or hash tables (which can be
3213 used to represent any collection whose elements have a hash function). Omitting
3214 standard implementation details, this would lead to the following declarations:
3216 instance Eq e => Collects e [e] where ...
3217 instance Eq e => Collects e (e -> Bool) where ...
3218 instance Collects Char BitSet where ...
3219 instance (Hashable e, Collects a ce)
3220 => Collects e (Array Int ce) where ...
3222 All this looks quite promising; we have a class and a range of interesting
3223 implementations. Unfortunately, there are some serious problems with the class
3224 declaration. First, the empty function has an ambiguous type:
3226 empty :: Collects e ce => ce
3228 By "ambiguous" we mean that there is a type variable e that appears on the left
3229 of the <literal>=></literal> symbol, but not on the right. The problem with
3230 this is that, according to the theoretical foundations of Haskell overloading,
3231 we cannot guarantee a well-defined semantics for any term with an ambiguous
3235 We can sidestep this specific problem by removing the empty member from the
3236 class declaration. However, although the remaining members, insert and member,
3237 do not have ambiguous types, we still run into problems when we try to use
3238 them. For example, consider the following two functions:
3240 f x y = insert x . insert y
3243 for which GHC infers the following types:
3245 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3246 g :: (Collects Bool c, Collects Char c) => c -> c
3248 Notice that the type for f allows the two parameters x and y to be assigned
3249 different types, even though it attempts to insert each of the two values, one
3250 after the other, into the same collection. If we're trying to model collections
3251 that contain only one type of value, then this is clearly an inaccurate
3252 type. Worse still, the definition for g is accepted, without causing a type
3253 error. As a result, the error in this code will not be flagged at the point
3254 where it appears. Instead, it will show up only when we try to use g, which
3255 might even be in a different module.
3258 <sect4><title>An attempt to use constructor classes</title>
3261 Faced with the problems described above, some Haskell programmers might be
3262 tempted to use something like the following version of the class declaration:
3264 class Collects e c where
3266 insert :: e -> c e -> c e
3267 member :: e -> c e -> Bool
3269 The key difference here is that we abstract over the type constructor c that is
3270 used to form the collection type c e, and not over that collection type itself,
3271 represented by ce in the original class declaration. This avoids the immediate
3272 problems that we mentioned above: empty has type <literal>Collects e c => c
3273 e</literal>, which is not ambiguous.
3276 The function f from the previous section has a more accurate type:
3278 f :: (Collects e c) => e -> e -> c e -> c e
3280 The function g from the previous section is now rejected with a type error as
3281 we would hope because the type of f does not allow the two arguments to have
3283 This, then, is an example of a multiple parameter class that does actually work
3284 quite well in practice, without ambiguity problems.
3285 There is, however, a catch. This version of the Collects class is nowhere near
3286 as general as the original class seemed to be: only one of the four instances
3287 for <literal>Collects</literal>
3288 given above can be used with this version of Collects because only one of
3289 them---the instance for lists---has a collection type that can be written in
3290 the form c e, for some type constructor c, and element type e.
3294 <sect4><title>Adding functional dependencies</title>
3297 To get a more useful version of the Collects class, Hugs provides a mechanism
3298 that allows programmers to specify dependencies between the parameters of a
3299 multiple parameter class (For readers with an interest in theoretical
3300 foundations and previous work: The use of dependency information can be seen
3301 both as a generalization of the proposal for `parametric type classes' that was
3302 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3303 later framework for "improvement" of qualified types. The
3304 underlying ideas are also discussed in a more theoretical and abstract setting
3305 in a manuscript [implparam], where they are identified as one point in a
3306 general design space for systems of implicit parameterization.).
3308 To start with an abstract example, consider a declaration such as:
3310 class C a b where ...
3312 which tells us simply that C can be thought of as a binary relation on types
3313 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3314 included in the definition of classes to add information about dependencies
3315 between parameters, as in the following examples:
3317 class D a b | a -> b where ...
3318 class E a b | a -> b, b -> a where ...
3320 The notation <literal>a -> b</literal> used here between the | and where
3321 symbols --- not to be
3322 confused with a function type --- indicates that the a parameter uniquely
3323 determines the b parameter, and might be read as "a determines b." Thus D is
3324 not just a relation, but actually a (partial) function. Similarly, from the two
3325 dependencies that are included in the definition of E, we can see that E
3326 represents a (partial) one-one mapping between types.
3329 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3330 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3331 m>=0, meaning that the y parameters are uniquely determined by the x
3332 parameters. Spaces can be used as separators if more than one variable appears
3333 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3334 annotated with multiple dependencies using commas as separators, as in the
3335 definition of E above. Some dependencies that we can write in this notation are
3336 redundant, and will be rejected because they don't serve any useful
3337 purpose, and may instead indicate an error in the program. Examples of
3338 dependencies like this include <literal>a -> a </literal>,
3339 <literal>a -> a a </literal>,
3340 <literal>a -> </literal>, etc. There can also be
3341 some redundancy if multiple dependencies are given, as in
3342 <literal>a->b</literal>,
3343 <literal>b->c </literal>, <literal>a->c </literal>, and
3344 in which some subset implies the remaining dependencies. Examples like this are
3345 not treated as errors. Note that dependencies appear only in class
3346 declarations, and not in any other part of the language. In particular, the
3347 syntax for instance declarations, class constraints, and types is completely
3351 By including dependencies in a class declaration, we provide a mechanism for
3352 the programmer to specify each multiple parameter class more precisely. The
3353 compiler, on the other hand, is responsible for ensuring that the set of
3354 instances that are in scope at any given point in the program is consistent
3355 with any declared dependencies. For example, the following pair of instance
3356 declarations cannot appear together in the same scope because they violate the
3357 dependency for D, even though either one on its own would be acceptable:
3359 instance D Bool Int where ...
3360 instance D Bool Char where ...
3362 Note also that the following declaration is not allowed, even by itself:
3364 instance D [a] b where ...
3366 The problem here is that this instance would allow one particular choice of [a]
3367 to be associated with more than one choice for b, which contradicts the
3368 dependency specified in the definition of D. More generally, this means that,
3369 in any instance of the form:
3371 instance D t s where ...
3373 for some particular types t and s, the only variables that can appear in s are
3374 the ones that appear in t, and hence, if the type t is known, then s will be
3375 uniquely determined.
3378 The benefit of including dependency information is that it allows us to define
3379 more general multiple parameter classes, without ambiguity problems, and with
3380 the benefit of more accurate types. To illustrate this, we return to the
3381 collection class example, and annotate the original definition of <literal>Collects</literal>
3382 with a simple dependency:
3384 class Collects e ce | ce -> e where
3386 insert :: e -> ce -> ce
3387 member :: e -> ce -> Bool
3389 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3390 determined by the type of the collection ce. Note that both parameters of
3391 Collects are of kind *; there are no constructor classes here. Note too that
3392 all of the instances of Collects that we gave earlier can be used
3393 together with this new definition.
3396 What about the ambiguity problems that we encountered with the original
3397 definition? The empty function still has type Collects e ce => ce, but it is no
3398 longer necessary to regard that as an ambiguous type: Although the variable e
3399 does not appear on the right of the => symbol, the dependency for class
3400 Collects tells us that it is uniquely determined by ce, which does appear on
3401 the right of the => symbol. Hence the context in which empty is used can still
3402 give enough information to determine types for both ce and e, without
3403 ambiguity. More generally, we need only regard a type as ambiguous if it
3404 contains a variable on the left of the => that is not uniquely determined
3405 (either directly or indirectly) by the variables on the right.
3408 Dependencies also help to produce more accurate types for user defined
3409 functions, and hence to provide earlier detection of errors, and less cluttered
3410 types for programmers to work with. Recall the previous definition for a
3413 f x y = insert x y = insert x . insert y
3415 for which we originally obtained a type:
3417 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3419 Given the dependency information that we have for Collects, however, we can
3420 deduce that a and b must be equal because they both appear as the second
3421 parameter in a Collects constraint with the same first parameter c. Hence we
3422 can infer a shorter and more accurate type for f:
3424 f :: (Collects a c) => a -> a -> c -> c
3426 In a similar way, the earlier definition of g will now be flagged as a type error.
3429 Although we have given only a few examples here, it should be clear that the
3430 addition of dependency information can help to make multiple parameter classes
3431 more useful in practice, avoiding ambiguity problems, and allowing more general
3432 sets of instance declarations.
3438 <sect2 id="instance-decls">
3439 <title>Instance declarations</title>
3441 <para>An instance declaration has the form
3443 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 ...
3445 The part before the "<literal>=></literal>" is the
3446 <emphasis>context</emphasis>, while the part after the
3447 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3450 <sect3 id="flexible-instance-head">
3451 <title>Relaxed rules for the instance head</title>
3454 In Haskell 98 the head of an instance declaration
3455 must be of the form <literal>C (T a1 ... an)</literal>, where
3456 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3457 and the <literal>a1 ... an</literal> are distinct type variables.
3458 GHC relaxes these rules in two ways.
3462 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3463 declaration to mention arbitrary nested types.
3464 For example, this becomes a legal instance declaration
3466 instance C (Maybe Int) where ...
3468 See also the <link linkend="instance-overlap">rules on overlap</link>.
3471 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3472 synonyms. As always, using a type synonym is just shorthand for
3473 writing the RHS of the type synonym definition. For example:
3477 type Point = (Int,Int)
3478 instance C Point where ...
3479 instance C [Point] where ...
3483 is legal. However, if you added
3487 instance C (Int,Int) where ...
3491 as well, then the compiler will complain about the overlapping
3492 (actually, identical) instance declarations. As always, type synonyms
3493 must be fully applied. You cannot, for example, write:
3497 instance Monad P where ...
3505 <sect3 id="instance-rules">
3506 <title>Relaxed rules for instance contexts</title>
3508 <para>In Haskell 98, the assertions in the context of the instance declaration
3509 must be of the form <literal>C a</literal> where <literal>a</literal>
3510 is a type variable that occurs in the head.
3514 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3515 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3516 With this flag the context of the instance declaration can each consist of arbitrary
3517 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3521 The Paterson Conditions: for each assertion in the context
3523 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3524 <listitem><para>The assertion has fewer constructors and variables (taken together
3525 and counting repetitions) than the head</para></listitem>
3529 <listitem><para>The Coverage Condition. For each functional dependency,
3530 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3531 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3532 every type variable in
3533 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3534 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3535 substitution mapping each type variable in the class declaration to the
3536 corresponding type in the instance declaration.
3539 These restrictions ensure that context reduction terminates: each reduction
3540 step makes the problem smaller by at least one
3541 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3542 if you give the <option>-XUndecidableInstances</option>
3543 flag (<xref linkend="undecidable-instances"/>).
3544 You can find lots of background material about the reason for these
3545 restrictions in the paper <ulink
3546 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3547 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3550 For example, these are OK:
3552 instance C Int [a] -- Multiple parameters
3553 instance Eq (S [a]) -- Structured type in head
3555 -- Repeated type variable in head
3556 instance C4 a a => C4 [a] [a]
3557 instance Stateful (ST s) (MutVar s)
3559 -- Head can consist of type variables only
3561 instance (Eq a, Show b) => C2 a b
3563 -- Non-type variables in context
3564 instance Show (s a) => Show (Sized s a)
3565 instance C2 Int a => C3 Bool [a]
3566 instance C2 Int a => C3 [a] b
3570 -- Context assertion no smaller than head
3571 instance C a => C a where ...
3572 -- (C b b) has more more occurrences of b than the head
3573 instance C b b => Foo [b] where ...
3578 The same restrictions apply to instances generated by
3579 <literal>deriving</literal> clauses. Thus the following is accepted:
3581 data MinHeap h a = H a (h a)
3584 because the derived instance
3586 instance (Show a, Show (h a)) => Show (MinHeap h a)
3588 conforms to the above rules.
3592 A useful idiom permitted by the above rules is as follows.
3593 If one allows overlapping instance declarations then it's quite
3594 convenient to have a "default instance" declaration that applies if
3595 something more specific does not:
3603 <sect3 id="undecidable-instances">
3604 <title>Undecidable instances</title>
3607 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3608 For example, sometimes you might want to use the following to get the
3609 effect of a "class synonym":
3611 class (C1 a, C2 a, C3 a) => C a where { }
3613 instance (C1 a, C2 a, C3 a) => C a where { }
3615 This allows you to write shorter signatures:
3621 f :: (C1 a, C2 a, C3 a) => ...
3623 The restrictions on functional dependencies (<xref
3624 linkend="functional-dependencies"/>) are particularly troublesome.
3625 It is tempting to introduce type variables in the context that do not appear in
3626 the head, something that is excluded by the normal rules. For example:
3628 class HasConverter a b | a -> b where
3631 data Foo a = MkFoo a
3633 instance (HasConverter a b,Show b) => Show (Foo a) where
3634 show (MkFoo value) = show (convert value)
3636 This is dangerous territory, however. Here, for example, is a program that would make the
3641 instance F [a] [[a]]
3642 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3644 Similarly, it can be tempting to lift the coverage condition:
3646 class Mul a b c | a b -> c where
3647 (.*.) :: a -> b -> c
3649 instance Mul Int Int Int where (.*.) = (*)
3650 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3651 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3653 The third instance declaration does not obey the coverage condition;
3654 and indeed the (somewhat strange) definition:
3656 f = \ b x y -> if b then x .*. [y] else y
3658 makes instance inference go into a loop, because it requires the constraint
3659 <literal>(Mul a [b] b)</literal>.
3662 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3663 the experimental flag <option>-XUndecidableInstances</option>
3664 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3665 both the Paterson Conditions and the Coverage Condition
3666 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3667 fixed-depth recursion stack. If you exceed the stack depth you get a
3668 sort of backtrace, and the opportunity to increase the stack depth
3669 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3675 <sect3 id="instance-overlap">
3676 <title>Overlapping instances</title>
3678 In general, <emphasis>GHC requires that that it be unambiguous which instance
3680 should be used to resolve a type-class constraint</emphasis>. This behaviour
3681 can be modified by two flags: <option>-XOverlappingInstances</option>
3682 <indexterm><primary>-XOverlappingInstances
3683 </primary></indexterm>
3684 and <option>-XIncoherentInstances</option>
3685 <indexterm><primary>-XIncoherentInstances
3686 </primary></indexterm>, as this section discusses. Both these
3687 flags are dynamic flags, and can be set on a per-module basis, using
3688 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3690 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3691 it tries to match every instance declaration against the
3693 by instantiating the head of the instance declaration. For example, consider
3696 instance context1 => C Int a where ... -- (A)
3697 instance context2 => C a Bool where ... -- (B)
3698 instance context3 => C Int [a] where ... -- (C)
3699 instance context4 => C Int [Int] where ... -- (D)
3701 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3702 but (C) and (D) do not. When matching, GHC takes
3703 no account of the context of the instance declaration
3704 (<literal>context1</literal> etc).
3705 GHC's default behaviour is that <emphasis>exactly one instance must match the
3706 constraint it is trying to resolve</emphasis>.
3707 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3708 including both declarations (A) and (B), say); an error is only reported if a
3709 particular constraint matches more than one.
3713 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3714 more than one instance to match, provided there is a most specific one. For
3715 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3716 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3717 most-specific match, the program is rejected.
3720 However, GHC is conservative about committing to an overlapping instance. For example:
3725 Suppose that from the RHS of <literal>f</literal> we get the constraint
3726 <literal>C Int [b]</literal>. But
3727 GHC does not commit to instance (C), because in a particular
3728 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3729 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3730 So GHC rejects the program.
3731 (If you add the flag <option>-XIncoherentInstances</option>,
3732 GHC will instead pick (C), without complaining about
3733 the problem of subsequent instantiations.)
3736 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3737 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3738 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3739 it instead. In this case, GHC will refrain from
3740 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3741 as before) but, rather than rejecting the program, it will infer the type
3743 f :: C Int [b] => [b] -> [b]
3745 That postpones the question of which instance to pick to the
3746 call site for <literal>f</literal>
3747 by which time more is known about the type <literal>b</literal>.
3748 You can write this type signature yourself if you use the
3749 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3753 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3757 instance Foo [b] where
3760 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3761 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3762 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3763 declaration. The solution is to postpone the choice by adding the constraint to the context
3764 of the instance declaration, thus:
3766 instance C Int [b] => Foo [b] where
3769 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3772 The willingness to be overlapped or incoherent is a property of
3773 the <emphasis>instance declaration</emphasis> itself, controlled by the
3774 presence or otherwise of the <option>-XOverlappingInstances</option>
3775 and <option>-XIncoherentInstances</option> flags when that module is
3776 being defined. Neither flag is required in a module that imports and uses the
3777 instance declaration. Specifically, during the lookup process:
3780 An instance declaration is ignored during the lookup process if (a) a more specific
3781 match is found, and (b) the instance declaration was compiled with
3782 <option>-XOverlappingInstances</option>. The flag setting for the
3783 more-specific instance does not matter.
3786 Suppose an instance declaration does not match the constraint being looked up, but
3787 does unify with it, so that it might match when the constraint is further
3788 instantiated. Usually GHC will regard this as a reason for not committing to
3789 some other constraint. But if the instance declaration was compiled with
3790 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3791 check for that declaration.
3794 These rules make it possible for a library author to design a library that relies on
3795 overlapping instances without the library client having to know.
3798 If an instance declaration is compiled without
3799 <option>-XOverlappingInstances</option>,
3800 then that instance can never be overlapped. This could perhaps be
3801 inconvenient. Perhaps the rule should instead say that the
3802 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3803 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3804 at a usage site should be permitted regardless of how the instance declarations
3805 are compiled, if the <option>-XOverlappingInstances</option> flag is
3806 used at the usage site. (Mind you, the exact usage site can occasionally be
3807 hard to pin down.) We are interested to receive feedback on these points.
3809 <para>The <option>-XIncoherentInstances</option> flag implies the
3810 <option>-XOverlappingInstances</option> flag, but not vice versa.
3818 <sect2 id="overloaded-strings">
3819 <title>Overloaded string literals
3823 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3824 string literal has type <literal>String</literal>, but with overloaded string
3825 literals enabled (with <literal>-XOverloadedStrings</literal>)
3826 a string literal has type <literal>(IsString a) => a</literal>.
3829 This means that the usual string syntax can be used, e.g., for packed strings
3830 and other variations of string like types. String literals behave very much
3831 like integer literals, i.e., they can be used in both expressions and patterns.
3832 If used in a pattern the literal with be replaced by an equality test, in the same
3833 way as an integer literal is.
3836 The class <literal>IsString</literal> is defined as:
3838 class IsString a where
3839 fromString :: String -> a
3841 The only predefined instance is the obvious one to make strings work as usual:
3843 instance IsString [Char] where
3846 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3847 it explicitly (for example, to give an instance declaration for it), you can import it
3848 from module <literal>GHC.Exts</literal>.
3851 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3855 Each type in a default declaration must be an
3856 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3860 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3861 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3862 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3863 <emphasis>or</emphasis> <literal>IsString</literal>.
3872 import GHC.Exts( IsString(..) )
3874 newtype MyString = MyString String deriving (Eq, Show)
3875 instance IsString MyString where
3876 fromString = MyString
3878 greet :: MyString -> MyString
3879 greet "hello" = "world"
3883 print $ greet "hello"
3884 print $ greet "fool"
3888 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3889 to work since it gets translated into an equality comparison.
3895 <sect1 id="type-families">
3896 <title>Type families</title>
3899 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3900 facilitate type-level
3901 programming. Type families are a generalisation of <firstterm>associated
3902 data types</firstterm>
3903 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3904 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3905 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3906 Symposium on Principles of Programming Languages (POPL'05)”, pages
3907 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3908 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3909 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3911 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3912 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3913 themselves are described in the paper “<ulink
3914 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3915 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3917 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3918 13th ACM SIGPLAN International Conference on Functional
3919 Programming”, ACM Press, pages 51-62, 2008. Type families
3920 essentially provide type-indexed data types and named functions on types,
3921 which are useful for generic programming and highly parameterised library
3922 interfaces as well as interfaces with enhanced static information, much like
3923 dependent types. They might also be regarded as an alternative to functional
3924 dependencies, but provide a more functional style of type-level programming
3925 than the relational style of functional dependencies.
3928 Indexed type families, or type families for short, are type constructors that
3929 represent sets of types. Set members are denoted by supplying the type family
3930 constructor with type parameters, which are called <firstterm>type
3931 indices</firstterm>. The
3932 difference between vanilla parametrised type constructors and family
3933 constructors is much like between parametrically polymorphic functions and
3934 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3935 behave the same at all type instances, whereas class methods can change their
3936 behaviour in dependence on the class type parameters. Similarly, vanilla type
3937 constructors imply the same data representation for all type instances, but
3938 family constructors can have varying representation types for varying type
3942 Indexed type families come in two flavours: <firstterm>data
3943 families</firstterm> and <firstterm>type synonym
3944 families</firstterm>. They are the indexed family variants of algebraic
3945 data types and type synonyms, respectively. The instances of data families
3946 can be data types and newtypes.
3949 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3950 Additional information on the use of type families in GHC is available on
3951 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3952 Haskell wiki page on type families</ulink>.
3955 <sect2 id="data-families">
3956 <title>Data families</title>
3959 Data families appear in two flavours: (1) they can be defined on the
3961 or (2) they can appear inside type classes (in which case they are known as
3962 associated types). The former is the more general variant, as it lacks the
3963 requirement for the type-indexes to coincide with the class
3964 parameters. However, the latter can lead to more clearly structured code and
3965 compiler warnings if some type instances were - possibly accidentally -
3966 omitted. In the following, we always discuss the general toplevel form first
3967 and then cover the additional constraints placed on associated types.
3970 <sect3 id="data-family-declarations">
3971 <title>Data family declarations</title>
3974 Indexed data families are introduced by a signature, such as
3976 data family GMap k :: * -> *
3978 The special <literal>family</literal> distinguishes family from standard
3979 data declarations. The result kind annotation is optional and, as
3980 usual, defaults to <literal>*</literal> if omitted. An example is
3984 Named arguments can also be given explicit kind signatures if needed.
3986 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3987 declarations] named arguments are entirely optional, so that we can
3988 declare <literal>Array</literal> alternatively with
3990 data family Array :: * -> *
3994 <sect4 id="assoc-data-family-decl">
3995 <title>Associated data family declarations</title>
3997 When a data family is declared as part of a type class, we drop
3998 the <literal>family</literal> special. The <literal>GMap</literal>
3999 declaration takes the following form
4001 class GMapKey k where
4002 data GMap k :: * -> *
4005 In contrast to toplevel declarations, named arguments must be used for
4006 all type parameters that are to be used as type-indexes. Moreover,
4007 the argument names must be class parameters. Each class parameter may
4008 only be used at most once per associated type, but some may be omitted
4009 and they may be in an order other than in the class head. Hence, the
4010 following contrived example is admissible:
4019 <sect3 id="data-instance-declarations">
4020 <title>Data instance declarations</title>
4023 Instance declarations of data and newtype families are very similar to
4024 standard data and newtype declarations. The only two differences are
4025 that the keyword <literal>data</literal> or <literal>newtype</literal>
4026 is followed by <literal>instance</literal> and that some or all of the
4027 type arguments can be non-variable types, but may not contain forall
4028 types or type synonym families. However, data families are generally
4029 allowed in type parameters, and type synonyms are allowed as long as
4030 they are fully applied and expand to a type that is itself admissible -
4031 exactly as this is required for occurrences of type synonyms in class
4032 instance parameters. For example, the <literal>Either</literal>
4033 instance for <literal>GMap</literal> is
4035 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4037 In this example, the declaration has only one variant. In general, it
4041 Data and newtype instance declarations are only permitted when an
4042 appropriate family declaration is in scope - just as a class instance declaratoin
4043 requires the class declaration to be visible. Moreover, each instance
4044 declaration has to conform to the kind determined by its family
4045 declaration. This implies that the number of parameters of an instance
4046 declaration matches the arity determined by the kind of the family.
4049 A data family instance declaration can use the full exprssiveness of
4050 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4052 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4053 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4054 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4057 data instance T Int = T1 Int | T2 Bool
4058 newtype instance T Char = TC Bool
4061 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4062 and indeed can define a GADT. For example:
4065 data instance G [a] b where
4066 G1 :: c -> G [Int] b
4070 <listitem><para> You can use a <literal>deriving</literal> clause on a
4071 <literal>data instance</literal> or <literal>newtype instance</literal>
4078 Even if type families are defined as toplevel declarations, functions
4079 that perform different computations for different family instances may still
4080 need to be defined as methods of type classes. In particular, the
4081 following is not possible:
4084 data instance T Int = A
4085 data instance T Char = B
4087 foo A = 1 -- WRONG: These two equations together...
4088 foo B = 2 -- ...will produce a type error.
4090 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4094 instance Foo Int where
4096 instance Foo Char where
4099 (Given the functionality provided by GADTs (Generalised Algebraic Data
4100 Types), it might seem as if a definition, such as the above, should be
4101 feasible. However, type families are - in contrast to GADTs - are
4102 <emphasis>open;</emphasis> i.e., new instances can always be added,
4104 modules. Supporting pattern matching across different data instances
4105 would require a form of extensible case construct.)
4108 <sect4 id="assoc-data-inst">
4109 <title>Associated data instances</title>
4111 When an associated data family instance is declared within a type
4112 class instance, we drop the <literal>instance</literal> keyword in the
4113 family instance. So, the <literal>Either</literal> instance
4114 for <literal>GMap</literal> becomes:
4116 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4117 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4120 The most important point about associated family instances is that the
4121 type indexes corresponding to class parameters must be identical to
4122 the type given in the instance head; here this is the first argument
4123 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4124 which coincides with the only class parameter. Any parameters to the
4125 family constructor that do not correspond to class parameters, need to
4126 be variables in every instance; here this is the
4127 variable <literal>v</literal>.
4130 Instances for an associated family can only appear as part of
4131 instances declarations of the class in which the family was declared -
4132 just as with the equations of the methods of a class. Also in
4133 correspondence to how methods are handled, declarations of associated
4134 types can be omitted in class instances. If an associated family
4135 instance is omitted, the corresponding instance type is not inhabited;
4136 i.e., only diverging expressions, such
4137 as <literal>undefined</literal>, can assume the type.
4141 <sect4 id="scoping-class-params">
4142 <title>Scoping of class parameters</title>
4144 In the case of multi-parameter type classes, the visibility of class
4145 parameters in the right-hand side of associated family instances
4146 depends <emphasis>solely</emphasis> on the parameters of the data
4147 family. As an example, consider the simple class declaration
4152 Only one of the two class parameters is a parameter to the data
4153 family. Hence, the following instance declaration is invalid:
4155 instance C [c] d where
4156 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4158 Here, the right-hand side of the data instance mentions the type
4159 variable <literal>d</literal> that does not occur in its left-hand
4160 side. We cannot admit such data instances as they would compromise
4165 <sect4 id="family-class-inst">
4166 <title>Type class instances of family instances</title>
4168 Type class instances of instances of data families can be defined as
4169 usual, and in particular data instance declarations can
4170 have <literal>deriving</literal> clauses. For example, we can write
4172 data GMap () v = GMapUnit (Maybe v)
4175 which implicitly defines an instance of the form
4177 instance Show v => Show (GMap () v) where ...
4181 Note that class instances are always for
4182 particular <emphasis>instances</emphasis> of a data family and never
4183 for an entire family as a whole. This is for essentially the same
4184 reasons that we cannot define a toplevel function that performs
4185 pattern matching on the data constructors
4186 of <emphasis>different</emphasis> instances of a single type family.
4187 It would require a form of extensible case construct.
4191 <sect4 id="data-family-overlap">
4192 <title>Overlap of data instances</title>
4194 The instance declarations of a data family used in a single program
4195 may not overlap at all, independent of whether they are associated or
4196 not. In contrast to type class instances, this is not only a matter
4197 of consistency, but one of type safety.
4203 <sect3 id="data-family-import-export">
4204 <title>Import and export</title>
4207 The association of data constructors with type families is more dynamic
4208 than that is the case with standard data and newtype declarations. In
4209 the standard case, the notation <literal>T(..)</literal> in an import or
4210 export list denotes the type constructor and all the data constructors
4211 introduced in its declaration. However, a family declaration never
4212 introduces any data constructors; instead, data constructors are
4213 introduced by family instances. As a result, which data constructors
4214 are associated with a type family depends on the currently visible
4215 instance declarations for that family. Consequently, an import or
4216 export item of the form <literal>T(..)</literal> denotes the family
4217 constructor and all currently visible data constructors - in the case of
4218 an export item, these may be either imported or defined in the current
4219 module. The treatment of import and export items that explicitly list
4220 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4224 <sect4 id="data-family-impexp-assoc">
4225 <title>Associated families</title>
4227 As expected, an import or export item of the
4228 form <literal>C(..)</literal> denotes all of the class' methods and
4229 associated types. However, when associated types are explicitly
4230 listed as subitems of a class, we need some new syntax, as uppercase
4231 identifiers as subitems are usually data constructors, not type
4232 constructors. To clarify that we denote types here, each associated
4233 type name needs to be prefixed by the keyword <literal>type</literal>.
4234 So for example, when explicitly listing the components of
4235 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4236 GMap, empty, lookup, insert)</literal>.
4240 <sect4 id="data-family-impexp-examples">
4241 <title>Examples</title>
4243 Assuming our running <literal>GMapKey</literal> class example, let us
4244 look at some export lists and their meaning:
4247 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4248 just the class name.</para>
4251 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4252 Exports the class, the associated type <literal>GMap</literal>
4254 functions <literal>empty</literal>, <literal>lookup</literal>,
4255 and <literal>insert</literal>. None of the data constructors is
4259 <para><literal>module GMap (GMapKey(..), GMap(..))
4260 where...</literal>: As before, but also exports all the data
4261 constructors <literal>GMapInt</literal>,
4262 <literal>GMapChar</literal>,
4263 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4264 and <literal>GMapUnit</literal>.</para>
4267 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4268 GMap(..)) where...</literal>: As before.</para>
4271 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4272 where...</literal>: As before.</para>
4277 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4278 both the class <literal>GMapKey</literal> as well as its associated
4279 type <literal>GMap</literal>. However, you cannot
4280 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4281 sub-component specifications cannot be nested. To
4282 specify <literal>GMap</literal>'s data constructors, you have to list
4287 <sect4 id="data-family-impexp-instances">
4288 <title>Instances</title>
4290 Family instances are implicitly exported, just like class instances.
4291 However, this applies only to the heads of instances, not to the data
4292 constructors an instance defines.
4300 <sect2 id="synonym-families">
4301 <title>Synonym families</title>
4304 Type families appear in two flavours: (1) they can be defined on the
4305 toplevel or (2) they can appear inside type classes (in which case they
4306 are known as associated type synonyms). The former is the more general
4307 variant, as it lacks the requirement for the type-indexes to coincide with
4308 the class parameters. However, the latter can lead to more clearly
4309 structured code and compiler warnings if some type instances were -
4310 possibly accidentally - omitted. In the following, we always discuss the
4311 general toplevel form first and then cover the additional constraints
4312 placed on associated types.
4315 <sect3 id="type-family-declarations">
4316 <title>Type family declarations</title>
4319 Indexed type families are introduced by a signature, such as
4321 type family Elem c :: *
4323 The special <literal>family</literal> distinguishes family from standard
4324 type declarations. The result kind annotation is optional and, as
4325 usual, defaults to <literal>*</literal> if omitted. An example is
4329 Parameters can also be given explicit kind signatures if needed. We
4330 call the number of parameters in a type family declaration, the family's
4331 arity, and all applications of a type family must be fully saturated
4332 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4333 and it implies that the kind of a type family is not sufficient to
4334 determine a family's arity, and hence in general, also insufficient to
4335 determine whether a type family application is well formed. As an
4336 example, consider the following declaration:
4338 type family F a b :: * -> * -- F's arity is 2,
4339 -- although its overall kind is * -> * -> * -> *
4341 Given this declaration the following are examples of well-formed and
4344 F Char [Int] -- OK! Kind: * -> *
4345 F Char [Int] Bool -- OK! Kind: *
4346 F IO Bool -- WRONG: kind mismatch in the first argument
4347 F Bool -- WRONG: unsaturated application
4351 <sect4 id="assoc-type-family-decl">
4352 <title>Associated type family declarations</title>
4354 When a type family is declared as part of a type class, we drop
4355 the <literal>family</literal> special. The <literal>Elem</literal>
4356 declaration takes the following form
4358 class Collects ce where
4362 The argument names of the type family must be class parameters. Each
4363 class parameter may only be used at most once per associated type, but
4364 some may be omitted and they may be in an order other than in the
4365 class head. Hence, the following contrived example is admissible:
4370 These rules are exactly as for associated data families.
4375 <sect3 id="type-instance-declarations">
4376 <title>Type instance declarations</title>
4378 Instance declarations of type families are very similar to standard type
4379 synonym declarations. The only two differences are that the
4380 keyword <literal>type</literal> is followed
4381 by <literal>instance</literal> and that some or all of the type
4382 arguments can be non-variable types, but may not contain forall types or
4383 type synonym families. However, data families are generally allowed, and
4384 type synonyms are allowed as long as they are fully applied and expand
4385 to a type that is admissible - these are the exact same requirements as
4386 for data instances. For example, the <literal>[e]</literal> instance
4387 for <literal>Elem</literal> is
4389 type instance Elem [e] = e
4393 Type family instance declarations are only legitimate when an
4394 appropriate family declaration is in scope - just like class instances
4395 require the class declaration to be visible. Moreover, each instance
4396 declaration has to conform to the kind determined by its family
4397 declaration, and the number of type parameters in an instance
4398 declaration must match the number of type parameters in the family
4399 declaration. Finally, the right-hand side of a type instance must be a
4400 monotype (i.e., it may not include foralls) and after the expansion of
4401 all saturated vanilla type synonyms, no synonyms, except family synonyms
4402 may remain. Here are some examples of admissible and illegal type
4405 type family F a :: *
4406 type instance F [Int] = Int -- OK!
4407 type instance F String = Char -- OK!
4408 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4409 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4410 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4412 type family G a b :: * -> *
4413 type instance G Int = (,) -- WRONG: must be two type parameters
4414 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4418 <sect4 id="assoc-type-instance">
4419 <title>Associated type instance declarations</title>
4421 When an associated family instance is declared within a type class
4422 instance, we drop the <literal>instance</literal> keyword in the family
4423 instance. So, the <literal>[e]</literal> instance
4424 for <literal>Elem</literal> becomes:
4426 instance (Eq (Elem [e])) => Collects ([e]) where
4430 The most important point about associated family instances is that the
4431 type indexes corresponding to class parameters must be identical to the
4432 type given in the instance head; here this is <literal>[e]</literal>,
4433 which coincides with the only class parameter.
4436 Instances for an associated family can only appear as part of instances
4437 declarations of the class in which the family was declared - just as
4438 with the equations of the methods of a class. Also in correspondence to
4439 how methods are handled, declarations of associated types can be omitted
4440 in class instances. If an associated family instance is omitted, the
4441 corresponding instance type is not inhabited; i.e., only diverging
4442 expressions, such as <literal>undefined</literal>, can assume the type.
4446 <sect4 id="type-family-overlap">
4447 <title>Overlap of type synonym instances</title>
4449 The instance declarations of a type family used in a single program
4450 may only overlap if the right-hand sides of the overlapping instances
4451 coincide for the overlapping types. More formally, two instance
4452 declarations overlap if there is a substitution that makes the
4453 left-hand sides of the instances syntactically the same. Whenever
4454 that is the case, the right-hand sides of the instances must also be
4455 syntactically equal under the same substitution. This condition is
4456 independent of whether the type family is associated or not, and it is
4457 not only a matter of consistency, but one of type safety.
4460 Here are two example to illustrate the condition under which overlap
4463 type instance F (a, Int) = [a]
4464 type instance F (Int, b) = [b] -- overlap permitted
4466 type instance G (a, Int) = [a]
4467 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4472 <sect4 id="type-family-decidability">
4473 <title>Decidability of type synonym instances</title>
4475 In order to guarantee that type inference in the presence of type
4476 families decidable, we need to place a number of additional
4477 restrictions on the formation of type instance declarations (c.f.,
4478 Definition 5 (Relaxed Conditions) of “<ulink
4479 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4480 Checking with Open Type Functions</ulink>”). Instance
4481 declarations have the general form
4483 type instance F t1 .. tn = t
4485 where we require that for every type family application <literal>(G s1
4486 .. sm)</literal> in <literal>t</literal>,
4489 <para><literal>s1 .. sm</literal> do not contain any type family
4490 constructors,</para>
4493 <para>the total number of symbols (data type constructors and type
4494 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4495 in <literal>t1 .. tn</literal>, and</para>
4498 <para>for every type
4499 variable <literal>a</literal>, <literal>a</literal> occurs
4500 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4501 .. tn</literal>.</para>
4504 These restrictions are easily verified and ensure termination of type
4505 inference. However, they are not sufficient to guarantee completeness
4506 of type inference in the presence of, so called, ''loopy equalities'',
4507 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4508 a type variable is underneath a family application and data
4509 constructor application - see the above mentioned paper for details.
4512 If the option <option>-XUndecidableInstances</option> is passed to the
4513 compiler, the above restrictions are not enforced and it is on the
4514 programmer to ensure termination of the normalisation of type families
4515 during type inference.
4520 <sect3 id-="equality-constraints">
4521 <title>Equality constraints</title>
4523 Type context can include equality constraints of the form <literal>t1 ~
4524 t2</literal>, which denote that the types <literal>t1</literal>
4525 and <literal>t2</literal> need to be the same. In the presence of type
4526 families, whether two types are equal cannot generally be decided
4527 locally. Hence, the contexts of function signatures may include
4528 equality constraints, as in the following example:
4530 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4532 where we require that the element type of <literal>c1</literal>
4533 and <literal>c2</literal> are the same. In general, the
4534 types <literal>t1</literal> and <literal>t2</literal> of an equality
4535 constraint may be arbitrary monotypes; i.e., they may not contain any
4536 quantifiers, independent of whether higher-rank types are otherwise
4540 Equality constraints can also appear in class and instance contexts.
4541 The former enable a simple translation of programs using functional
4542 dependencies into programs using family synonyms instead. The general
4543 idea is to rewrite a class declaration of the form
4545 class C a b | a -> b
4549 class (F a ~ b) => C a b where
4552 That is, we represent every functional dependency (FD) <literal>a1 .. an
4553 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4554 superclass context equality <literal>F a1 .. an ~ b</literal>,
4555 essentially giving a name to the functional dependency. In class
4556 instances, we define the type instances of FD families in accordance
4557 with the class head. Method signatures are not affected by that
4561 NB: Equalities in superclass contexts are not fully implemented in
4566 <sect3 id-="ty-fams-in-instances">
4567 <title>Type families and instance declarations</title>
4568 <para>Type families require us to extend the rules for
4569 the form of instance heads, which are given
4570 in <xref linkend="flexible-instance-head"/>.
4573 <listitem><para>Data type families may appear in an instance head</para></listitem>
4574 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4576 The reason for the latter restriction is that there is no way to check for. Consider
4579 type instance F Bool = Int
4586 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4587 The situation is especially bad because the type instance for <literal>F Bool</literal>
4588 might be in another module, or even in a module that is not yet written.
4595 <sect1 id="other-type-extensions">
4596 <title>Other type system extensions</title>
4598 <sect2 id="type-restrictions">
4599 <title>Type signatures</title>
4601 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4603 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4604 that the type-class constraints in a type signature must have the
4605 form <emphasis>(class type-variable)</emphasis> or
4606 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4607 With <option>-XFlexibleContexts</option>
4608 these type signatures are perfectly OK
4611 g :: Ord (T a ()) => ...
4615 GHC imposes the following restrictions on the constraints in a type signature.
4619 forall tv1..tvn (c1, ...,cn) => type
4622 (Here, we write the "foralls" explicitly, although the Haskell source
4623 language omits them; in Haskell 98, all the free type variables of an
4624 explicit source-language type signature are universally quantified,
4625 except for the class type variables in a class declaration. However,
4626 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4635 <emphasis>Each universally quantified type variable
4636 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4638 A type variable <literal>a</literal> is "reachable" if it appears
4639 in the same constraint as either a type variable free in
4640 <literal>type</literal>, or another reachable type variable.
4641 A value with a type that does not obey
4642 this reachability restriction cannot be used without introducing
4643 ambiguity; that is why the type is rejected.
4644 Here, for example, is an illegal type:
4648 forall a. Eq a => Int
4652 When a value with this type was used, the constraint <literal>Eq tv</literal>
4653 would be introduced where <literal>tv</literal> is a fresh type variable, and
4654 (in the dictionary-translation implementation) the value would be
4655 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4656 can never know which instance of <literal>Eq</literal> to use because we never
4657 get any more information about <literal>tv</literal>.
4661 that the reachability condition is weaker than saying that <literal>a</literal> is
4662 functionally dependent on a type variable free in
4663 <literal>type</literal> (see <xref
4664 linkend="functional-dependencies"/>). The reason for this is there
4665 might be a "hidden" dependency, in a superclass perhaps. So
4666 "reachable" is a conservative approximation to "functionally dependent".
4667 For example, consider:
4669 class C a b | a -> b where ...
4670 class C a b => D a b where ...
4671 f :: forall a b. D a b => a -> a
4673 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4674 but that is not immediately apparent from <literal>f</literal>'s type.
4680 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4681 universally quantified type variables <literal>tvi</literal></emphasis>.
4683 For example, this type is OK because <literal>C a b</literal> mentions the
4684 universally quantified type variable <literal>b</literal>:
4688 forall a. C a b => burble
4692 The next type is illegal because the constraint <literal>Eq b</literal> does not
4693 mention <literal>a</literal>:
4697 forall a. Eq b => burble
4701 The reason for this restriction is milder than the other one. The
4702 excluded types are never useful or necessary (because the offending
4703 context doesn't need to be witnessed at this point; it can be floated
4704 out). Furthermore, floating them out increases sharing. Lastly,
4705 excluding them is a conservative choice; it leaves a patch of
4706 territory free in case we need it later.
4720 <sect2 id="implicit-parameters">
4721 <title>Implicit parameters</title>
4723 <para> Implicit parameters are implemented as described in
4724 "Implicit parameters: dynamic scoping with static types",
4725 J Lewis, MB Shields, E Meijer, J Launchbury,
4726 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4730 <para>(Most of the following, still rather incomplete, documentation is
4731 due to Jeff Lewis.)</para>
4733 <para>Implicit parameter support is enabled with the option
4734 <option>-XImplicitParams</option>.</para>
4737 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4738 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4739 context. In Haskell, all variables are statically bound. Dynamic
4740 binding of variables is a notion that goes back to Lisp, but was later
4741 discarded in more modern incarnations, such as Scheme. Dynamic binding
4742 can be very confusing in an untyped language, and unfortunately, typed
4743 languages, in particular Hindley-Milner typed languages like Haskell,
4744 only support static scoping of variables.
4747 However, by a simple extension to the type class system of Haskell, we
4748 can support dynamic binding. Basically, we express the use of a
4749 dynamically bound variable as a constraint on the type. These
4750 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4751 function uses a dynamically-bound variable <literal>?x</literal>
4752 of type <literal>t'</literal>". For
4753 example, the following expresses the type of a sort function,
4754 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4756 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4758 The dynamic binding constraints are just a new form of predicate in the type class system.
4761 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4762 where <literal>x</literal> is
4763 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4764 Use of this construct also introduces a new
4765 dynamic-binding constraint in the type of the expression.
4766 For example, the following definition
4767 shows how we can define an implicitly parameterized sort function in
4768 terms of an explicitly parameterized <literal>sortBy</literal> function:
4770 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4772 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4778 <title>Implicit-parameter type constraints</title>
4780 Dynamic binding constraints behave just like other type class
4781 constraints in that they are automatically propagated. Thus, when a
4782 function is used, its implicit parameters are inherited by the
4783 function that called it. For example, our <literal>sort</literal> function might be used
4784 to pick out the least value in a list:
4786 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4787 least xs = head (sort xs)
4789 Without lifting a finger, the <literal>?cmp</literal> parameter is
4790 propagated to become a parameter of <literal>least</literal> as well. With explicit
4791 parameters, the default is that parameters must always be explicit
4792 propagated. With implicit parameters, the default is to always
4796 An implicit-parameter type constraint differs from other type class constraints in the
4797 following way: All uses of a particular implicit parameter must have
4798 the same type. This means that the type of <literal>(?x, ?x)</literal>
4799 is <literal>(?x::a) => (a,a)</literal>, and not
4800 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4804 <para> You can't have an implicit parameter in the context of a class or instance
4805 declaration. For example, both these declarations are illegal:
4807 class (?x::Int) => C a where ...
4808 instance (?x::a) => Foo [a] where ...
4810 Reason: exactly which implicit parameter you pick up depends on exactly where
4811 you invoke a function. But the ``invocation'' of instance declarations is done
4812 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4813 Easiest thing is to outlaw the offending types.</para>
4815 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4817 f :: (?x :: [a]) => Int -> Int
4820 g :: (Read a, Show a) => String -> String
4823 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4824 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4825 quite unambiguous, and fixes the type <literal>a</literal>.
4830 <title>Implicit-parameter bindings</title>
4833 An implicit parameter is <emphasis>bound</emphasis> using the standard
4834 <literal>let</literal> or <literal>where</literal> binding forms.
4835 For example, we define the <literal>min</literal> function by binding
4836 <literal>cmp</literal>.
4839 min = let ?cmp = (<=) in least
4843 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4844 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4845 (including in a list comprehension, or do-notation, or pattern guards),
4846 or a <literal>where</literal> clause.
4847 Note the following points:
4850 An implicit-parameter binding group must be a
4851 collection of simple bindings to implicit-style variables (no
4852 function-style bindings, and no type signatures); these bindings are
4853 neither polymorphic or recursive.
4856 You may not mix implicit-parameter bindings with ordinary bindings in a
4857 single <literal>let</literal>
4858 expression; use two nested <literal>let</literal>s instead.
4859 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4863 You may put multiple implicit-parameter bindings in a
4864 single binding group; but they are <emphasis>not</emphasis> treated
4865 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4866 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4867 parameter. The bindings are not nested, and may be re-ordered without changing
4868 the meaning of the program.
4869 For example, consider:
4871 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4873 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4874 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4876 f :: (?x::Int) => Int -> Int
4884 <sect3><title>Implicit parameters and polymorphic recursion</title>
4887 Consider these two definitions:
4890 len1 xs = let ?acc = 0 in len_acc1 xs
4893 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4898 len2 xs = let ?acc = 0 in len_acc2 xs
4900 len_acc2 :: (?acc :: Int) => [a] -> Int
4902 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4904 The only difference between the two groups is that in the second group
4905 <literal>len_acc</literal> is given a type signature.
4906 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4907 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4908 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4909 has a type signature, the recursive call is made to the
4910 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4911 as an implicit parameter. So we get the following results in GHCi:
4918 Adding a type signature dramatically changes the result! This is a rather
4919 counter-intuitive phenomenon, worth watching out for.
4923 <sect3><title>Implicit parameters and monomorphism</title>
4925 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4926 Haskell Report) to implicit parameters. For example, consider:
4934 Since the binding for <literal>y</literal> falls under the Monomorphism
4935 Restriction it is not generalised, so the type of <literal>y</literal> is
4936 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4937 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4938 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4939 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4940 <literal>y</literal> in the body of the <literal>let</literal> will see the
4941 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4942 <literal>14</literal>.
4947 <!-- ======================= COMMENTED OUT ========================
4949 We intend to remove linear implicit parameters, so I'm at least removing
4950 them from the 6.6 user manual
4952 <sect2 id="linear-implicit-parameters">
4953 <title>Linear implicit parameters</title>
4955 Linear implicit parameters are an idea developed by Koen Claessen,
4956 Mark Shields, and Simon PJ. They address the long-standing
4957 problem that monads seem over-kill for certain sorts of problem, notably:
4960 <listitem> <para> distributing a supply of unique names </para> </listitem>
4961 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4962 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4966 Linear implicit parameters are just like ordinary implicit parameters,
4967 except that they are "linear"; that is, they cannot be copied, and
4968 must be explicitly "split" instead. Linear implicit parameters are
4969 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4970 (The '/' in the '%' suggests the split!)
4975 import GHC.Exts( Splittable )
4977 data NameSupply = ...
4979 splitNS :: NameSupply -> (NameSupply, NameSupply)
4980 newName :: NameSupply -> Name
4982 instance Splittable NameSupply where
4986 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4987 f env (Lam x e) = Lam x' (f env e)
4990 env' = extend env x x'
4991 ...more equations for f...
4993 Notice that the implicit parameter %ns is consumed
4995 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4996 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5000 So the translation done by the type checker makes
5001 the parameter explicit:
5003 f :: NameSupply -> Env -> Expr -> Expr
5004 f ns env (Lam x e) = Lam x' (f ns1 env e)
5006 (ns1,ns2) = splitNS ns
5008 env = extend env x x'
5010 Notice the call to 'split' introduced by the type checker.
5011 How did it know to use 'splitNS'? Because what it really did
5012 was to introduce a call to the overloaded function 'split',
5013 defined by the class <literal>Splittable</literal>:
5015 class Splittable a where
5018 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5019 split for name supplies. But we can simply write
5025 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5027 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5028 <literal>GHC.Exts</literal>.
5033 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5034 are entirely distinct implicit parameters: you
5035 can use them together and they won't interfere with each other. </para>
5038 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5040 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5041 in the context of a class or instance declaration. </para></listitem>
5045 <sect3><title>Warnings</title>
5048 The monomorphism restriction is even more important than usual.
5049 Consider the example above:
5051 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5052 f env (Lam x e) = Lam x' (f env e)
5055 env' = extend env x x'
5057 If we replaced the two occurrences of x' by (newName %ns), which is
5058 usually a harmless thing to do, we get:
5060 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5061 f env (Lam x e) = Lam (newName %ns) (f env e)
5063 env' = extend env x (newName %ns)
5065 But now the name supply is consumed in <emphasis>three</emphasis> places
5066 (the two calls to newName,and the recursive call to f), so
5067 the result is utterly different. Urk! We don't even have
5071 Well, this is an experimental change. With implicit
5072 parameters we have already lost beta reduction anyway, and
5073 (as John Launchbury puts it) we can't sensibly reason about
5074 Haskell programs without knowing their typing.
5079 <sect3><title>Recursive functions</title>
5080 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5083 foo :: %x::T => Int -> [Int]
5085 foo n = %x : foo (n-1)
5087 where T is some type in class Splittable.</para>
5089 Do you get a list of all the same T's or all different T's
5090 (assuming that split gives two distinct T's back)?
5092 If you supply the type signature, taking advantage of polymorphic
5093 recursion, you get what you'd probably expect. Here's the
5094 translated term, where the implicit param is made explicit:
5097 foo x n = let (x1,x2) = split x
5098 in x1 : foo x2 (n-1)
5100 But if you don't supply a type signature, GHC uses the Hindley
5101 Milner trick of using a single monomorphic instance of the function
5102 for the recursive calls. That is what makes Hindley Milner type inference
5103 work. So the translation becomes
5107 foom n = x : foom (n-1)
5111 Result: 'x' is not split, and you get a list of identical T's. So the
5112 semantics of the program depends on whether or not foo has a type signature.
5115 You may say that this is a good reason to dislike linear implicit parameters
5116 and you'd be right. That is why they are an experimental feature.
5122 ================ END OF Linear Implicit Parameters commented out -->
5124 <sect2 id="kinding">
5125 <title>Explicitly-kinded quantification</title>
5128 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5129 to give the kind explicitly as (machine-checked) documentation,
5130 just as it is nice to give a type signature for a function. On some occasions,
5131 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5132 John Hughes had to define the data type:
5134 data Set cxt a = Set [a]
5135 | Unused (cxt a -> ())
5137 The only use for the <literal>Unused</literal> constructor was to force the correct
5138 kind for the type variable <literal>cxt</literal>.
5141 GHC now instead allows you to specify the kind of a type variable directly, wherever
5142 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5145 This flag enables kind signatures in the following places:
5147 <listitem><para><literal>data</literal> declarations:
5149 data Set (cxt :: * -> *) a = Set [a]
5150 </screen></para></listitem>
5151 <listitem><para><literal>type</literal> declarations:
5153 type T (f :: * -> *) = f Int
5154 </screen></para></listitem>
5155 <listitem><para><literal>class</literal> declarations:
5157 class (Eq a) => C (f :: * -> *) a where ...
5158 </screen></para></listitem>
5159 <listitem><para><literal>forall</literal>'s in type signatures:
5161 f :: forall (cxt :: * -> *). Set cxt Int
5162 </screen></para></listitem>
5167 The parentheses are required. Some of the spaces are required too, to
5168 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5169 will get a parse error, because "<literal>::*->*</literal>" is a
5170 single lexeme in Haskell.
5174 As part of the same extension, you can put kind annotations in types
5177 f :: (Int :: *) -> Int
5178 g :: forall a. a -> (a :: *)
5182 atype ::= '(' ctype '::' kind ')
5184 The parentheses are required.
5189 <sect2 id="universal-quantification">
5190 <title>Arbitrary-rank polymorphism
5194 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5195 allows us to say exactly what this means. For example:
5203 g :: forall b. (b -> b)
5205 The two are treated identically.
5209 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5210 explicit universal quantification in
5212 For example, all the following types are legal:
5214 f1 :: forall a b. a -> b -> a
5215 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5217 f2 :: (forall a. a->a) -> Int -> Int
5218 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5220 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5222 f4 :: Int -> (forall a. a -> a)
5224 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5225 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5226 The <literal>forall</literal> makes explicit the universal quantification that
5227 is implicitly added by Haskell.
5230 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5231 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5232 shows, the polymorphic type on the left of the function arrow can be overloaded.
5235 The function <literal>f3</literal> has a rank-3 type;
5236 it has rank-2 types on the left of a function arrow.
5239 GHC has three flags to control higher-rank types:
5242 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5245 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5248 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5249 That is, you can nest <literal>forall</literal>s
5250 arbitrarily deep in function arrows.
5251 In particular, a forall-type (also called a "type scheme"),
5252 including an operational type class context, is legal:
5254 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5255 of a function arrow </para> </listitem>
5256 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5257 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5258 field type signatures.</para> </listitem>
5259 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5260 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5264 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5265 a type variable any more!
5274 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5275 the types of the constructor arguments. Here are several examples:
5281 data T a = T1 (forall b. b -> b -> b) a
5283 data MonadT m = MkMonad { return :: forall a. a -> m a,
5284 bind :: forall a b. m a -> (a -> m b) -> m b
5287 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5293 The constructors have rank-2 types:
5299 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5300 MkMonad :: forall m. (forall a. a -> m a)
5301 -> (forall a b. m a -> (a -> m b) -> m b)
5303 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5309 Notice that you don't need to use a <literal>forall</literal> if there's an
5310 explicit context. For example in the first argument of the
5311 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5312 prefixed to the argument type. The implicit <literal>forall</literal>
5313 quantifies all type variables that are not already in scope, and are
5314 mentioned in the type quantified over.
5318 As for type signatures, implicit quantification happens for non-overloaded
5319 types too. So if you write this:
5322 data T a = MkT (Either a b) (b -> b)
5325 it's just as if you had written this:
5328 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5331 That is, since the type variable <literal>b</literal> isn't in scope, it's
5332 implicitly universally quantified. (Arguably, it would be better
5333 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5334 where that is what is wanted. Feedback welcomed.)
5338 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5339 the constructor to suitable values, just as usual. For example,
5350 a3 = MkSwizzle reverse
5353 a4 = let r x = Just x
5360 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5361 mkTs f x y = [T1 f x, T1 f y]
5367 The type of the argument can, as usual, be more general than the type
5368 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5369 does not need the <literal>Ord</literal> constraint.)
5373 When you use pattern matching, the bound variables may now have
5374 polymorphic types. For example:
5380 f :: T a -> a -> (a, Char)
5381 f (T1 w k) x = (w k x, w 'c' 'd')
5383 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5384 g (MkSwizzle s) xs f = s (map f (s xs))
5386 h :: MonadT m -> [m a] -> m [a]
5387 h m [] = return m []
5388 h m (x:xs) = bind m x $ \y ->
5389 bind m (h m xs) $ \ys ->
5396 In the function <function>h</function> we use the record selectors <literal>return</literal>
5397 and <literal>bind</literal> to extract the polymorphic bind and return functions
5398 from the <literal>MonadT</literal> data structure, rather than using pattern
5404 <title>Type inference</title>
5407 In general, type inference for arbitrary-rank types is undecidable.
5408 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5409 to get a decidable algorithm by requiring some help from the programmer.
5410 We do not yet have a formal specification of "some help" but the rule is this:
5413 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5414 provides an explicit polymorphic type for x, or GHC's type inference will assume
5415 that x's type has no foralls in it</emphasis>.
5418 What does it mean to "provide" an explicit type for x? You can do that by
5419 giving a type signature for x directly, using a pattern type signature
5420 (<xref linkend="scoped-type-variables"/>), thus:
5422 \ f :: (forall a. a->a) -> (f True, f 'c')
5424 Alternatively, you can give a type signature to the enclosing
5425 context, which GHC can "push down" to find the type for the variable:
5427 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5429 Here the type signature on the expression can be pushed inwards
5430 to give a type signature for f. Similarly, and more commonly,
5431 one can give a type signature for the function itself:
5433 h :: (forall a. a->a) -> (Bool,Char)
5434 h f = (f True, f 'c')
5436 You don't need to give a type signature if the lambda bound variable
5437 is a constructor argument. Here is an example we saw earlier:
5439 f :: T a -> a -> (a, Char)
5440 f (T1 w k) x = (w k x, w 'c' 'd')
5442 Here we do not need to give a type signature to <literal>w</literal>, because
5443 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5450 <sect3 id="implicit-quant">
5451 <title>Implicit quantification</title>
5454 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5455 user-written types, if and only if there is no explicit <literal>forall</literal>,
5456 GHC finds all the type variables mentioned in the type that are not already
5457 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5461 f :: forall a. a -> a
5468 h :: forall b. a -> b -> b
5474 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5477 f :: (a -> a) -> Int
5479 f :: forall a. (a -> a) -> Int
5481 f :: (forall a. a -> a) -> Int
5484 g :: (Ord a => a -> a) -> Int
5485 -- MEANS the illegal type
5486 g :: forall a. (Ord a => a -> a) -> Int
5488 g :: (forall a. Ord a => a -> a) -> Int
5490 The latter produces an illegal type, which you might think is silly,
5491 but at least the rule is simple. If you want the latter type, you
5492 can write your for-alls explicitly. Indeed, doing so is strongly advised
5499 <sect2 id="impredicative-polymorphism">
5500 <title>Impredicative polymorphism
5502 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5503 enabled with <option>-XImpredicativeTypes</option>.
5505 that you can call a polymorphic function at a polymorphic type, and
5506 parameterise data structures over polymorphic types. For example:
5508 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5509 f (Just g) = Just (g [3], g "hello")
5512 Notice here that the <literal>Maybe</literal> type is parameterised by the
5513 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5516 <para>The technical details of this extension are described in the paper
5517 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5518 type inference for higher-rank types and impredicativity</ulink>,
5519 which appeared at ICFP 2006.
5523 <sect2 id="scoped-type-variables">
5524 <title>Lexically scoped type variables
5528 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5529 which some type signatures are simply impossible to write. For example:
5531 f :: forall a. [a] -> [a]
5537 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5538 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5539 The type variables bound by a <literal>forall</literal> scope over
5540 the entire definition of the accompanying value declaration.
5541 In this example, the type variable <literal>a</literal> scopes over the whole
5542 definition of <literal>f</literal>, including over
5543 the type signature for <varname>ys</varname>.
5544 In Haskell 98 it is not possible to declare
5545 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5546 it becomes possible to do so.
5548 <para>Lexically-scoped type variables are enabled by
5549 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5551 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5552 variables work, compared to earlier releases. Read this section
5556 <title>Overview</title>
5558 <para>The design follows the following principles
5560 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5561 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5562 design.)</para></listitem>
5563 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5564 type variables. This means that every programmer-written type signature
5565 (including one that contains free scoped type variables) denotes a
5566 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5567 checker, and no inference is involved.</para></listitem>
5568 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5569 changing the program.</para></listitem>
5573 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5575 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5576 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5577 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5578 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5582 In Haskell, a programmer-written type signature is implicitly quantified over
5583 its free type variables (<ulink
5584 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5586 of the Haskell Report).
5587 Lexically scoped type variables affect this implicit quantification rules
5588 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5589 quantified. For example, if type variable <literal>a</literal> is in scope,
5592 (e :: a -> a) means (e :: a -> a)
5593 (e :: b -> b) means (e :: forall b. b->b)
5594 (e :: a -> b) means (e :: forall b. a->b)
5602 <sect3 id="decl-type-sigs">
5603 <title>Declaration type signatures</title>
5604 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5605 quantification (using <literal>forall</literal>) brings into scope the
5606 explicitly-quantified
5607 type variables, in the definition of the named function. For example:
5609 f :: forall a. [a] -> [a]
5610 f (x:xs) = xs ++ [ x :: a ]
5612 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5613 the definition of "<literal>f</literal>".
5615 <para>This only happens if:
5617 <listitem><para> The quantification in <literal>f</literal>'s type
5618 signature is explicit. For example:
5621 g (x:xs) = xs ++ [ x :: a ]
5623 This program will be rejected, because "<literal>a</literal>" does not scope
5624 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5625 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5626 quantification rules.
5628 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5629 not a pattern binding.
5632 f1 :: forall a. [a] -> [a]
5633 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5635 f2 :: forall a. [a] -> [a]
5636 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5638 f3 :: forall a. [a] -> [a]
5639 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5641 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5642 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5643 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5644 the type signature brings <literal>a</literal> into scope.
5650 <sect3 id="exp-type-sigs">
5651 <title>Expression type signatures</title>
5653 <para>An expression type signature that has <emphasis>explicit</emphasis>
5654 quantification (using <literal>forall</literal>) brings into scope the
5655 explicitly-quantified
5656 type variables, in the annotated expression. For example:
5658 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5660 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5661 type variable <literal>s</literal> into scope, in the annotated expression
5662 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5667 <sect3 id="pattern-type-sigs">
5668 <title>Pattern type signatures</title>
5670 A type signature may occur in any pattern; this is a <emphasis>pattern type
5671 signature</emphasis>.
5674 -- f and g assume that 'a' is already in scope
5675 f = \(x::Int, y::a) -> x
5677 h ((x,y) :: (Int,Bool)) = (y,x)
5679 In the case where all the type variables in the pattern type signature are
5680 already in scope (i.e. bound by the enclosing context), matters are simple: the
5681 signature simply constrains the type of the pattern in the obvious way.
5684 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5685 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5686 that are already in scope. For example:
5688 f :: forall a. [a] -> (Int, [a])
5691 (ys::[a], n) = (reverse xs, length xs) -- OK
5692 zs::[a] = xs ++ ys -- OK
5694 Just (v::b) = ... -- Not OK; b is not in scope
5696 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5697 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5701 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5702 type signature may mention a type variable that is not in scope; in this case,
5703 <emphasis>the signature brings that type variable into scope</emphasis>.
5704 This is particularly important for existential data constructors. For example:
5706 data T = forall a. MkT [a]
5709 k (MkT [t::a]) = MkT t3
5713 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5714 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5715 because it is bound by the pattern match. GHC's rule is that in this situation
5716 (and only then), a pattern type signature can mention a type variable that is
5717 not already in scope; the effect is to bring it into scope, standing for the
5718 existentially-bound type variable.
5721 When a pattern type signature binds a type variable in this way, GHC insists that the
5722 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5723 This means that any user-written type signature always stands for a completely known type.
5726 If all this seems a little odd, we think so too. But we must have
5727 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5728 could not name existentially-bound type variables in subsequent type signatures.
5731 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5732 signature is allowed to mention a lexical variable that is not already in
5734 For example, both <literal>f</literal> and <literal>g</literal> would be
5735 illegal if <literal>a</literal> was not already in scope.
5741 <!-- ==================== Commented out part about result type signatures
5743 <sect3 id="result-type-sigs">
5744 <title>Result type signatures</title>
5747 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5750 {- f assumes that 'a' is already in scope -}
5751 f x y :: [a] = [x,y,x]
5753 g = \ x :: [Int] -> [3,4]
5755 h :: forall a. [a] -> a
5759 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5760 the result of the function. Similarly, the body of the lambda in the RHS of
5761 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5762 alternative in <literal>h</literal> is <literal>a</literal>.
5764 <para> A result type signature never brings new type variables into scope.</para>
5766 There are a couple of syntactic wrinkles. First, notice that all three
5767 examples would parse quite differently with parentheses:
5769 {- f assumes that 'a' is already in scope -}
5770 f x (y :: [a]) = [x,y,x]
5772 g = \ (x :: [Int]) -> [3,4]
5774 h :: forall a. [a] -> a
5778 Now the signature is on the <emphasis>pattern</emphasis>; and
5779 <literal>h</literal> would certainly be ill-typed (since the pattern
5780 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5782 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5783 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5784 token or a parenthesised type of some sort). To see why,
5785 consider how one would parse this:
5794 <sect3 id="cls-inst-scoped-tyvars">
5795 <title>Class and instance declarations</title>
5798 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5799 scope over the methods defined in the <literal>where</literal> part. For example:
5817 <sect2 id="typing-binds">
5818 <title>Generalised typing of mutually recursive bindings</title>
5821 The Haskell Report specifies that a group of bindings (at top level, or in a
5822 <literal>let</literal> or <literal>where</literal>) should be sorted into
5823 strongly-connected components, and then type-checked in dependency order
5824 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5825 Report, Section 4.5.1</ulink>).
5826 As each group is type-checked, any binders of the group that
5828 an explicit type signature are put in the type environment with the specified
5830 and all others are monomorphic until the group is generalised
5831 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5834 <para>Following a suggestion of Mark Jones, in his paper
5835 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5837 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5839 <emphasis>the dependency analysis ignores references to variables that have an explicit
5840 type signature</emphasis>.
5841 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5842 typecheck. For example, consider:
5844 f :: Eq a => a -> Bool
5845 f x = (x == x) || g True || g "Yes"
5847 g y = (y <= y) || f True
5849 This is rejected by Haskell 98, but under Jones's scheme the definition for
5850 <literal>g</literal> is typechecked first, separately from that for
5851 <literal>f</literal>,
5852 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5853 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5854 type is generalised, to get
5856 g :: Ord a => a -> Bool
5858 Now, the definition for <literal>f</literal> is typechecked, with this type for
5859 <literal>g</literal> in the type environment.
5863 The same refined dependency analysis also allows the type signatures of
5864 mutually-recursive functions to have different contexts, something that is illegal in
5865 Haskell 98 (Section 4.5.2, last sentence). With
5866 <option>-XRelaxedPolyRec</option>
5867 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5868 type signatures; in practice this means that only variables bound by the same
5869 pattern binding must have the same context. For example, this is fine:
5871 f :: Eq a => a -> Bool
5872 f x = (x == x) || g True
5874 g :: Ord a => a -> Bool
5875 g y = (y <= y) || f True
5881 <!-- ==================== End of type system extensions ================= -->
5883 <!-- ====================== TEMPLATE HASKELL ======================= -->
5885 <sect1 id="template-haskell">
5886 <title>Template Haskell</title>
5888 <para>Template Haskell allows you to do compile-time meta-programming in
5891 the main technical innovations is discussed in "<ulink
5892 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5893 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5896 There is a Wiki page about
5897 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5898 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5902 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5903 Haskell library reference material</ulink>
5904 (look for module <literal>Language.Haskell.TH</literal>).
5905 Many changes to the original design are described in
5906 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5907 Notes on Template Haskell version 2</ulink>.
5908 Not all of these changes are in GHC, however.
5911 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5912 as a worked example to help get you started.
5916 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5917 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5922 <title>Syntax</title>
5924 <para> Template Haskell has the following new syntactic
5925 constructions. You need to use the flag
5926 <option>-XTemplateHaskell</option>
5927 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5928 </indexterm>to switch these syntactic extensions on
5929 (<option>-XTemplateHaskell</option> is no longer implied by
5930 <option>-fglasgow-exts</option>).</para>
5934 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5935 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5936 There must be no space between the "$" and the identifier or parenthesis. This use
5937 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5938 of "." as an infix operator. If you want the infix operator, put spaces around it.
5940 <para> A splice can occur in place of
5942 <listitem><para> an expression; the spliced expression must
5943 have type <literal>Q Exp</literal></para></listitem>
5944 <listitem><para> an type; the spliced expression must
5945 have type <literal>Q Typ</literal></para></listitem>
5946 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5949 Inside a splice you can can only call functions defined in imported modules,
5950 not functions defined elsewhere in the same module.</listitem>
5954 A expression quotation is written in Oxford brackets, thus:
5956 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5957 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5958 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5959 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5960 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5961 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5962 </itemizedlist></para></listitem>
5965 A quasi-quotation can appear in either a pattern context or an
5966 expression context and is also written in Oxford brackets:
5968 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5969 where the "..." is an arbitrary string; a full description of the
5970 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5971 </itemizedlist></para></listitem>
5974 A name can be quoted with either one or two prefix single quotes:
5976 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5977 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5978 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5980 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5981 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5984 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5985 may also be given as an argument to the <literal>reify</literal> function.
5991 (Compared to the original paper, there are many differences of detail.
5992 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5993 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5994 Pattern splices and quotations are not implemented.)
5998 <sect2> <title> Using Template Haskell </title>
6002 The data types and monadic constructor functions for Template Haskell are in the library
6003 <literal>Language.Haskell.THSyntax</literal>.
6007 You can only run a function at compile time if it is imported from another module. That is,
6008 you can't define a function in a module, and call it from within a splice in the same module.
6009 (It would make sense to do so, but it's hard to implement.)
6013 You can only run a function at compile time if it is imported
6014 from another module <emphasis>that is not part of a mutually-recursive group of modules
6015 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6016 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6017 splice is to be run.</para>
6019 For example, when compiling module A,
6020 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6021 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6025 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6028 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6029 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6030 compiles and runs a program, and then looks at the result. So it's important that
6031 the program it compiles produces results whose representations are identical to
6032 those of the compiler itself.
6036 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6037 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6042 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6043 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6044 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6051 -- Import our template "pr"
6052 import Printf ( pr )
6054 -- The splice operator $ takes the Haskell source code
6055 -- generated at compile time by "pr" and splices it into
6056 -- the argument of "putStrLn".
6057 main = putStrLn ( $(pr "Hello") )
6063 -- Skeletal printf from the paper.
6064 -- It needs to be in a separate module to the one where
6065 -- you intend to use it.
6067 -- Import some Template Haskell syntax
6068 import Language.Haskell.TH
6070 -- Describe a format string
6071 data Format = D | S | L String
6073 -- Parse a format string. This is left largely to you
6074 -- as we are here interested in building our first ever
6075 -- Template Haskell program and not in building printf.
6076 parse :: String -> [Format]
6079 -- Generate Haskell source code from a parsed representation
6080 -- of the format string. This code will be spliced into
6081 -- the module which calls "pr", at compile time.
6082 gen :: [Format] -> Q Exp
6083 gen [D] = [| \n -> show n |]
6084 gen [S] = [| \s -> s |]
6085 gen [L s] = stringE s
6087 -- Here we generate the Haskell code for the splice
6088 -- from an input format string.
6089 pr :: String -> Q Exp
6090 pr s = gen (parse s)
6093 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6096 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6099 <para>Run "main.exe" and here is your output:</para>
6109 <title>Using Template Haskell with Profiling</title>
6110 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6112 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6113 interpreter to run the splice expressions. The bytecode interpreter
6114 runs the compiled expression on top of the same runtime on which GHC
6115 itself is running; this means that the compiled code referred to by
6116 the interpreted expression must be compatible with this runtime, and
6117 in particular this means that object code that is compiled for
6118 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6119 expression, because profiled object code is only compatible with the
6120 profiling version of the runtime.</para>
6122 <para>This causes difficulties if you have a multi-module program
6123 containing Template Haskell code and you need to compile it for
6124 profiling, because GHC cannot load the profiled object code and use it
6125 when executing the splices. Fortunately GHC provides a workaround.
6126 The basic idea is to compile the program twice:</para>
6130 <para>Compile the program or library first the normal way, without
6131 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6134 <para>Then compile it again with <option>-prof</option>, and
6135 additionally use <option>-osuf
6136 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6137 to name the object files differently (you can choose any suffix
6138 that isn't the normal object suffix here). GHC will automatically
6139 load the object files built in the first step when executing splice
6140 expressions. If you omit the <option>-osuf</option> flag when
6141 building with <option>-prof</option> and Template Haskell is used,
6142 GHC will emit an error message. </para>
6147 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6148 <para>Quasi-quotation allows patterns and expressions to be written using
6149 programmer-defined concrete syntax; the motivation behind the extension and
6150 several examples are documented in
6151 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6152 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6153 2007). The example below shows how to write a quasiquoter for a simple
6154 expression language.</para>
6157 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6158 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6159 functions for quoting expressions and patterns, respectively. The first argument
6160 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6161 context of the quasi-quotation statement determines which of the two parsers is
6162 called: if the quasi-quotation occurs in an expression context, the expression
6163 parser is called, and if it occurs in a pattern context, the pattern parser is
6167 Note that in the example we make use of an antiquoted
6168 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6169 (this syntax for anti-quotation was defined by the parser's
6170 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6171 integer value argument of the constructor <literal>IntExpr</literal> when
6172 pattern matching. Please see the referenced paper for further details regarding
6173 anti-quotation as well as the description of a technique that uses SYB to
6174 leverage a single parser of type <literal>String -> a</literal> to generate both
6175 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6176 pattern parser that returns a value of type <literal>Q Pat</literal>.
6179 <para>In general, a quasi-quote has the form
6180 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6181 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6182 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6183 can be arbitrary, and may contain newlines.
6186 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6187 the example, <literal>expr</literal> cannot be defined
6188 in <literal>Main.hs</literal> where it is used, but must be imported.
6199 main = do { print $ eval [$expr|1 + 2|]
6201 { [$expr|'int:n|] -> print n
6210 import qualified Language.Haskell.TH as TH
6211 import Language.Haskell.TH.Quote
6213 data Expr = IntExpr Integer
6214 | AntiIntExpr String
6215 | BinopExpr BinOp Expr Expr
6217 deriving(Show, Typeable, Data)
6223 deriving(Show, Typeable, Data)
6225 eval :: Expr -> Integer
6226 eval (IntExpr n) = n
6227 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6234 expr = QuasiQuoter parseExprExp parseExprPat
6236 -- Parse an Expr, returning its representation as
6237 -- either a Q Exp or a Q Pat. See the referenced paper
6238 -- for how to use SYB to do this by writing a single
6239 -- parser of type String -> Expr instead of two
6240 -- separate parsers.
6242 parseExprExp :: String -> Q Exp
6245 parseExprPat :: String -> Q Pat
6249 <para>Now run the compiler:
6252 $ ghc --make -XQuasiQuotes Main.hs -o main
6255 <para>Run "main" and here is your output:</para>
6267 <!-- ===================== Arrow notation =================== -->
6269 <sect1 id="arrow-notation">
6270 <title>Arrow notation
6273 <para>Arrows are a generalization of monads introduced by John Hughes.
6274 For more details, see
6279 “Generalising Monads to Arrows”,
6280 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6281 pp67–111, May 2000.
6282 The paper that introduced arrows: a friendly introduction, motivated with
6283 programming examples.
6289 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6290 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6291 Introduced the notation described here.
6297 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6298 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6305 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6306 John Hughes, in <citetitle>5th International Summer School on
6307 Advanced Functional Programming</citetitle>,
6308 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6310 This paper includes another introduction to the notation,
6311 with practical examples.
6317 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6318 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6319 A terse enumeration of the formal rules used
6320 (extracted from comments in the source code).
6326 The arrows web page at
6327 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6332 With the <option>-XArrows</option> flag, GHC supports the arrow
6333 notation described in the second of these papers,
6334 translating it using combinators from the
6335 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6337 What follows is a brief introduction to the notation;
6338 it won't make much sense unless you've read Hughes's paper.
6341 <para>The extension adds a new kind of expression for defining arrows:
6343 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6344 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6346 where <literal>proc</literal> is a new keyword.
6347 The variables of the pattern are bound in the body of the
6348 <literal>proc</literal>-expression,
6349 which is a new sort of thing called a <firstterm>command</firstterm>.
6350 The syntax of commands is as follows:
6352 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6353 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6354 | <replaceable>cmd</replaceable><superscript>0</superscript>
6356 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6357 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6358 infix operators as for expressions, and
6360 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6361 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6362 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6363 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6364 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6365 | <replaceable>fcmd</replaceable>
6367 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6368 | ( <replaceable>cmd</replaceable> )
6369 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6371 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6372 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6373 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6374 | <replaceable>cmd</replaceable>
6376 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6377 except that the bodies are commands instead of expressions.
6381 Commands produce values, but (like monadic computations)
6382 may yield more than one value,
6383 or none, and may do other things as well.
6384 For the most part, familiarity with monadic notation is a good guide to
6386 However the values of expressions, even monadic ones,
6387 are determined by the values of the variables they contain;
6388 this is not necessarily the case for commands.
6392 A simple example of the new notation is the expression
6394 proc x -> f -< x+1
6396 We call this a <firstterm>procedure</firstterm> or
6397 <firstterm>arrow abstraction</firstterm>.
6398 As with a lambda expression, the variable <literal>x</literal>
6399 is a new variable bound within the <literal>proc</literal>-expression.
6400 It refers to the input to the arrow.
6401 In the above example, <literal>-<</literal> is not an identifier but an
6402 new reserved symbol used for building commands from an expression of arrow
6403 type and an expression to be fed as input to that arrow.
6404 (The weird look will make more sense later.)
6405 It may be read as analogue of application for arrows.
6406 The above example is equivalent to the Haskell expression
6408 arr (\ x -> x+1) >>> f
6410 That would make no sense if the expression to the left of
6411 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6412 More generally, the expression to the left of <literal>-<</literal>
6413 may not involve any <firstterm>local variable</firstterm>,
6414 i.e. a variable bound in the current arrow abstraction.
6415 For such a situation there is a variant <literal>-<<</literal>, as in
6417 proc x -> f x -<< x+1
6419 which is equivalent to
6421 arr (\ x -> (f x, x+1)) >>> app
6423 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6425 Such an arrow is equivalent to a monad, so if you're using this form
6426 you may find a monadic formulation more convenient.
6430 <title>do-notation for commands</title>
6433 Another form of command is a form of <literal>do</literal>-notation.
6434 For example, you can write
6443 You can read this much like ordinary <literal>do</literal>-notation,
6444 but with commands in place of monadic expressions.
6445 The first line sends the value of <literal>x+1</literal> as an input to
6446 the arrow <literal>f</literal>, and matches its output against
6447 <literal>y</literal>.
6448 In the next line, the output is discarded.
6449 The arrow <function>returnA</function> is defined in the
6450 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6451 module as <literal>arr id</literal>.
6452 The above example is treated as an abbreviation for
6454 arr (\ x -> (x, x)) >>>
6455 first (arr (\ x -> x+1) >>> f) >>>
6456 arr (\ (y, x) -> (y, (x, y))) >>>
6457 first (arr (\ y -> 2*y) >>> g) >>>
6459 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6460 first (arr (\ (x, z) -> x*z) >>> h) >>>
6461 arr (\ (t, z) -> t+z) >>>
6464 Note that variables not used later in the composition are projected out.
6465 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6467 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6468 module, this reduces to
6470 arr (\ x -> (x+1, x)) >>>
6472 arr (\ (y, x) -> (2*y, (x, y))) >>>
6474 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6476 arr (\ (t, z) -> t+z)
6478 which is what you might have written by hand.
6479 With arrow notation, GHC keeps track of all those tuples of variables for you.
6483 Note that although the above translation suggests that
6484 <literal>let</literal>-bound variables like <literal>z</literal> must be
6485 monomorphic, the actual translation produces Core,
6486 so polymorphic variables are allowed.
6490 It's also possible to have mutually recursive bindings,
6491 using the new <literal>rec</literal> keyword, as in the following example:
6493 counter :: ArrowCircuit a => a Bool Int
6494 counter = proc reset -> do
6495 rec output <- returnA -< if reset then 0 else next
6496 next <- delay 0 -< output+1
6497 returnA -< output
6499 The translation of such forms uses the <function>loop</function> combinator,
6500 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6506 <title>Conditional commands</title>
6509 In the previous example, we used a conditional expression to construct the
6511 Sometimes we want to conditionally execute different commands, as in
6518 which is translated to
6520 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6521 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6523 Since the translation uses <function>|||</function>,
6524 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6528 There are also <literal>case</literal> commands, like
6534 y <- h -< (x1, x2)
6538 The syntax is the same as for <literal>case</literal> expressions,
6539 except that the bodies of the alternatives are commands rather than expressions.
6540 The translation is similar to that of <literal>if</literal> commands.
6546 <title>Defining your own control structures</title>
6549 As we're seen, arrow notation provides constructs,
6550 modelled on those for expressions,
6551 for sequencing, value recursion and conditionals.
6552 But suitable combinators,
6553 which you can define in ordinary Haskell,
6554 may also be used to build new commands out of existing ones.
6555 The basic idea is that a command defines an arrow from environments to values.
6556 These environments assign values to the free local variables of the command.
6557 Thus combinators that produce arrows from arrows
6558 may also be used to build commands from commands.
6559 For example, the <literal>ArrowChoice</literal> class includes a combinator
6561 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6563 so we can use it to build commands:
6565 expr' = proc x -> do
6568 symbol Plus -< ()
6569 y <- term -< ()
6572 symbol Minus -< ()
6573 y <- term -< ()
6576 (The <literal>do</literal> on the first line is needed to prevent the first
6577 <literal><+> ...</literal> from being interpreted as part of the
6578 expression on the previous line.)
6579 This is equivalent to
6581 expr' = (proc x -> returnA -< x)
6582 <+> (proc x -> do
6583 symbol Plus -< ()
6584 y <- term -< ()
6586 <+> (proc x -> do
6587 symbol Minus -< ()
6588 y <- term -< ()
6591 It is essential that this operator be polymorphic in <literal>e</literal>
6592 (representing the environment input to the command
6593 and thence to its subcommands)
6594 and satisfy the corresponding naturality property
6596 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6598 at least for strict <literal>k</literal>.
6599 (This should be automatic if you're not using <function>seq</function>.)
6600 This ensures that environments seen by the subcommands are environments
6601 of the whole command,
6602 and also allows the translation to safely trim these environments.
6603 The operator must also not use any variable defined within the current
6608 We could define our own operator
6610 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6611 untilA body cond = proc x ->
6612 b <- cond -< x
6613 if b then returnA -< ()
6616 untilA body cond -< x
6618 and use it in the same way.
6619 Of course this infix syntax only makes sense for binary operators;
6620 there is also a more general syntax involving special brackets:
6624 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6631 <title>Primitive constructs</title>
6634 Some operators will need to pass additional inputs to their subcommands.
6635 For example, in an arrow type supporting exceptions,
6636 the operator that attaches an exception handler will wish to pass the
6637 exception that occurred to the handler.
6638 Such an operator might have a type
6640 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6642 where <literal>Ex</literal> is the type of exceptions handled.
6643 You could then use this with arrow notation by writing a command
6645 body `handleA` \ ex -> handler
6647 so that if an exception is raised in the command <literal>body</literal>,
6648 the variable <literal>ex</literal> is bound to the value of the exception
6649 and the command <literal>handler</literal>,
6650 which typically refers to <literal>ex</literal>, is entered.
6651 Though the syntax here looks like a functional lambda,
6652 we are talking about commands, and something different is going on.
6653 The input to the arrow represented by a command consists of values for
6654 the free local variables in the command, plus a stack of anonymous values.
6655 In all the prior examples, this stack was empty.
6656 In the second argument to <function>handleA</function>,
6657 this stack consists of one value, the value of the exception.
6658 The command form of lambda merely gives this value a name.
6663 the values on the stack are paired to the right of the environment.
6664 So operators like <function>handleA</function> that pass
6665 extra inputs to their subcommands can be designed for use with the notation
6666 by pairing the values with the environment in this way.
6667 More precisely, the type of each argument of the operator (and its result)
6668 should have the form
6670 a (...(e,t1), ... tn) t
6672 where <replaceable>e</replaceable> is a polymorphic variable
6673 (representing the environment)
6674 and <replaceable>ti</replaceable> are the types of the values on the stack,
6675 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6676 The polymorphic variable <replaceable>e</replaceable> must not occur in
6677 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6678 <replaceable>t</replaceable>.
6679 However the arrows involved need not be the same.
6680 Here are some more examples of suitable operators:
6682 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6683 runReader :: ... => a e c -> a' (e,State) c
6684 runState :: ... => a e c -> a' (e,State) (c,State)
6686 We can supply the extra input required by commands built with the last two
6687 by applying them to ordinary expressions, as in
6691 (|runReader (do { ... })|) s
6693 which adds <literal>s</literal> to the stack of inputs to the command
6694 built using <function>runReader</function>.
6698 The command versions of lambda abstraction and application are analogous to
6699 the expression versions.
6700 In particular, the beta and eta rules describe equivalences of commands.
6701 These three features (operators, lambda abstraction and application)
6702 are the core of the notation; everything else can be built using them,
6703 though the results would be somewhat clumsy.
6704 For example, we could simulate <literal>do</literal>-notation by defining
6706 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6707 u `bind` f = returnA &&& u >>> f
6709 bind_ :: Arrow a => a e b -> a e c -> a e c
6710 u `bind_` f = u `bind` (arr fst >>> f)
6712 We could simulate <literal>if</literal> by defining
6714 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6715 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6722 <title>Differences with the paper</title>
6727 <para>Instead of a single form of arrow application (arrow tail) with two
6728 translations, the implementation provides two forms
6729 <quote><literal>-<</literal></quote> (first-order)
6730 and <quote><literal>-<<</literal></quote> (higher-order).
6735 <para>User-defined operators are flagged with banana brackets instead of
6736 a new <literal>form</literal> keyword.
6745 <title>Portability</title>
6748 Although only GHC implements arrow notation directly,
6749 there is also a preprocessor
6751 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6752 that translates arrow notation into Haskell 98
6753 for use with other Haskell systems.
6754 You would still want to check arrow programs with GHC;
6755 tracing type errors in the preprocessor output is not easy.
6756 Modules intended for both GHC and the preprocessor must observe some
6757 additional restrictions:
6762 The module must import
6763 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6769 The preprocessor cannot cope with other Haskell extensions.
6770 These would have to go in separate modules.
6776 Because the preprocessor targets Haskell (rather than Core),
6777 <literal>let</literal>-bound variables are monomorphic.
6788 <!-- ==================== BANG PATTERNS ================= -->
6790 <sect1 id="bang-patterns">
6791 <title>Bang patterns
6792 <indexterm><primary>Bang patterns</primary></indexterm>
6794 <para>GHC supports an extension of pattern matching called <emphasis>bang
6795 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6796 Bang patterns are under consideration for Haskell Prime.
6798 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6799 prime feature description</ulink> contains more discussion and examples
6800 than the material below.
6803 The key change is the addition of a new rule to the
6804 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6805 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6806 against a value <replaceable>v</replaceable> behaves as follows:
6808 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6809 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6813 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6816 <sect2 id="bang-patterns-informal">
6817 <title>Informal description of bang patterns
6820 The main idea is to add a single new production to the syntax of patterns:
6824 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6825 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6830 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6831 whereas without the bang it would be lazy.
6832 Bang patterns can be nested of course:
6836 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6837 <literal>y</literal>.
6838 A bang only really has an effect if it precedes a variable or wild-card pattern:
6843 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6844 putting a bang before a pattern that
6845 forces evaluation anyway does nothing.
6848 There is one (apparent) exception to this general rule that a bang only
6849 makes a difference when it precedes a variable or wild-card: a bang at the
6850 top level of a <literal>let</literal> or <literal>where</literal>
6851 binding makes the binding strict, regardless of the pattern. For example:
6855 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6856 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6857 (We say "apparent" exception because the Right Way to think of it is that the bang
6858 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6859 is part of the syntax of the <emphasis>binding</emphasis>.)
6860 Nested bangs in a pattern binding behave uniformly with all other forms of
6861 pattern matching. For example
6863 let (!x,[y]) = e in b
6865 is equivalent to this:
6867 let { t = case e of (x,[y]) -> x `seq` (x,y)
6872 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6873 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6874 evaluation of <literal>x</literal>.
6877 Bang patterns work in <literal>case</literal> expressions too, of course:
6879 g5 x = let y = f x in body
6880 g6 x = case f x of { y -> body }
6881 g7 x = case f x of { !y -> body }
6883 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6884 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6885 result, and then evaluates <literal>body</literal>.
6890 <sect2 id="bang-patterns-sem">
6891 <title>Syntax and semantics
6895 We add a single new production to the syntax of patterns:
6899 There is one problem with syntactic ambiguity. Consider:
6903 Is this a definition of the infix function "<literal>(!)</literal>",
6904 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6905 ambiguity in favour of the latter. If you want to define
6906 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6911 The semantics of Haskell pattern matching is described in <ulink
6912 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6913 Section 3.17.2</ulink> of the Haskell Report. To this description add
6914 one extra item 10, saying:
6915 <itemizedlist><listitem><para>Matching
6916 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6917 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6918 <listitem><para>otherwise, <literal>pat</literal> is matched against
6919 <literal>v</literal></para></listitem>
6921 </para></listitem></itemizedlist>
6922 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6923 Section 3.17.3</ulink>, add a new case (t):
6925 case v of { !pat -> e; _ -> e' }
6926 = v `seq` case v of { pat -> e; _ -> e' }
6929 That leaves let expressions, whose translation is given in
6930 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6932 of the Haskell Report.
6933 In the translation box, first apply
6934 the following transformation: for each pattern <literal>pi</literal> that is of
6935 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6936 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6937 have a bang at the top, apply the rules in the existing box.
6939 <para>The effect of the let rule is to force complete matching of the pattern
6940 <literal>qi</literal> before evaluation of the body is begun. The bang is
6941 retained in the translated form in case <literal>qi</literal> is a variable,
6949 The let-binding can be recursive. However, it is much more common for
6950 the let-binding to be non-recursive, in which case the following law holds:
6951 <literal>(let !p = rhs in body)</literal>
6953 <literal>(case rhs of !p -> body)</literal>
6956 A pattern with a bang at the outermost level is not allowed at the top level of
6962 <!-- ==================== ASSERTIONS ================= -->
6964 <sect1 id="assertions">
6966 <indexterm><primary>Assertions</primary></indexterm>
6970 If you want to make use of assertions in your standard Haskell code, you
6971 could define a function like the following:
6977 assert :: Bool -> a -> a
6978 assert False x = error "assertion failed!"
6985 which works, but gives you back a less than useful error message --
6986 an assertion failed, but which and where?
6990 One way out is to define an extended <function>assert</function> function which also
6991 takes a descriptive string to include in the error message and
6992 perhaps combine this with the use of a pre-processor which inserts
6993 the source location where <function>assert</function> was used.
6997 Ghc offers a helping hand here, doing all of this for you. For every
6998 use of <function>assert</function> in the user's source:
7004 kelvinToC :: Double -> Double
7005 kelvinToC k = assert (k >= 0.0) (k+273.15)
7011 Ghc will rewrite this to also include the source location where the
7018 assert pred val ==> assertError "Main.hs|15" pred val
7024 The rewrite is only performed by the compiler when it spots
7025 applications of <function>Control.Exception.assert</function>, so you
7026 can still define and use your own versions of
7027 <function>assert</function>, should you so wish. If not, import
7028 <literal>Control.Exception</literal> to make use
7029 <function>assert</function> in your code.
7033 GHC ignores assertions when optimisation is turned on with the
7034 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7035 <literal>assert pred e</literal> will be rewritten to
7036 <literal>e</literal>. You can also disable assertions using the
7037 <option>-fignore-asserts</option>
7038 option<indexterm><primary><option>-fignore-asserts</option></primary>
7039 </indexterm>.</para>
7042 Assertion failures can be caught, see the documentation for the
7043 <literal>Control.Exception</literal> library for the details.
7049 <!-- =============================== PRAGMAS =========================== -->
7051 <sect1 id="pragmas">
7052 <title>Pragmas</title>
7054 <indexterm><primary>pragma</primary></indexterm>
7056 <para>GHC supports several pragmas, or instructions to the
7057 compiler placed in the source code. Pragmas don't normally affect
7058 the meaning of the program, but they might affect the efficiency
7059 of the generated code.</para>
7061 <para>Pragmas all take the form
7063 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7065 where <replaceable>word</replaceable> indicates the type of
7066 pragma, and is followed optionally by information specific to that
7067 type of pragma. Case is ignored in
7068 <replaceable>word</replaceable>. The various values for
7069 <replaceable>word</replaceable> that GHC understands are described
7070 in the following sections; any pragma encountered with an
7071 unrecognised <replaceable>word</replaceable> is
7072 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7073 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7075 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7079 pragma must precede the <literal>module</literal> keyword in the file.
7082 There can be as many file-header pragmas as you please, and they can be
7083 preceded or followed by comments.
7086 File-header pragmas are read once only, before
7087 pre-processing the file (e.g. with cpp).
7090 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7091 <literal>{-# OPTIONS_GHC #-}</literal>, and
7092 <literal>{-# INCLUDE #-}</literal>.
7097 <sect2 id="language-pragma">
7098 <title>LANGUAGE pragma</title>
7100 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7101 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7103 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7105 It is the intention that all Haskell compilers support the
7106 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7107 all extensions are supported by all compilers, of
7108 course. The <literal>LANGUAGE</literal> pragma should be used instead
7109 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7111 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7113 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7115 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7117 <para>Every language extension can also be turned into a command-line flag
7118 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7119 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7122 <para>A list of all supported language extensions can be obtained by invoking
7123 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7125 <para>Any extension from the <literal>Extension</literal> type defined in
7127 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7128 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7132 <sect2 id="options-pragma">
7133 <title>OPTIONS_GHC pragma</title>
7134 <indexterm><primary>OPTIONS_GHC</primary>
7136 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7139 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7140 additional options that are given to the compiler when compiling
7141 this source file. See <xref linkend="source-file-options"/> for
7144 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7145 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7148 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7150 <sect2 id="include-pragma">
7151 <title>INCLUDE pragma</title>
7153 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
7154 of C header files that should be <literal>#include</literal>'d into
7155 the C source code generated by the compiler for the current module (if
7156 compiling via C). For example:</para>
7159 {-# INCLUDE "foo.h" #-}
7160 {-# INCLUDE <stdio.h> #-}</programlisting>
7162 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7164 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
7165 to the <option>-#include</option> option (<xref
7166 linkend="options-C-compiler" />), because the
7167 <literal>INCLUDE</literal> pragma is understood by other
7168 compilers. Yet another alternative is to add the include file to each
7169 <literal>foreign import</literal> declaration in your code, but we
7170 don't recommend using this approach with GHC.</para>
7173 <sect2 id="warning-deprecated-pragma">
7174 <title>WARNING and DEPRECATED pragmas</title>
7175 <indexterm><primary>WARNING</primary></indexterm>
7176 <indexterm><primary>DEPRECATED</primary></indexterm>
7178 <para>The WARNING pragma allows you to attach an arbitrary warning
7179 to a particular function, class, or type.
7180 A DEPRECATED pragma lets you specify that
7181 a particular function, class, or type is deprecated.
7182 There are two ways of using these pragmas.
7186 <para>You can work on an entire module thus:</para>
7188 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7193 module Wibble {-# WARNING "This is an unstable interface." #-} where
7196 <para>When you compile any module that import
7197 <literal>Wibble</literal>, GHC will print the specified
7202 <para>You can attach a warning to a function, class, type, or data constructor, with the
7203 following top-level declarations:</para>
7205 {-# DEPRECATED f, C, T "Don't use these" #-}
7206 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7208 <para>When you compile any module that imports and uses any
7209 of the specified entities, GHC will print the specified
7211 <para> You can only attach to entities declared at top level in the module
7212 being compiled, and you can only use unqualified names in the list of
7213 entities. A capitalised name, such as <literal>T</literal>
7214 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7215 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7216 both are in scope. If both are in scope, there is currently no way to
7217 specify one without the other (c.f. fixities
7218 <xref linkend="infix-tycons"/>).</para>
7221 Warnings and deprecations are not reported for
7222 (a) uses within the defining module, and
7223 (b) uses in an export list.
7224 The latter reduces spurious complaints within a library
7225 in which one module gathers together and re-exports
7226 the exports of several others.
7228 <para>You can suppress the warnings with the flag
7229 <option>-fno-warn-warnings-deprecations</option>.</para>
7232 <sect2 id="inline-noinline-pragma">
7233 <title>INLINE and NOINLINE pragmas</title>
7235 <para>These pragmas control the inlining of function
7238 <sect3 id="inline-pragma">
7239 <title>INLINE pragma</title>
7240 <indexterm><primary>INLINE</primary></indexterm>
7242 <para>GHC (with <option>-O</option>, as always) tries to
7243 inline (or “unfold”) functions/values that are
7244 “small enough,” thus avoiding the call overhead
7245 and possibly exposing other more-wonderful optimisations.
7246 Normally, if GHC decides a function is “too
7247 expensive” to inline, it will not do so, nor will it
7248 export that unfolding for other modules to use.</para>
7250 <para>The sledgehammer you can bring to bear is the
7251 <literal>INLINE</literal><indexterm><primary>INLINE
7252 pragma</primary></indexterm> pragma, used thusly:</para>
7255 key_function :: Int -> String -> (Bool, Double)
7256 {-# INLINE key_function #-}
7259 <para>The major effect of an <literal>INLINE</literal> pragma
7260 is to declare a function's “cost” to be very low.
7261 The normal unfolding machinery will then be very keen to
7262 inline it. However, an <literal>INLINE</literal> pragma for a
7263 function "<literal>f</literal>" has a number of other effects:
7266 No functions are inlined into <literal>f</literal>. Otherwise
7267 GHC might inline a big function into <literal>f</literal>'s right hand side,
7268 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7271 The float-in, float-out, and common-sub-expression transformations are not
7272 applied to the body of <literal>f</literal>.
7275 An INLINE function is not worker/wrappered by strictness analysis.
7276 It's going to be inlined wholesale instead.
7279 All of these effects are aimed at ensuring that what gets inlined is
7280 exactly what you asked for, no more and no less.
7282 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7283 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7284 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7285 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7286 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7287 when there is no choice even an INLINE function can be selected, in which case
7288 the INLINE pragma is ignored.
7289 For example, for a self-recursive function, the loop breaker can only be the function
7290 itself, so an INLINE pragma is always ignored.</para>
7292 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7293 function can be put anywhere its type signature could be
7296 <para><literal>INLINE</literal> pragmas are a particularly
7298 <literal>then</literal>/<literal>return</literal> (or
7299 <literal>bind</literal>/<literal>unit</literal>) functions in
7300 a monad. For example, in GHC's own
7301 <literal>UniqueSupply</literal> monad code, we have:</para>
7304 {-# INLINE thenUs #-}
7305 {-# INLINE returnUs #-}
7308 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7309 linkend="noinline-pragma"/>).</para>
7311 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7312 so if you want your code to be HBC-compatible you'll have to surround
7313 the pragma with C pre-processor directives
7314 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7318 <sect3 id="noinline-pragma">
7319 <title>NOINLINE pragma</title>
7321 <indexterm><primary>NOINLINE</primary></indexterm>
7322 <indexterm><primary>NOTINLINE</primary></indexterm>
7324 <para>The <literal>NOINLINE</literal> pragma does exactly what
7325 you'd expect: it stops the named function from being inlined
7326 by the compiler. You shouldn't ever need to do this, unless
7327 you're very cautious about code size.</para>
7329 <para><literal>NOTINLINE</literal> is a synonym for
7330 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7331 specified by Haskell 98 as the standard way to disable
7332 inlining, so it should be used if you want your code to be
7336 <sect3 id="phase-control">
7337 <title>Phase control</title>
7339 <para> Sometimes you want to control exactly when in GHC's
7340 pipeline the INLINE pragma is switched on. Inlining happens
7341 only during runs of the <emphasis>simplifier</emphasis>. Each
7342 run of the simplifier has a different <emphasis>phase
7343 number</emphasis>; the phase number decreases towards zero.
7344 If you use <option>-dverbose-core2core</option> you'll see the
7345 sequence of phase numbers for successive runs of the
7346 simplifier. In an INLINE pragma you can optionally specify a
7350 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7351 <literal>f</literal>
7352 until phase <literal>k</literal>, but from phase
7353 <literal>k</literal> onwards be very keen to inline it.
7356 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7357 <literal>f</literal>
7358 until phase <literal>k</literal>, but from phase
7359 <literal>k</literal> onwards do not inline it.
7362 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7363 <literal>f</literal>
7364 until phase <literal>k</literal>, but from phase
7365 <literal>k</literal> onwards be willing to inline it (as if
7366 there was no pragma).
7369 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7370 <literal>f</literal>
7371 until phase <literal>k</literal>, but from phase
7372 <literal>k</literal> onwards do not inline it.
7375 The same information is summarised here:
7377 -- Before phase 2 Phase 2 and later
7378 {-# INLINE [2] f #-} -- No Yes
7379 {-# INLINE [~2] f #-} -- Yes No
7380 {-# NOINLINE [2] f #-} -- No Maybe
7381 {-# NOINLINE [~2] f #-} -- Maybe No
7383 {-# INLINE f #-} -- Yes Yes
7384 {-# NOINLINE f #-} -- No No
7386 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7387 function body is small, or it is applied to interesting-looking arguments etc).
7388 Another way to understand the semantics is this:
7390 <listitem><para>For both INLINE and NOINLINE, the phase number says
7391 when inlining is allowed at all.</para></listitem>
7392 <listitem><para>The INLINE pragma has the additional effect of making the
7393 function body look small, so that when inlining is allowed it is very likely to
7398 <para>The same phase-numbering control is available for RULES
7399 (<xref linkend="rewrite-rules"/>).</para>
7403 <sect2 id="annotation-pragmas">
7404 <title>ANN pragmas</title>
7406 <para>GHC offers the ability to annotate various code constructs with additional
7407 data by using three pragmas. This data can then be inspected at a later date by
7408 using GHC-as-a-library.</para>
7410 <sect3 id="ann-pragma">
7411 <title>Annotating values</title>
7413 <indexterm><primary>ANN</primary></indexterm>
7415 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7416 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7417 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7418 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7419 you would do this:</para>
7422 {-# ANN foo (Just "Hello") #-}
7427 A number of restrictions apply to use of annotations:
7429 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7430 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7431 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7432 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7433 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7435 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7436 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7439 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7440 please give the GHC team a shout</ulink>.
7443 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7444 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7447 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7452 <sect3 id="typeann-pragma">
7453 <title>Annotating types</title>
7455 <indexterm><primary>ANN type</primary></indexterm>
7456 <indexterm><primary>ANN</primary></indexterm>
7458 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7461 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7466 <sect3 id="modann-pragma">
7467 <title>Annotating modules</title>
7469 <indexterm><primary>ANN module</primary></indexterm>
7470 <indexterm><primary>ANN</primary></indexterm>
7472 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7475 {-# ANN module (Just "A `Maybe String' annotation") #-}
7480 <sect2 id="line-pragma">
7481 <title>LINE pragma</title>
7483 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7484 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7485 <para>This pragma is similar to C's <literal>#line</literal>
7486 pragma, and is mainly for use in automatically generated Haskell
7487 code. It lets you specify the line number and filename of the
7488 original code; for example</para>
7490 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7492 <para>if you'd generated the current file from something called
7493 <filename>Foo.vhs</filename> and this line corresponds to line
7494 42 in the original. GHC will adjust its error messages to refer
7495 to the line/file named in the <literal>LINE</literal>
7500 <title>RULES pragma</title>
7502 <para>The RULES pragma lets you specify rewrite rules. It is
7503 described in <xref linkend="rewrite-rules"/>.</para>
7506 <sect2 id="specialize-pragma">
7507 <title>SPECIALIZE pragma</title>
7509 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7510 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7511 <indexterm><primary>overloading, death to</primary></indexterm>
7513 <para>(UK spelling also accepted.) For key overloaded
7514 functions, you can create extra versions (NB: more code space)
7515 specialised to particular types. Thus, if you have an
7516 overloaded function:</para>
7519 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7522 <para>If it is heavily used on lists with
7523 <literal>Widget</literal> keys, you could specialise it as
7527 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7530 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7531 be put anywhere its type signature could be put.</para>
7533 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7534 (a) a specialised version of the function and (b) a rewrite rule
7535 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7536 un-specialised function into a call to the specialised one.</para>
7538 <para>The type in a SPECIALIZE pragma can be any type that is less
7539 polymorphic than the type of the original function. In concrete terms,
7540 if the original function is <literal>f</literal> then the pragma
7542 {-# SPECIALIZE f :: <type> #-}
7544 is valid if and only if the definition
7546 f_spec :: <type>
7549 is valid. Here are some examples (where we only give the type signature
7550 for the original function, not its code):
7552 f :: Eq a => a -> b -> b
7553 {-# SPECIALISE f :: Int -> b -> b #-}
7555 g :: (Eq a, Ix b) => a -> b -> b
7556 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7558 h :: Eq a => a -> a -> a
7559 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7561 The last of these examples will generate a
7562 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7563 well. If you use this kind of specialisation, let us know how well it works.
7566 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7567 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7568 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7569 The <literal>INLINE</literal> pragma affects the specialised version of the
7570 function (only), and applies even if the function is recursive. The motivating
7573 -- A GADT for arrays with type-indexed representation
7575 ArrInt :: !Int -> ByteArray# -> Arr Int
7576 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7578 (!:) :: Arr e -> Int -> e
7579 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7580 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7581 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7582 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7584 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7585 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7586 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7587 the specialised function will be inlined. It has two calls to
7588 <literal>(!:)</literal>,
7589 both at type <literal>Int</literal>. Both these calls fire the first
7590 specialisation, whose body is also inlined. The result is a type-based
7591 unrolling of the indexing function.</para>
7592 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7593 on an ordinarily-recursive function.</para>
7595 <para>Note: In earlier versions of GHC, it was possible to provide your own
7596 specialised function for a given type:
7599 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7602 This feature has been removed, as it is now subsumed by the
7603 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7607 <sect2 id="specialize-instance-pragma">
7608 <title>SPECIALIZE instance pragma
7612 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7613 <indexterm><primary>overloading, death to</primary></indexterm>
7614 Same idea, except for instance declarations. For example:
7617 instance (Eq a) => Eq (Foo a) where {
7618 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7622 The pragma must occur inside the <literal>where</literal> part
7623 of the instance declaration.
7626 Compatible with HBC, by the way, except perhaps in the placement
7632 <sect2 id="unpack-pragma">
7633 <title>UNPACK pragma</title>
7635 <indexterm><primary>UNPACK</primary></indexterm>
7637 <para>The <literal>UNPACK</literal> indicates to the compiler
7638 that it should unpack the contents of a constructor field into
7639 the constructor itself, removing a level of indirection. For
7643 data T = T {-# UNPACK #-} !Float
7644 {-# UNPACK #-} !Float
7647 <para>will create a constructor <literal>T</literal> containing
7648 two unboxed floats. This may not always be an optimisation: if
7649 the <function>T</function> constructor is scrutinised and the
7650 floats passed to a non-strict function for example, they will
7651 have to be reboxed (this is done automatically by the
7654 <para>Unpacking constructor fields should only be used in
7655 conjunction with <option>-O</option>, in order to expose
7656 unfoldings to the compiler so the reboxing can be removed as
7657 often as possible. For example:</para>
7661 f (T f1 f2) = f1 + f2
7664 <para>The compiler will avoid reboxing <function>f1</function>
7665 and <function>f2</function> by inlining <function>+</function>
7666 on floats, but only when <option>-O</option> is on.</para>
7668 <para>Any single-constructor data is eligible for unpacking; for
7672 data T = T {-# UNPACK #-} !(Int,Int)
7675 <para>will store the two <literal>Int</literal>s directly in the
7676 <function>T</function> constructor, by flattening the pair.
7677 Multi-level unpacking is also supported:
7680 data T = T {-# UNPACK #-} !S
7681 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7684 will store two unboxed <literal>Int#</literal>s
7685 directly in the <function>T</function> constructor. The
7686 unpacker can see through newtypes, too.</para>
7688 <para>If a field cannot be unpacked, you will not get a warning,
7689 so it might be an idea to check the generated code with
7690 <option>-ddump-simpl</option>.</para>
7692 <para>See also the <option>-funbox-strict-fields</option> flag,
7693 which essentially has the effect of adding
7694 <literal>{-# UNPACK #-}</literal> to every strict
7695 constructor field.</para>
7698 <sect2 id="source-pragma">
7699 <title>SOURCE pragma</title>
7701 <indexterm><primary>SOURCE</primary></indexterm>
7702 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7703 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7709 <!-- ======================= REWRITE RULES ======================== -->
7711 <sect1 id="rewrite-rules">
7712 <title>Rewrite rules
7714 <indexterm><primary>RULES pragma</primary></indexterm>
7715 <indexterm><primary>pragma, RULES</primary></indexterm>
7716 <indexterm><primary>rewrite rules</primary></indexterm></title>
7719 The programmer can specify rewrite rules as part of the source program
7725 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7730 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7731 If you need more information, then <option>-ddump-rule-firings</option> shows you
7732 each individual rule firing in detail.
7736 <title>Syntax</title>
7739 From a syntactic point of view:
7745 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7746 may be generated by the layout rule).
7752 The layout rule applies in a pragma.
7753 Currently no new indentation level
7754 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7755 you must lay out the starting in the same column as the enclosing definitions.
7758 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7759 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7762 Furthermore, the closing <literal>#-}</literal>
7763 should start in a column to the right of the opening <literal>{-#</literal>.
7769 Each rule has a name, enclosed in double quotes. The name itself has
7770 no significance at all. It is only used when reporting how many times the rule fired.
7776 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7777 immediately after the name of the rule. Thus:
7780 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7783 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7784 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7793 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7794 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7795 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7796 by spaces, just like in a type <literal>forall</literal>.
7802 A pattern variable may optionally have a type signature.
7803 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7804 For example, here is the <literal>foldr/build</literal> rule:
7807 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7808 foldr k z (build g) = g k z
7811 Since <function>g</function> has a polymorphic type, it must have a type signature.
7818 The left hand side of a rule must consist of a top-level variable applied
7819 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7822 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7823 "wrong2" forall f. f True = True
7826 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7833 A rule does not need to be in the same module as (any of) the
7834 variables it mentions, though of course they need to be in scope.
7840 All rules are implicitly exported from the module, and are therefore
7841 in force in any module that imports the module that defined the rule, directly
7842 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7843 in force when compiling A.) The situation is very similar to that for instance
7851 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7852 any other flag settings. Furthermore, inside a RULE, the language extension
7853 <option>-XScopedTypeVariables</option> is automatically enabled; see
7854 <xref linkend="scoped-type-variables"/>.
7860 Like other pragmas, RULE pragmas are always checked for scope errors, and
7861 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7862 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7863 if the <option>-fenable-rewrite-rules</option> flag is
7864 on (see <xref linkend="rule-semantics"/>).
7873 <sect2 id="rule-semantics">
7874 <title>Semantics</title>
7877 From a semantic point of view:
7882 Rules are enabled (that is, used during optimisation)
7883 by the <option>-fenable-rewrite-rules</option> flag.
7884 This flag is implied by <option>-O</option>, and may be switched
7885 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7886 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7887 may not do what you expect, though, because without <option>-O</option> GHC
7888 ignores all optimisation information in interface files;
7889 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7890 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7891 has no effect on parsing or typechecking.
7897 Rules are regarded as left-to-right rewrite rules.
7898 When GHC finds an expression that is a substitution instance of the LHS
7899 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7900 By "a substitution instance" we mean that the LHS can be made equal to the
7901 expression by substituting for the pattern variables.
7908 GHC makes absolutely no attempt to verify that the LHS and RHS
7909 of a rule have the same meaning. That is undecidable in general, and
7910 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7917 GHC makes no attempt to make sure that the rules are confluent or
7918 terminating. For example:
7921 "loop" forall x y. f x y = f y x
7924 This rule will cause the compiler to go into an infinite loop.
7931 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7937 GHC currently uses a very simple, syntactic, matching algorithm
7938 for matching a rule LHS with an expression. It seeks a substitution
7939 which makes the LHS and expression syntactically equal modulo alpha
7940 conversion. The pattern (rule), but not the expression, is eta-expanded if
7941 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7942 But not beta conversion (that's called higher-order matching).
7946 Matching is carried out on GHC's intermediate language, which includes
7947 type abstractions and applications. So a rule only matches if the
7948 types match too. See <xref linkend="rule-spec"/> below.
7954 GHC keeps trying to apply the rules as it optimises the program.
7955 For example, consider:
7964 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7965 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7966 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7967 not be substituted, and the rule would not fire.
7974 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7975 results. Consider this (artificial) example
7978 {-# RULES "f" f True = False #-}
7984 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7989 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7991 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7992 would have been a better chance that <literal>f</literal>'s RULE might fire.
7995 The way to get predictable behaviour is to use a NOINLINE
7996 pragma on <literal>f</literal>, to ensure
7997 that it is not inlined until its RULEs have had a chance to fire.
8007 <title>List fusion</title>
8010 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8011 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8012 intermediate list should be eliminated entirely.
8016 The following are good producers:
8028 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8034 Explicit lists (e.g. <literal>[True, False]</literal>)
8040 The cons constructor (e.g <literal>3:4:[]</literal>)
8046 <function>++</function>
8052 <function>map</function>
8058 <function>take</function>, <function>filter</function>
8064 <function>iterate</function>, <function>repeat</function>
8070 <function>zip</function>, <function>zipWith</function>
8079 The following are good consumers:
8091 <function>array</function> (on its second argument)
8097 <function>++</function> (on its first argument)
8103 <function>foldr</function>
8109 <function>map</function>
8115 <function>take</function>, <function>filter</function>
8121 <function>concat</function>
8127 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8133 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8134 will fuse with one but not the other)
8140 <function>partition</function>
8146 <function>head</function>
8152 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8158 <function>sequence_</function>
8164 <function>msum</function>
8170 <function>sortBy</function>
8179 So, for example, the following should generate no intermediate lists:
8182 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8188 This list could readily be extended; if there are Prelude functions that you use
8189 a lot which are not included, please tell us.
8193 If you want to write your own good consumers or producers, look at the
8194 Prelude definitions of the above functions to see how to do so.
8199 <sect2 id="rule-spec">
8200 <title>Specialisation
8204 Rewrite rules can be used to get the same effect as a feature
8205 present in earlier versions of GHC.
8206 For example, suppose that:
8209 genericLookup :: Ord a => Table a b -> a -> b
8210 intLookup :: Table Int b -> Int -> b
8213 where <function>intLookup</function> is an implementation of
8214 <function>genericLookup</function> that works very fast for
8215 keys of type <literal>Int</literal>. You might wish
8216 to tell GHC to use <function>intLookup</function> instead of
8217 <function>genericLookup</function> whenever the latter was called with
8218 type <literal>Table Int b -> Int -> b</literal>.
8219 It used to be possible to write
8222 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8225 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8228 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8231 This slightly odd-looking rule instructs GHC to replace
8232 <function>genericLookup</function> by <function>intLookup</function>
8233 <emphasis>whenever the types match</emphasis>.
8234 What is more, this rule does not need to be in the same
8235 file as <function>genericLookup</function>, unlike the
8236 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8237 have an original definition available to specialise).
8240 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8241 <function>intLookup</function> really behaves as a specialised version
8242 of <function>genericLookup</function>!!!</para>
8244 <para>An example in which using <literal>RULES</literal> for
8245 specialisation will Win Big:
8248 toDouble :: Real a => a -> Double
8249 toDouble = fromRational . toRational
8251 {-# RULES "toDouble/Int" toDouble = i2d #-}
8252 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8255 The <function>i2d</function> function is virtually one machine
8256 instruction; the default conversion—via an intermediate
8257 <literal>Rational</literal>—is obscenely expensive by
8264 <title>Controlling what's going on</title>
8272 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8278 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8279 If you add <option>-dppr-debug</option> you get a more detailed listing.
8285 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8288 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8289 {-# INLINE build #-}
8293 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8294 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8295 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8296 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8303 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8304 see how to write rules that will do fusion and yet give an efficient
8305 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8315 <sect2 id="core-pragma">
8316 <title>CORE pragma</title>
8318 <indexterm><primary>CORE pragma</primary></indexterm>
8319 <indexterm><primary>pragma, CORE</primary></indexterm>
8320 <indexterm><primary>core, annotation</primary></indexterm>
8323 The external core format supports <quote>Note</quote> annotations;
8324 the <literal>CORE</literal> pragma gives a way to specify what these
8325 should be in your Haskell source code. Syntactically, core
8326 annotations are attached to expressions and take a Haskell string
8327 literal as an argument. The following function definition shows an
8331 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8334 Semantically, this is equivalent to:
8342 However, when external core is generated (via
8343 <option>-fext-core</option>), there will be Notes attached to the
8344 expressions <function>show</function> and <varname>x</varname>.
8345 The core function declaration for <function>f</function> is:
8349 f :: %forall a . GHCziShow.ZCTShow a ->
8350 a -> GHCziBase.ZMZN GHCziBase.Char =
8351 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8353 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8355 (tpl1::GHCziBase.Int ->
8357 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8359 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8360 (tpl3::GHCziBase.ZMZN a ->
8361 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8369 Here, we can see that the function <function>show</function> (which
8370 has been expanded out to a case expression over the Show dictionary)
8371 has a <literal>%note</literal> attached to it, as does the
8372 expression <varname>eta</varname> (which used to be called
8373 <varname>x</varname>).
8380 <sect1 id="special-ids">
8381 <title>Special built-in functions</title>
8382 <para>GHC has a few built-in functions with special behaviour. These
8383 are now described in the module <ulink
8384 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8385 in the library documentation.</para>
8389 <sect1 id="generic-classes">
8390 <title>Generic classes</title>
8393 The ideas behind this extension are described in detail in "Derivable type classes",
8394 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8395 An example will give the idea:
8403 fromBin :: [Int] -> (a, [Int])
8405 toBin {| Unit |} Unit = []
8406 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8407 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8408 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8410 fromBin {| Unit |} bs = (Unit, bs)
8411 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8412 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8413 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8414 (y,bs'') = fromBin bs'
8417 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8418 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8419 which are defined thus in the library module <literal>Generics</literal>:
8423 data a :+: b = Inl a | Inr b
8424 data a :*: b = a :*: b
8427 Now you can make a data type into an instance of Bin like this:
8429 instance (Bin a, Bin b) => Bin (a,b)
8430 instance Bin a => Bin [a]
8432 That is, just leave off the "where" clause. Of course, you can put in the
8433 where clause and over-ride whichever methods you please.
8437 <title> Using generics </title>
8438 <para>To use generics you need to</para>
8441 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8442 <option>-XGenerics</option> (to generate extra per-data-type code),
8443 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8447 <para>Import the module <literal>Generics</literal> from the
8448 <literal>lang</literal> package. This import brings into
8449 scope the data types <literal>Unit</literal>,
8450 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8451 don't need this import if you don't mention these types
8452 explicitly; for example, if you are simply giving instance
8453 declarations.)</para>
8458 <sect2> <title> Changes wrt the paper </title>
8460 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8461 can be written infix (indeed, you can now use
8462 any operator starting in a colon as an infix type constructor). Also note that
8463 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8464 Finally, note that the syntax of the type patterns in the class declaration
8465 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8466 alone would ambiguous when they appear on right hand sides (an extension we
8467 anticipate wanting).
8471 <sect2> <title>Terminology and restrictions</title>
8473 Terminology. A "generic default method" in a class declaration
8474 is one that is defined using type patterns as above.
8475 A "polymorphic default method" is a default method defined as in Haskell 98.
8476 A "generic class declaration" is a class declaration with at least one
8477 generic default method.
8485 Alas, we do not yet implement the stuff about constructor names and
8492 A generic class can have only one parameter; you can't have a generic
8493 multi-parameter class.
8499 A default method must be defined entirely using type patterns, or entirely
8500 without. So this is illegal:
8503 op :: a -> (a, Bool)
8504 op {| Unit |} Unit = (Unit, True)
8507 However it is perfectly OK for some methods of a generic class to have
8508 generic default methods and others to have polymorphic default methods.
8514 The type variable(s) in the type pattern for a generic method declaration
8515 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:
8519 op {| p :*: q |} (x :*: y) = op (x :: p)
8527 The type patterns in a generic default method must take one of the forms:
8533 where "a" and "b" are type variables. Furthermore, all the type patterns for
8534 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8535 must use the same type variables. So this is illegal:
8539 op {| a :+: b |} (Inl x) = True
8540 op {| p :+: q |} (Inr y) = False
8542 The type patterns must be identical, even in equations for different methods of the class.
8543 So this too is illegal:
8547 op1 {| a :*: b |} (x :*: y) = True
8550 op2 {| p :*: q |} (x :*: y) = False
8552 (The reason for this restriction is that we gather all the equations for a particular type constructor
8553 into a single generic instance declaration.)
8559 A generic method declaration must give a case for each of the three type constructors.
8565 The type for a generic method can be built only from:
8567 <listitem> <para> Function arrows </para> </listitem>
8568 <listitem> <para> Type variables </para> </listitem>
8569 <listitem> <para> Tuples </para> </listitem>
8570 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8572 Here are some example type signatures for generic methods:
8575 op2 :: Bool -> (a,Bool)
8576 op3 :: [Int] -> a -> a
8579 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8583 This restriction is an implementation restriction: we just haven't got around to
8584 implementing the necessary bidirectional maps over arbitrary type constructors.
8585 It would be relatively easy to add specific type constructors, such as Maybe and list,
8586 to the ones that are allowed.</para>
8591 In an instance declaration for a generic class, the idea is that the compiler
8592 will fill in the methods for you, based on the generic templates. However it can only
8597 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8602 No constructor of the instance type has unboxed fields.
8606 (Of course, these things can only arise if you are already using GHC extensions.)
8607 However, you can still give an instance declarations for types which break these rules,
8608 provided you give explicit code to override any generic default methods.
8616 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8617 what the compiler does with generic declarations.
8622 <sect2> <title> Another example </title>
8624 Just to finish with, here's another example I rather like:
8628 nCons {| Unit |} _ = 1
8629 nCons {| a :*: b |} _ = 1
8630 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8633 tag {| Unit |} _ = 1
8634 tag {| a :*: b |} _ = 1
8635 tag {| a :+: b |} (Inl x) = tag x
8636 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8642 <sect1 id="monomorphism">
8643 <title>Control over monomorphism</title>
8645 <para>GHC supports two flags that control the way in which generalisation is
8646 carried out at let and where bindings.
8650 <title>Switching off the dreaded Monomorphism Restriction</title>
8651 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8653 <para>Haskell's monomorphism restriction (see
8654 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8656 of the Haskell Report)
8657 can be completely switched off by
8658 <option>-XNoMonomorphismRestriction</option>.
8663 <title>Monomorphic pattern bindings</title>
8664 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8665 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8667 <para> As an experimental change, we are exploring the possibility of
8668 making pattern bindings monomorphic; that is, not generalised at all.
8669 A pattern binding is a binding whose LHS has no function arguments,
8670 and is not a simple variable. For example:
8672 f x = x -- Not a pattern binding
8673 f = \x -> x -- Not a pattern binding
8674 f :: Int -> Int = \x -> x -- Not a pattern binding
8676 (g,h) = e -- A pattern binding
8677 (f) = e -- A pattern binding
8678 [x] = e -- A pattern binding
8680 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8681 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8690 ;;; Local Variables: ***
8692 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8693 ;;; ispell-local-dictionary: "british" ***
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