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 <!-- ===================== n+k patterns =================== -->
845 <sect2 id="n-k-patterns">
846 <title>n+k patterns</title>
847 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
850 <literal>n+k</literal> pattern support is enabled by default. To disable
851 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
856 <!-- ===================== Recursive do-notation =================== -->
858 <sect2 id="mdo-notation">
859 <title>The recursive do-notation
862 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
863 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
864 by Levent Erkok, John Launchbury,
865 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
866 This paper is essential reading for anyone making non-trivial use of mdo-notation,
867 and we do not repeat it here.
870 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
871 that is, the variables bound in a do-expression are visible only in the textually following
872 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
873 group. It turns out that several applications can benefit from recursive bindings in
874 the do-notation, and this extension provides the necessary syntactic support.
877 Here is a simple (yet contrived) example:
880 import Control.Monad.Fix
882 justOnes = mdo xs <- Just (1:xs)
886 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
890 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. Its definition is:
893 class Monad m => MonadFix m where
894 mfix :: (a -> m a) -> m a
897 The function <literal>mfix</literal>
898 dictates how the required recursion operation should be performed. For example,
899 <literal>justOnes</literal> desugars as follows:
901 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
903 For full details of the way in which mdo is typechecked and desugared, see
904 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
905 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
908 If recursive bindings are required for a monad,
909 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
910 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
911 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
912 for Haskell's internal state monad (strict and lazy, respectively).
915 Here are some important points in using the recursive-do notation:
918 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
919 than <literal>do</literal>).
923 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
924 <literal>-fglasgow-exts</literal>.
928 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
929 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
930 be distinct (Section 3.3 of the paper).
934 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
935 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
936 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
937 and improve termination (Section 3.2 of the paper).
943 Historical note: The old implementation of the mdo-notation (and most
944 of the existing documents) used the name
945 <literal>MonadRec</literal> for the class and the corresponding library.
946 This name is not supported by GHC.
952 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
954 <sect2 id="parallel-list-comprehensions">
955 <title>Parallel List Comprehensions</title>
956 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
958 <indexterm><primary>parallel list comprehensions</primary>
961 <para>Parallel list comprehensions are a natural extension to list
962 comprehensions. List comprehensions can be thought of as a nice
963 syntax for writing maps and filters. Parallel comprehensions
964 extend this to include the zipWith family.</para>
966 <para>A parallel list comprehension has multiple independent
967 branches of qualifier lists, each separated by a `|' symbol. For
968 example, the following zips together two lists:</para>
971 [ (x, y) | x <- xs | y <- ys ]
974 <para>The behavior of parallel list comprehensions follows that of
975 zip, in that the resulting list will have the same length as the
976 shortest branch.</para>
978 <para>We can define parallel list comprehensions by translation to
979 regular comprehensions. Here's the basic idea:</para>
981 <para>Given a parallel comprehension of the form: </para>
984 [ e | p1 <- e11, p2 <- e12, ...
985 | q1 <- e21, q2 <- e22, ...
990 <para>This will be translated to: </para>
993 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
994 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
999 <para>where `zipN' is the appropriate zip for the given number of
1004 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1006 <sect2 id="generalised-list-comprehensions">
1007 <title>Generalised (SQL-Like) List Comprehensions</title>
1008 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1010 <indexterm><primary>extended list comprehensions</primary>
1012 <indexterm><primary>group</primary></indexterm>
1013 <indexterm><primary>sql</primary></indexterm>
1016 <para>Generalised list comprehensions are a further enhancement to the
1017 list comprehension syntactic sugar to allow operations such as sorting
1018 and grouping which are familiar from SQL. They are fully described in the
1019 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1020 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1021 except that the syntax we use differs slightly from the paper.</para>
1022 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1023 <para>Here is an example:
1025 employees = [ ("Simon", "MS", 80)
1026 , ("Erik", "MS", 100)
1027 , ("Phil", "Ed", 40)
1028 , ("Gordon", "Ed", 45)
1029 , ("Paul", "Yale", 60)]
1031 output = [ (the dept, sum salary)
1032 | (name, dept, salary) <- employees
1033 , then group by dept
1034 , then sortWith by (sum salary)
1037 In this example, the list <literal>output</literal> would take on
1041 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1044 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1045 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1046 function that is exported by <literal>GHC.Exts</literal>.)</para>
1048 <para>There are five new forms of comprehension qualifier,
1049 all introduced by the (existing) keyword <literal>then</literal>:
1057 This statement requires that <literal>f</literal> have the type <literal>
1058 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1059 motivating example, as this form is used to apply <literal>take 5</literal>.
1070 This form is similar to the previous one, but allows you to create a function
1071 which will be passed as the first argument to f. As a consequence f must have
1072 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1073 from the type, this function lets f "project out" some information
1074 from the elements of the list it is transforming.</para>
1076 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1077 is supplied with a function that lets it find out the <literal>sum salary</literal>
1078 for any item in the list comprehension it transforms.</para>
1086 then group by e using f
1089 <para>This is the most general of the grouping-type statements. In this form,
1090 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1091 As with the <literal>then f by e</literal> case above, the first argument
1092 is a function supplied to f by the compiler which lets it compute e on every
1093 element of the list being transformed. However, unlike the non-grouping case,
1094 f additionally partitions the list into a number of sublists: this means that
1095 at every point after this statement, binders occurring before it in the comprehension
1096 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1097 this, let's look at an example:</para>
1100 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1101 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1102 groupRuns f = groupBy (\x y -> f x == f y)
1104 output = [ (the x, y)
1105 | x <- ([1..3] ++ [1..2])
1107 , then group by x using groupRuns ]
1110 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1113 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1116 <para>Note that we have used the <literal>the</literal> function to change the type
1117 of x from a list to its original numeric type. The variable y, in contrast, is left
1118 unchanged from the list form introduced by the grouping.</para>
1128 <para>This form of grouping is essentially the same as the one described above. However,
1129 since no function to use for the grouping has been supplied it will fall back on the
1130 <literal>groupWith</literal> function defined in
1131 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1132 is the form of the group statement that we made use of in the opening example.</para>
1143 <para>With this form of the group statement, f is required to simply have the type
1144 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1145 comprehension so far directly. An example of this form is as follows:</para>
1151 , then group using inits]
1154 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1157 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1165 <!-- ===================== REBINDABLE SYNTAX =================== -->
1167 <sect2 id="rebindable-syntax">
1168 <title>Rebindable syntax and the implicit Prelude import</title>
1170 <para><indexterm><primary>-XNoImplicitPrelude
1171 option</primary></indexterm> GHC normally imports
1172 <filename>Prelude.hi</filename> files for you. If you'd
1173 rather it didn't, then give it a
1174 <option>-XNoImplicitPrelude</option> option. The idea is
1175 that you can then import a Prelude of your own. (But don't
1176 call it <literal>Prelude</literal>; the Haskell module
1177 namespace is flat, and you must not conflict with any
1178 Prelude module.)</para>
1180 <para>Suppose you are importing a Prelude of your own
1181 in order to define your own numeric class
1182 hierarchy. It completely defeats that purpose if the
1183 literal "1" means "<literal>Prelude.fromInteger
1184 1</literal>", which is what the Haskell Report specifies.
1185 So the <option>-XNoImplicitPrelude</option>
1186 flag <emphasis>also</emphasis> causes
1187 the following pieces of built-in syntax to refer to
1188 <emphasis>whatever is in scope</emphasis>, not the Prelude
1192 <para>An integer literal <literal>368</literal> means
1193 "<literal>fromInteger (368::Integer)</literal>", rather than
1194 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1197 <listitem><para>Fractional literals are handed in just the same way,
1198 except that the translation is
1199 <literal>fromRational (3.68::Rational)</literal>.
1202 <listitem><para>The equality test in an overloaded numeric pattern
1203 uses whatever <literal>(==)</literal> is in scope.
1206 <listitem><para>The subtraction operation, and the
1207 greater-than-or-equal test, in <literal>n+k</literal> patterns
1208 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1212 <para>Negation (e.g. "<literal>- (f x)</literal>")
1213 means "<literal>negate (f x)</literal>", both in numeric
1214 patterns, and expressions.
1218 <para>"Do" notation is translated using whatever
1219 functions <literal>(>>=)</literal>,
1220 <literal>(>>)</literal>, and <literal>fail</literal>,
1221 are in scope (not the Prelude
1222 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1223 comprehensions, are unaffected. </para></listitem>
1227 notation (see <xref linkend="arrow-notation"/>)
1228 uses whatever <literal>arr</literal>,
1229 <literal>(>>>)</literal>, <literal>first</literal>,
1230 <literal>app</literal>, <literal>(|||)</literal> and
1231 <literal>loop</literal> functions are in scope. But unlike the
1232 other constructs, the types of these functions must match the
1233 Prelude types very closely. Details are in flux; if you want
1237 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1238 even if that is a little unexpected. For example, the
1239 static semantics of the literal <literal>368</literal>
1240 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1241 <literal>fromInteger</literal> to have any of the types:
1243 fromInteger :: Integer -> Integer
1244 fromInteger :: forall a. Foo a => Integer -> a
1245 fromInteger :: Num a => a -> Integer
1246 fromInteger :: Integer -> Bool -> Bool
1250 <para>Be warned: this is an experimental facility, with
1251 fewer checks than usual. Use <literal>-dcore-lint</literal>
1252 to typecheck the desugared program. If Core Lint is happy
1253 you should be all right.</para>
1257 <sect2 id="postfix-operators">
1258 <title>Postfix operators</title>
1261 The <option>-XPostfixOperators</option> flag enables a small
1262 extension to the syntax of left operator sections, which allows you to
1263 define postfix operators. The extension is this: the left section
1267 is equivalent (from the point of view of both type checking and execution) to the expression
1271 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1272 The strict Haskell 98 interpretation is that the section is equivalent to
1276 That is, the operator must be a function of two arguments. GHC allows it to
1277 take only one argument, and that in turn allows you to write the function
1280 <para>The extension does not extend to the left-hand side of function
1281 definitions; you must define such a function in prefix form.</para>
1285 <sect2 id="tuple-sections">
1286 <title>Tuple sections</title>
1289 The <option>-XTupleSections</option> flag enables Python-style partially applied
1290 tuple constructors. For example, the following program
1294 is considered to be an alternative notation for the more unwieldy alternative
1298 You can omit any combination of arguments to the tuple, as in the following
1300 (, "I", , , "Love", , 1337)
1304 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1309 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1310 will also be available for them, like so
1314 Because there is no unboxed unit tuple, the following expression
1318 continues to stand for the unboxed singleton tuple data constructor.
1323 <sect2 id="disambiguate-fields">
1324 <title>Record field disambiguation</title>
1326 In record construction and record pattern matching
1327 it is entirely unambiguous which field is referred to, even if there are two different
1328 data types in scope with a common field name. For example:
1331 data S = MkS { x :: Int, y :: Bool }
1336 data T = MkT { x :: Int }
1338 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1339 ok2 n = MkT { x = n+1 } -- Unambiguous
1341 bad1 k = k { x = 3 } -- Ambiguous
1342 bad2 k = x k -- Ambiguous
1344 Even though there are two <literal>x</literal>'s in scope,
1345 it is clear that the <literal>x</literal> in the pattern in the
1346 definition of <literal>ok1</literal> can only mean the field
1347 <literal>x</literal> from type <literal>S</literal>. Similarly for
1348 the function <literal>ok2</literal>. However, in the record update
1349 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1350 it is not clear which of the two types is intended.
1353 Haskell 98 regards all four as ambiguous, but with the
1354 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1355 the former two. The rules are precisely the same as those for instance
1356 declarations in Haskell 98, where the method names on the left-hand side
1357 of the method bindings in an instance declaration refer unambiguously
1358 to the method of that class (provided they are in scope at all), even
1359 if there are other variables in scope with the same name.
1360 This reduces the clutter of qualified names when you import two
1361 records from different modules that use the same field name.
1367 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1372 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1377 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1378 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1379 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1382 import qualified M -- Note qualified
1384 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1386 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1387 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1388 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1389 is not. (In effect, it is qualified by the constructor.)
1396 <!-- ===================== Record puns =================== -->
1398 <sect2 id="record-puns">
1403 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1407 When using records, it is common to write a pattern that binds a
1408 variable with the same name as a record field, such as:
1411 data C = C {a :: Int}
1417 Record punning permits the variable name to be elided, so one can simply
1424 to mean the same pattern as above. That is, in a record pattern, the
1425 pattern <literal>a</literal> expands into the pattern <literal>a =
1426 a</literal> for the same name <literal>a</literal>.
1433 Record punning can also be used in an expression, writing, for example,
1439 let a = 1 in C {a = a}
1441 The expansion is purely syntactic, so the expanded right-hand side
1442 expression refers to the nearest enclosing variable that is spelled the
1443 same as the field name.
1447 Puns and other patterns can be mixed in the same record:
1449 data C = C {a :: Int, b :: Int}
1450 f (C {a, b = 4}) = a
1455 Puns can be used wherever record patterns occur (e.g. in
1456 <literal>let</literal> bindings or at the top-level).
1460 A pun on a qualified field name is expanded by stripping off the module qualifier.
1467 f (M.C {M.a = a}) = a
1469 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1470 is only in scope in qualified form.)
1478 <!-- ===================== Record wildcards =================== -->
1480 <sect2 id="record-wildcards">
1481 <title>Record wildcards
1485 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1486 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1490 For records with many fields, it can be tiresome to write out each field
1491 individually in a record pattern, as in
1493 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1494 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1499 Record wildcard syntax permits a "<literal>..</literal>" in a record
1500 pattern, where each elided field <literal>f</literal> is replaced by the
1501 pattern <literal>f = f</literal>. For example, the above pattern can be
1504 f (C {a = 1, ..}) = b + c + d
1512 Wildcards can be mixed with other patterns, including puns
1513 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1514 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1515 wherever record patterns occur, including in <literal>let</literal>
1516 bindings and at the top-level. For example, the top-level binding
1520 defines <literal>b</literal>, <literal>c</literal>, and
1521 <literal>d</literal>.
1525 Record wildcards can also be used in expressions, writing, for example,
1527 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1531 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1533 The expansion is purely syntactic, so the record wildcard
1534 expression refers to the nearest enclosing variables that are spelled
1535 the same as the omitted field names.
1539 The "<literal>..</literal>" expands to the missing
1540 <emphasis>in-scope</emphasis> record fields, where "in scope"
1541 includes both unqualified and qualified-only.
1542 Any fields that are not in scope are not filled in. For example
1545 data R = R { a,b,c :: Int }
1547 import qualified M( R(a,b) )
1550 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1551 omitting <literal>c</literal> since it is not in scope at all.
1558 <!-- ===================== Local fixity declarations =================== -->
1560 <sect2 id="local-fixity-declarations">
1561 <title>Local Fixity Declarations
1564 <para>A careful reading of the Haskell 98 Report reveals that fixity
1565 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1566 <literal>infixr</literal>) are permitted to appear inside local bindings
1567 such those introduced by <literal>let</literal> and
1568 <literal>where</literal>. However, the Haskell Report does not specify
1569 the semantics of such bindings very precisely.
1572 <para>In GHC, a fixity declaration may accompany a local binding:
1579 and the fixity declaration applies wherever the binding is in scope.
1580 For example, in a <literal>let</literal>, it applies in the right-hand
1581 sides of other <literal>let</literal>-bindings and the body of the
1582 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1583 expressions (<xref linkend="mdo-notation"/>), the local fixity
1584 declarations of a <literal>let</literal> statement scope over other
1585 statements in the group, just as the bound name does.
1589 Moreover, a local fixity declaration *must* accompany a local binding of
1590 that name: it is not possible to revise the fixity of name bound
1593 let infixr 9 $ in ...
1596 Because local fixity declarations are technically Haskell 98, no flag is
1597 necessary to enable them.
1601 <sect2 id="package-imports">
1602 <title>Package-qualified imports</title>
1604 <para>With the <option>-XPackageImports</option> flag, GHC allows
1605 import declarations to be qualified by the package name that the
1606 module is intended to be imported from. For example:</para>
1609 import "network" Network.Socket
1612 <para>would import the module <literal>Network.Socket</literal> from
1613 the package <literal>network</literal> (any version). This may
1614 be used to disambiguate an import when the same module is
1615 available from multiple packages, or is present in both the
1616 current package being built and an external package.</para>
1618 <para>Note: you probably don't need to use this feature, it was
1619 added mainly so that we can build backwards-compatible versions of
1620 packages when APIs change. It can lead to fragile dependencies in
1621 the common case: modules occasionally move from one package to
1622 another, rendering any package-qualified imports broken.</para>
1625 <sect2 id="syntax-stolen">
1626 <title>Summary of stolen syntax</title>
1628 <para>Turning on an option that enables special syntax
1629 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1630 to compile, perhaps because it uses a variable name which has
1631 become a reserved word. This section lists the syntax that is
1632 "stolen" by language extensions.
1634 notation and nonterminal names from the Haskell 98 lexical syntax
1635 (see the Haskell 98 Report).
1636 We only list syntax changes here that might affect
1637 existing working programs (i.e. "stolen" syntax). Many of these
1638 extensions will also enable new context-free syntax, but in all
1639 cases programs written to use the new syntax would not be
1640 compilable without the option enabled.</para>
1642 <para>There are two classes of special
1647 <para>New reserved words and symbols: character sequences
1648 which are no longer available for use as identifiers in the
1652 <para>Other special syntax: sequences of characters that have
1653 a different meaning when this particular option is turned
1658 The following syntax is stolen:
1663 <literal>forall</literal>
1664 <indexterm><primary><literal>forall</literal></primary></indexterm>
1667 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1668 <option>-XLiberalTypeSynonyms</option>,
1669 <option>-XRank2Types</option>,
1670 <option>-XRankNTypes</option>,
1671 <option>-XPolymorphicComponents</option>,
1672 <option>-XExistentialQuantification</option>
1678 <literal>mdo</literal>
1679 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1682 Stolen by: <option>-XRecursiveDo</option>,
1688 <literal>foreign</literal>
1689 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1692 Stolen by: <option>-XForeignFunctionInterface</option>,
1698 <literal>rec</literal>,
1699 <literal>proc</literal>, <literal>-<</literal>,
1700 <literal>>-</literal>, <literal>-<<</literal>,
1701 <literal>>>-</literal>, and <literal>(|</literal>,
1702 <literal>|)</literal> brackets
1703 <indexterm><primary><literal>proc</literal></primary></indexterm>
1706 Stolen by: <option>-XArrows</option>,
1712 <literal>?<replaceable>varid</replaceable></literal>,
1713 <literal>%<replaceable>varid</replaceable></literal>
1714 <indexterm><primary>implicit parameters</primary></indexterm>
1717 Stolen by: <option>-XImplicitParams</option>,
1723 <literal>[|</literal>,
1724 <literal>[e|</literal>, <literal>[p|</literal>,
1725 <literal>[d|</literal>, <literal>[t|</literal>,
1726 <literal>$(</literal>,
1727 <literal>$<replaceable>varid</replaceable></literal>
1728 <indexterm><primary>Template Haskell</primary></indexterm>
1731 Stolen by: <option>-XTemplateHaskell</option>,
1737 <literal>[:<replaceable>varid</replaceable>|</literal>
1738 <indexterm><primary>quasi-quotation</primary></indexterm>
1741 Stolen by: <option>-XQuasiQuotes</option>,
1747 <replaceable>varid</replaceable>{<literal>#</literal>},
1748 <replaceable>char</replaceable><literal>#</literal>,
1749 <replaceable>string</replaceable><literal>#</literal>,
1750 <replaceable>integer</replaceable><literal>#</literal>,
1751 <replaceable>float</replaceable><literal>#</literal>,
1752 <replaceable>float</replaceable><literal>##</literal>,
1753 <literal>(#</literal>, <literal>#)</literal>,
1756 Stolen by: <option>-XMagicHash</option>,
1765 <!-- TYPE SYSTEM EXTENSIONS -->
1766 <sect1 id="data-type-extensions">
1767 <title>Extensions to data types and type synonyms</title>
1769 <sect2 id="nullary-types">
1770 <title>Data types with no constructors</title>
1772 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1773 a data type with no constructors. For example:</para>
1777 data T a -- T :: * -> *
1780 <para>Syntactically, the declaration lacks the "= constrs" part. The
1781 type can be parameterised over types of any kind, but if the kind is
1782 not <literal>*</literal> then an explicit kind annotation must be used
1783 (see <xref linkend="kinding"/>).</para>
1785 <para>Such data types have only one value, namely bottom.
1786 Nevertheless, they can be useful when defining "phantom types".</para>
1789 <sect2 id="infix-tycons">
1790 <title>Infix type constructors, classes, and type variables</title>
1793 GHC allows type constructors, classes, and type variables to be operators, and
1794 to be written infix, very much like expressions. More specifically:
1797 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1798 The lexical syntax is the same as that for data constructors.
1801 Data type and type-synonym declarations can be written infix, parenthesised
1802 if you want further arguments. E.g.
1804 data a :*: b = Foo a b
1805 type a :+: b = Either a b
1806 class a :=: b where ...
1808 data (a :**: b) x = Baz a b x
1809 type (a :++: b) y = Either (a,b) y
1813 Types, and class constraints, can be written infix. For example
1816 f :: (a :=: b) => a -> b
1820 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1821 The lexical syntax is the same as that for variable operators, excluding "(.)",
1822 "(!)", and "(*)". In a binding position, the operator must be
1823 parenthesised. For example:
1825 type T (+) = Int + Int
1829 liftA2 :: Arrow (~>)
1830 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1836 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1837 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1840 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1841 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1842 sets the fixity for a data constructor and the corresponding type constructor. For example:
1846 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1847 and similarly for <literal>:*:</literal>.
1848 <literal>Int `a` Bool</literal>.
1851 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1858 <sect2 id="type-synonyms">
1859 <title>Liberalised type synonyms</title>
1862 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1863 on individual synonym declarations.
1864 With the <option>-XLiberalTypeSynonyms</option> extension,
1865 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1866 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1869 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1870 in a type synonym, thus:
1872 type Discard a = forall b. Show b => a -> b -> (a, String)
1877 g :: Discard Int -> (Int,String) -- A rank-2 type
1884 If you also use <option>-XUnboxedTuples</option>,
1885 you can write an unboxed tuple in a type synonym:
1887 type Pr = (# Int, Int #)
1895 You can apply a type synonym to a forall type:
1897 type Foo a = a -> a -> Bool
1899 f :: Foo (forall b. b->b)
1901 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1903 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1908 You can apply a type synonym to a partially applied type synonym:
1910 type Generic i o = forall x. i x -> o x
1913 foo :: Generic Id []
1915 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1917 foo :: forall x. x -> [x]
1925 GHC currently does kind checking before expanding synonyms (though even that
1929 After expanding type synonyms, GHC does validity checking on types, looking for
1930 the following mal-formedness which isn't detected simply by kind checking:
1933 Type constructor applied to a type involving for-alls.
1936 Unboxed tuple on left of an arrow.
1939 Partially-applied type synonym.
1943 this will be rejected:
1945 type Pr = (# Int, Int #)
1950 because GHC does not allow unboxed tuples on the left of a function arrow.
1955 <sect2 id="existential-quantification">
1956 <title>Existentially quantified data constructors
1960 The idea of using existential quantification in data type declarations
1961 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1962 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1963 London, 1991). It was later formalised by Laufer and Odersky
1964 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1965 TOPLAS, 16(5), pp1411-1430, 1994).
1966 It's been in Lennart
1967 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1968 proved very useful. Here's the idea. Consider the declaration:
1974 data Foo = forall a. MkFoo a (a -> Bool)
1981 The data type <literal>Foo</literal> has two constructors with types:
1987 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1994 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1995 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1996 For example, the following expression is fine:
2002 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2008 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2009 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2010 isUpper</function> packages a character with a compatible function. These
2011 two things are each of type <literal>Foo</literal> and can be put in a list.
2015 What can we do with a value of type <literal>Foo</literal>?. In particular,
2016 what happens when we pattern-match on <function>MkFoo</function>?
2022 f (MkFoo val fn) = ???
2028 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2029 are compatible, the only (useful) thing we can do with them is to
2030 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2037 f (MkFoo val fn) = fn val
2043 What this allows us to do is to package heterogeneous values
2044 together with a bunch of functions that manipulate them, and then treat
2045 that collection of packages in a uniform manner. You can express
2046 quite a bit of object-oriented-like programming this way.
2049 <sect3 id="existential">
2050 <title>Why existential?
2054 What has this to do with <emphasis>existential</emphasis> quantification?
2055 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2061 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2067 But Haskell programmers can safely think of the ordinary
2068 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2069 adding a new existential quantification construct.
2074 <sect3 id="existential-with-context">
2075 <title>Existentials and type classes</title>
2078 An easy extension is to allow
2079 arbitrary contexts before the constructor. For example:
2085 data Baz = forall a. Eq a => Baz1 a a
2086 | forall b. Show b => Baz2 b (b -> b)
2092 The two constructors have the types you'd expect:
2098 Baz1 :: forall a. Eq a => a -> a -> Baz
2099 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2105 But when pattern matching on <function>Baz1</function> the matched values can be compared
2106 for equality, and when pattern matching on <function>Baz2</function> the first matched
2107 value can be converted to a string (as well as applying the function to it).
2108 So this program is legal:
2115 f (Baz1 p q) | p == q = "Yes"
2117 f (Baz2 v fn) = show (fn v)
2123 Operationally, in a dictionary-passing implementation, the
2124 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2125 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2126 extract it on pattern matching.
2131 <sect3 id="existential-records">
2132 <title>Record Constructors</title>
2135 GHC allows existentials to be used with records syntax as well. For example:
2138 data Counter a = forall self. NewCounter
2140 , _inc :: self -> self
2141 , _display :: self -> IO ()
2145 Here <literal>tag</literal> is a public field, with a well-typed selector
2146 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2147 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2148 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2149 compile-time error. In other words, <emphasis>GHC defines a record selector function
2150 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2151 (This example used an underscore in the fields for which record selectors
2152 will not be defined, but that is only programming style; GHC ignores them.)
2156 To make use of these hidden fields, we need to create some helper functions:
2159 inc :: Counter a -> Counter a
2160 inc (NewCounter x i d t) = NewCounter
2161 { _this = i x, _inc = i, _display = d, tag = t }
2163 display :: Counter a -> IO ()
2164 display NewCounter{ _this = x, _display = d } = d x
2167 Now we can define counters with different underlying implementations:
2170 counterA :: Counter String
2171 counterA = NewCounter
2172 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2174 counterB :: Counter String
2175 counterB = NewCounter
2176 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2179 display (inc counterA) -- prints "1"
2180 display (inc (inc counterB)) -- prints "##"
2183 Record update syntax is supported for existentials (and GADTs):
2185 setTag :: Counter a -> a -> Counter a
2186 setTag obj t = obj{ tag = t }
2188 The rule for record update is this: <emphasis>
2189 the types of the updated fields may
2190 mention only the universally-quantified type variables
2191 of the data constructor. For GADTs, the field may mention only types
2192 that appear as a simple type-variable argument in the constructor's result
2193 type</emphasis>. For example:
2195 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2196 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2197 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2198 -- existentially quantified)
2200 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2201 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2202 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2203 -- type-variable argument in G1's result type)
2211 <title>Restrictions</title>
2214 There are several restrictions on the ways in which existentially-quantified
2215 constructors can be use.
2224 When pattern matching, each pattern match introduces a new,
2225 distinct, type for each existential type variable. These types cannot
2226 be unified with any other type, nor can they escape from the scope of
2227 the pattern match. For example, these fragments are incorrect:
2235 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2236 is the result of <function>f1</function>. One way to see why this is wrong is to
2237 ask what type <function>f1</function> has:
2241 f1 :: Foo -> a -- Weird!
2245 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2250 f1 :: forall a. Foo -> a -- Wrong!
2254 The original program is just plain wrong. Here's another sort of error
2258 f2 (Baz1 a b) (Baz1 p q) = a==q
2262 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2263 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2264 from the two <function>Baz1</function> constructors.
2272 You can't pattern-match on an existentially quantified
2273 constructor in a <literal>let</literal> or <literal>where</literal> group of
2274 bindings. So this is illegal:
2278 f3 x = a==b where { Baz1 a b = x }
2281 Instead, use a <literal>case</literal> expression:
2284 f3 x = case x of Baz1 a b -> a==b
2287 In general, you can only pattern-match
2288 on an existentially-quantified constructor in a <literal>case</literal> expression or
2289 in the patterns of a function definition.
2291 The reason for this restriction is really an implementation one.
2292 Type-checking binding groups is already a nightmare without
2293 existentials complicating the picture. Also an existential pattern
2294 binding at the top level of a module doesn't make sense, because it's
2295 not clear how to prevent the existentially-quantified type "escaping".
2296 So for now, there's a simple-to-state restriction. We'll see how
2304 You can't use existential quantification for <literal>newtype</literal>
2305 declarations. So this is illegal:
2309 newtype T = forall a. Ord a => MkT a
2313 Reason: a value of type <literal>T</literal> must be represented as a
2314 pair of a dictionary for <literal>Ord t</literal> and a value of type
2315 <literal>t</literal>. That contradicts the idea that
2316 <literal>newtype</literal> should have no concrete representation.
2317 You can get just the same efficiency and effect by using
2318 <literal>data</literal> instead of <literal>newtype</literal>. If
2319 there is no overloading involved, then there is more of a case for
2320 allowing an existentially-quantified <literal>newtype</literal>,
2321 because the <literal>data</literal> version does carry an
2322 implementation cost, but single-field existentially quantified
2323 constructors aren't much use. So the simple restriction (no
2324 existential stuff on <literal>newtype</literal>) stands, unless there
2325 are convincing reasons to change it.
2333 You can't use <literal>deriving</literal> to define instances of a
2334 data type with existentially quantified data constructors.
2336 Reason: in most cases it would not make sense. For example:;
2339 data T = forall a. MkT [a] deriving( Eq )
2342 To derive <literal>Eq</literal> in the standard way we would need to have equality
2343 between the single component of two <function>MkT</function> constructors:
2347 (MkT a) == (MkT b) = ???
2350 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2351 It's just about possible to imagine examples in which the derived instance
2352 would make sense, but it seems altogether simpler simply to prohibit such
2353 declarations. Define your own instances!
2364 <!-- ====================== Generalised algebraic data types ======================= -->
2366 <sect2 id="gadt-style">
2367 <title>Declaring data types with explicit constructor signatures</title>
2369 <para>GHC allows you to declare an algebraic data type by
2370 giving the type signatures of constructors explicitly. For example:
2374 Just :: a -> Maybe a
2376 The form is called a "GADT-style declaration"
2377 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2378 can only be declared using this form.</para>
2379 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2380 For example, these two declarations are equivalent:
2382 data Foo = forall a. MkFoo a (a -> Bool)
2383 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2386 <para>Any data type that can be declared in standard Haskell-98 syntax
2387 can also be declared using GADT-style syntax.
2388 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2389 they treat class constraints on the data constructors differently.
2390 Specifically, if the constructor is given a type-class context, that
2391 context is made available by pattern matching. For example:
2394 MkSet :: Eq a => [a] -> Set a
2396 makeSet :: Eq a => [a] -> Set a
2397 makeSet xs = MkSet (nub xs)
2399 insert :: a -> Set a -> Set a
2400 insert a (MkSet as) | a `elem` as = MkSet as
2401 | otherwise = MkSet (a:as)
2403 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2404 gives rise to a <literal>(Eq a)</literal>
2405 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2406 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2407 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2408 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2409 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2410 In the example, the equality dictionary is used to satisfy the equality constraint
2411 generated by the call to <literal>elem</literal>, so that the type of
2412 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2415 For example, one possible application is to reify dictionaries:
2417 data NumInst a where
2418 MkNumInst :: Num a => NumInst a
2420 intInst :: NumInst Int
2423 plus :: NumInst a -> a -> a -> a
2424 plus MkNumInst p q = p + q
2426 Here, a value of type <literal>NumInst a</literal> is equivalent
2427 to an explicit <literal>(Num a)</literal> dictionary.
2430 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2431 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2435 = Num a => MkNumInst (NumInst a)
2437 Notice that, unlike the situation when declaring an existential, there is
2438 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2439 data type's universally quantified type variable <literal>a</literal>.
2440 A constructor may have both universal and existential type variables: for example,
2441 the following two declarations are equivalent:
2444 = forall b. (Num a, Eq b) => MkT1 a b
2446 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2449 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2450 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2451 In Haskell 98 the definition
2453 data Eq a => Set' a = MkSet' [a]
2455 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2456 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2457 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2458 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2459 GHC's behaviour is much more useful, as well as much more intuitive.
2463 The rest of this section gives further details about GADT-style data
2468 The result type of each data constructor must begin with the type constructor being defined.
2469 If the result type of all constructors
2470 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2471 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2472 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2476 As with other type signatures, you can give a single signature for several data constructors.
2477 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2486 The type signature of
2487 each constructor is independent, and is implicitly universally quantified as usual.
2488 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2489 have no scope, and different constructors may have different universally-quantified type variables:
2491 data T a where -- The 'a' has no scope
2492 T1,T2 :: b -> T b -- Means forall b. b -> T b
2493 T3 :: T a -- Means forall a. T a
2498 A constructor signature may mention type class constraints, which can differ for
2499 different constructors. For example, this is fine:
2502 T1 :: Eq b => b -> b -> T b
2503 T2 :: (Show c, Ix c) => c -> [c] -> T c
2505 When patten matching, these constraints are made available to discharge constraints
2506 in the body of the match. For example:
2509 f (T1 x y) | x==y = "yes"
2513 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2514 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2515 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2519 Unlike a Haskell-98-style
2520 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2521 have no scope. Indeed, one can write a kind signature instead:
2523 data Set :: * -> * where ...
2525 or even a mixture of the two:
2527 data Bar a :: (* -> *) -> * where ...
2529 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2532 data Bar a (b :: * -> *) where ...
2538 You can use strictness annotations, in the obvious places
2539 in the constructor type:
2542 Lit :: !Int -> Term Int
2543 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2544 Pair :: Term a -> Term b -> Term (a,b)
2549 You can use a <literal>deriving</literal> clause on a GADT-style data type
2550 declaration. For example, these two declarations are equivalent
2552 data Maybe1 a where {
2553 Nothing1 :: Maybe1 a ;
2554 Just1 :: a -> Maybe1 a
2555 } deriving( Eq, Ord )
2557 data Maybe2 a = Nothing2 | Just2 a
2563 The type signature may have quantified type variables that do not appear
2567 MkFoo :: a -> (a->Bool) -> Foo
2570 Here the type variable <literal>a</literal> does not appear in the result type
2571 of either constructor.
2572 Although it is universally quantified in the type of the constructor, such
2573 a type variable is often called "existential".
2574 Indeed, the above declaration declares precisely the same type as
2575 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2577 The type may contain a class context too, of course:
2580 MkShowable :: Show a => a -> Showable
2585 You can use record syntax on a GADT-style data type declaration:
2589 Adult :: { name :: String, children :: [Person] } -> Person
2590 Child :: Show a => { name :: !String, funny :: a } -> Person
2592 As usual, for every constructor that has a field <literal>f</literal>, the type of
2593 field <literal>f</literal> must be the same (modulo alpha conversion).
2594 The <literal>Child</literal> constructor above shows that the signature
2595 may have a context, existentially-quantified variables, and strictness annotations,
2596 just as in the non-record case. (NB: the "type" that follows the double-colon
2597 is not really a type, because of the record syntax and strictness annotations.
2598 A "type" of this form can appear only in a constructor signature.)
2602 Record updates are allowed with GADT-style declarations,
2603 only fields that have the following property: the type of the field
2604 mentions no existential type variables.
2608 As in the case of existentials declared using the Haskell-98-like record syntax
2609 (<xref linkend="existential-records"/>),
2610 record-selector functions are generated only for those fields that have well-typed
2612 Here is the example of that section, in GADT-style syntax:
2614 data Counter a where
2615 NewCounter { _this :: self
2616 , _inc :: self -> self
2617 , _display :: self -> IO ()
2622 As before, only one selector function is generated here, that for <literal>tag</literal>.
2623 Nevertheless, you can still use all the field names in pattern matching and record construction.
2625 </itemizedlist></para>
2629 <title>Generalised Algebraic Data Types (GADTs)</title>
2631 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2632 by allowing constructors to have richer return types. Here is an example:
2635 Lit :: Int -> Term Int
2636 Succ :: Term Int -> Term Int
2637 IsZero :: Term Int -> Term Bool
2638 If :: Term Bool -> Term a -> Term a -> Term a
2639 Pair :: Term a -> Term b -> Term (a,b)
2641 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2642 case with ordinary data types. This generality allows us to
2643 write a well-typed <literal>eval</literal> function
2644 for these <literal>Terms</literal>:
2648 eval (Succ t) = 1 + eval t
2649 eval (IsZero t) = eval t == 0
2650 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2651 eval (Pair e1 e2) = (eval e1, eval e2)
2653 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2654 For example, in the right hand side of the equation
2659 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2660 A precise specification of the type rules is beyond what this user manual aspires to,
2661 but the design closely follows that described in
2663 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2664 unification-based type inference for GADTs</ulink>,
2666 The general principle is this: <emphasis>type refinement is only carried out
2667 based on user-supplied type annotations</emphasis>.
2668 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2669 and lots of obscure error messages will
2670 occur. However, the refinement is quite general. For example, if we had:
2672 eval :: Term a -> a -> a
2673 eval (Lit i) j = i+j
2675 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2676 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2677 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2680 These and many other examples are given in papers by Hongwei Xi, and
2681 Tim Sheard. There is a longer introduction
2682 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2684 <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
2685 may use different notation to that implemented in GHC.
2688 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2689 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2692 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2693 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2694 The result type of each constructor must begin with the type constructor being defined,
2695 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2696 For example, in the <literal>Term</literal> data
2697 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2698 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2703 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2704 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2705 whose result type is not just <literal>T a b</literal>.
2709 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2710 an ordinary data type.
2714 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2718 Lit { val :: Int } :: Term Int
2719 Succ { num :: Term Int } :: Term Int
2720 Pred { num :: Term Int } :: Term Int
2721 IsZero { arg :: Term Int } :: Term Bool
2722 Pair { arg1 :: Term a
2725 If { cnd :: Term Bool
2730 However, for GADTs there is the following additional constraint:
2731 every constructor that has a field <literal>f</literal> must have
2732 the same result type (modulo alpha conversion)
2733 Hence, in the above example, we cannot merge the <literal>num</literal>
2734 and <literal>arg</literal> fields above into a
2735 single name. Although their field types are both <literal>Term Int</literal>,
2736 their selector functions actually have different types:
2739 num :: Term Int -> Term Int
2740 arg :: Term Bool -> Term Int
2745 When pattern-matching against data constructors drawn from a GADT,
2746 for example in a <literal>case</literal> expression, the following rules apply:
2748 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2749 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2750 <listitem><para>The type of any free variable mentioned in any of
2751 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2753 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2754 way to ensure that a variable a rigid type is to give it a type signature.
2755 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2756 Simple unification-based type inference for GADTs
2757 </ulink>. The criteria implemented by GHC are given in the Appendix.
2767 <!-- ====================== End of Generalised algebraic data types ======================= -->
2769 <sect1 id="deriving">
2770 <title>Extensions to the "deriving" mechanism</title>
2772 <sect2 id="deriving-inferred">
2773 <title>Inferred context for deriving clauses</title>
2776 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2779 data T0 f a = MkT0 a deriving( Eq )
2780 data T1 f a = MkT1 (f a) deriving( Eq )
2781 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2783 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2785 instance Eq a => Eq (T0 f a) where ...
2786 instance Eq (f a) => Eq (T1 f a) where ...
2787 instance Eq (f (f a)) => Eq (T2 f a) where ...
2789 The first of these is obviously fine. The second is still fine, although less obviously.
2790 The third is not Haskell 98, and risks losing termination of instances.
2793 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2794 each constraint in the inferred instance context must consist only of type variables,
2795 with no repetitions.
2798 This rule is applied regardless of flags. If you want a more exotic context, you can write
2799 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2803 <sect2 id="stand-alone-deriving">
2804 <title>Stand-alone deriving declarations</title>
2807 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2809 data Foo a = Bar a | Baz String
2811 deriving instance Eq a => Eq (Foo a)
2813 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2814 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2815 Note the following points:
2818 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2819 exactly as you would in an ordinary instance declaration.
2820 (In contrast, in a <literal>deriving</literal> clause
2821 attached to a data type declaration, the context is inferred.)
2825 A <literal>deriving instance</literal> declaration
2826 must obey the same rules concerning form and termination as ordinary instance declarations,
2827 controlled by the same flags; see <xref linkend="instance-decls"/>.
2831 Unlike a <literal>deriving</literal>
2832 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2833 than the data type (assuming you also use
2834 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2837 data Foo a = Bar a | Baz String
2839 deriving instance Eq a => Eq (Foo [a])
2840 deriving instance Eq a => Eq (Foo (Maybe a))
2842 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2843 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2847 Unlike a <literal>deriving</literal>
2848 declaration attached to a <literal>data</literal> declaration,
2849 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2850 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2851 your problem. (GHC will show you the offending code if it has a type error.)
2852 The merit of this is that you can derive instances for GADTs and other exotic
2853 data types, providing only that the boilerplate code does indeed typecheck. For example:
2859 deriving instance Show (T a)
2861 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2862 data type declaration for <literal>T</literal>,
2863 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2864 the instance declaration using stand-alone deriving.
2869 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2870 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2873 newtype Foo a = MkFoo (State Int a)
2875 deriving instance MonadState Int Foo
2877 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2878 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2880 </itemizedlist></para>
2885 <sect2 id="deriving-typeable">
2886 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2889 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2890 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2891 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2892 classes <literal>Eq</literal>, <literal>Ord</literal>,
2893 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2896 GHC extends this list with several more classes that may be automatically derived:
2898 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2899 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2900 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2902 <para>An instance of <literal>Typeable</literal> can only be derived if the
2903 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2904 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2906 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2907 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2909 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2910 are used, and only <literal>Typeable1</literal> up to
2911 <literal>Typeable7</literal> are provided in the library.)
2912 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2913 class, whose kind suits that of the data type constructor, and
2914 then writing the data type instance by hand.
2918 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2919 the class <literal>Functor</literal>,
2920 defined in <literal>GHC.Base</literal>.
2923 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2924 the class <literal>Foldable</literal>,
2925 defined in <literal>Data.Foldable</literal>.
2928 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2929 the class <literal>Traversable</literal>,
2930 defined in <literal>Data.Traversable</literal>.
2933 In each case the appropriate class must be in scope before it
2934 can be mentioned in the <literal>deriving</literal> clause.
2938 <sect2 id="newtype-deriving">
2939 <title>Generalised derived instances for newtypes</title>
2942 When you define an abstract type using <literal>newtype</literal>, you may want
2943 the new type to inherit some instances from its representation. In
2944 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2945 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2946 other classes you have to write an explicit instance declaration. For
2947 example, if you define
2950 newtype Dollars = Dollars Int
2953 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2954 explicitly define an instance of <literal>Num</literal>:
2957 instance Num Dollars where
2958 Dollars a + Dollars b = Dollars (a+b)
2961 All the instance does is apply and remove the <literal>newtype</literal>
2962 constructor. It is particularly galling that, since the constructor
2963 doesn't appear at run-time, this instance declaration defines a
2964 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2965 dictionary, only slower!
2969 <sect3> <title> Generalising the deriving clause </title>
2971 GHC now permits such instances to be derived instead,
2972 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2975 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2978 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2979 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2980 derives an instance declaration of the form
2983 instance Num Int => Num Dollars
2986 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2990 We can also derive instances of constructor classes in a similar
2991 way. For example, suppose we have implemented state and failure monad
2992 transformers, such that
2995 instance Monad m => Monad (State s m)
2996 instance Monad m => Monad (Failure m)
2998 In Haskell 98, we can define a parsing monad by
3000 type Parser tok m a = State [tok] (Failure m) a
3003 which is automatically a monad thanks to the instance declarations
3004 above. With the extension, we can make the parser type abstract,
3005 without needing to write an instance of class <literal>Monad</literal>, via
3008 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3011 In this case the derived instance declaration is of the form
3013 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3016 Notice that, since <literal>Monad</literal> is a constructor class, the
3017 instance is a <emphasis>partial application</emphasis> of the new type, not the
3018 entire left hand side. We can imagine that the type declaration is
3019 "eta-converted" to generate the context of the instance
3024 We can even derive instances of multi-parameter classes, provided the
3025 newtype is the last class parameter. In this case, a ``partial
3026 application'' of the class appears in the <literal>deriving</literal>
3027 clause. For example, given the class
3030 class StateMonad s m | m -> s where ...
3031 instance Monad m => StateMonad s (State s m) where ...
3033 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3035 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3036 deriving (Monad, StateMonad [tok])
3039 The derived instance is obtained by completing the application of the
3040 class to the new type:
3043 instance StateMonad [tok] (State [tok] (Failure m)) =>
3044 StateMonad [tok] (Parser tok m)
3049 As a result of this extension, all derived instances in newtype
3050 declarations are treated uniformly (and implemented just by reusing
3051 the dictionary for the representation type), <emphasis>except</emphasis>
3052 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3053 the newtype and its representation.
3057 <sect3> <title> A more precise specification </title>
3059 Derived instance declarations are constructed as follows. Consider the
3060 declaration (after expansion of any type synonyms)
3063 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3069 The <literal>ci</literal> are partial applications of
3070 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3071 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3074 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3077 The type <literal>t</literal> is an arbitrary type.
3080 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3081 nor in the <literal>ci</literal>, and
3084 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3085 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3086 should not "look through" the type or its constructor. You can still
3087 derive these classes for a newtype, but it happens in the usual way, not
3088 via this new mechanism.
3091 Then, for each <literal>ci</literal>, the derived instance
3094 instance ci t => ci (T v1...vk)
3096 As an example which does <emphasis>not</emphasis> work, consider
3098 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3100 Here we cannot derive the instance
3102 instance Monad (State s m) => Monad (NonMonad m)
3105 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3106 and so cannot be "eta-converted" away. It is a good thing that this
3107 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3108 not, in fact, a monad --- for the same reason. Try defining
3109 <literal>>>=</literal> with the correct type: you won't be able to.
3113 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3114 important, since we can only derive instances for the last one. If the
3115 <literal>StateMonad</literal> class above were instead defined as
3118 class StateMonad m s | m -> s where ...
3121 then we would not have been able to derive an instance for the
3122 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3123 classes usually have one "main" parameter for which deriving new
3124 instances is most interesting.
3126 <para>Lastly, all of this applies only for classes other than
3127 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3128 and <literal>Data</literal>, for which the built-in derivation applies (section
3129 4.3.3. of the Haskell Report).
3130 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3131 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3132 the standard method is used or the one described here.)
3139 <!-- TYPE SYSTEM EXTENSIONS -->
3140 <sect1 id="type-class-extensions">
3141 <title>Class and instances declarations</title>
3143 <sect2 id="multi-param-type-classes">
3144 <title>Class declarations</title>
3147 This section, and the next one, documents GHC's type-class extensions.
3148 There's lots of background in the paper <ulink
3149 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3150 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3151 Jones, Erik Meijer).
3154 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3158 <title>Multi-parameter type classes</title>
3160 Multi-parameter type classes are permitted. For example:
3164 class Collection c a where
3165 union :: c a -> c a -> c a
3173 <title>The superclasses of a class declaration</title>
3176 There are no restrictions on the context in a class declaration
3177 (which introduces superclasses), except that the class hierarchy must
3178 be acyclic. So these class declarations are OK:
3182 class Functor (m k) => FiniteMap m k where
3185 class (Monad m, Monad (t m)) => Transform t m where
3186 lift :: m a -> (t m) a
3192 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3193 of "acyclic" involves only the superclass relationships. For example,
3199 op :: D b => a -> b -> b
3202 class C a => D a where { ... }
3206 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3207 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3208 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3215 <sect3 id="class-method-types">
3216 <title>Class method types</title>
3219 Haskell 98 prohibits class method types to mention constraints on the
3220 class type variable, thus:
3223 fromList :: [a] -> s a
3224 elem :: Eq a => a -> s a -> Bool
3226 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3227 contains the constraint <literal>Eq a</literal>, constrains only the
3228 class type variable (in this case <literal>a</literal>).
3229 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3236 <sect2 id="functional-dependencies">
3237 <title>Functional dependencies
3240 <para> Functional dependencies are implemented as described by Mark Jones
3241 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3242 In Proceedings of the 9th European Symposium on Programming,
3243 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3247 Functional dependencies are introduced by a vertical bar in the syntax of a
3248 class declaration; e.g.
3250 class (Monad m) => MonadState s m | m -> s where ...
3252 class Foo a b c | a b -> c where ...
3254 There should be more documentation, but there isn't (yet). Yell if you need it.
3257 <sect3><title>Rules for functional dependencies </title>
3259 In a class declaration, all of the class type variables must be reachable (in the sense
3260 mentioned in <xref linkend="type-restrictions"/>)
3261 from the free variables of each method type.
3265 class Coll s a where
3267 insert :: s -> a -> s
3270 is not OK, because the type of <literal>empty</literal> doesn't mention
3271 <literal>a</literal>. Functional dependencies can make the type variable
3274 class Coll s a | s -> a where
3276 insert :: s -> a -> s
3279 Alternatively <literal>Coll</literal> might be rewritten
3282 class Coll s a where
3284 insert :: s a -> a -> s a
3288 which makes the connection between the type of a collection of
3289 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3290 Occasionally this really doesn't work, in which case you can split the
3298 class CollE s => Coll s a where
3299 insert :: s -> a -> s
3306 <title>Background on functional dependencies</title>
3308 <para>The following description of the motivation and use of functional dependencies is taken
3309 from the Hugs user manual, reproduced here (with minor changes) by kind
3310 permission of Mark Jones.
3313 Consider the following class, intended as part of a
3314 library for collection types:
3316 class Collects e ce where
3318 insert :: e -> ce -> ce
3319 member :: e -> ce -> Bool
3321 The type variable e used here represents the element type, while ce is the type
3322 of the container itself. Within this framework, we might want to define
3323 instances of this class for lists or characteristic functions (both of which
3324 can be used to represent collections of any equality type), bit sets (which can
3325 be used to represent collections of characters), or hash tables (which can be
3326 used to represent any collection whose elements have a hash function). Omitting
3327 standard implementation details, this would lead to the following declarations:
3329 instance Eq e => Collects e [e] where ...
3330 instance Eq e => Collects e (e -> Bool) where ...
3331 instance Collects Char BitSet where ...
3332 instance (Hashable e, Collects a ce)
3333 => Collects e (Array Int ce) where ...
3335 All this looks quite promising; we have a class and a range of interesting
3336 implementations. Unfortunately, there are some serious problems with the class
3337 declaration. First, the empty function has an ambiguous type:
3339 empty :: Collects e ce => ce
3341 By "ambiguous" we mean that there is a type variable e that appears on the left
3342 of the <literal>=></literal> symbol, but not on the right. The problem with
3343 this is that, according to the theoretical foundations of Haskell overloading,
3344 we cannot guarantee a well-defined semantics for any term with an ambiguous
3348 We can sidestep this specific problem by removing the empty member from the
3349 class declaration. However, although the remaining members, insert and member,
3350 do not have ambiguous types, we still run into problems when we try to use
3351 them. For example, consider the following two functions:
3353 f x y = insert x . insert y
3356 for which GHC infers the following types:
3358 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3359 g :: (Collects Bool c, Collects Char c) => c -> c
3361 Notice that the type for f allows the two parameters x and y to be assigned
3362 different types, even though it attempts to insert each of the two values, one
3363 after the other, into the same collection. If we're trying to model collections
3364 that contain only one type of value, then this is clearly an inaccurate
3365 type. Worse still, the definition for g is accepted, without causing a type
3366 error. As a result, the error in this code will not be flagged at the point
3367 where it appears. Instead, it will show up only when we try to use g, which
3368 might even be in a different module.
3371 <sect4><title>An attempt to use constructor classes</title>
3374 Faced with the problems described above, some Haskell programmers might be
3375 tempted to use something like the following version of the class declaration:
3377 class Collects e c where
3379 insert :: e -> c e -> c e
3380 member :: e -> c e -> Bool
3382 The key difference here is that we abstract over the type constructor c that is
3383 used to form the collection type c e, and not over that collection type itself,
3384 represented by ce in the original class declaration. This avoids the immediate
3385 problems that we mentioned above: empty has type <literal>Collects e c => c
3386 e</literal>, which is not ambiguous.
3389 The function f from the previous section has a more accurate type:
3391 f :: (Collects e c) => e -> e -> c e -> c e
3393 The function g from the previous section is now rejected with a type error as
3394 we would hope because the type of f does not allow the two arguments to have
3396 This, then, is an example of a multiple parameter class that does actually work
3397 quite well in practice, without ambiguity problems.
3398 There is, however, a catch. This version of the Collects class is nowhere near
3399 as general as the original class seemed to be: only one of the four instances
3400 for <literal>Collects</literal>
3401 given above can be used with this version of Collects because only one of
3402 them---the instance for lists---has a collection type that can be written in
3403 the form c e, for some type constructor c, and element type e.
3407 <sect4><title>Adding functional dependencies</title>
3410 To get a more useful version of the Collects class, Hugs provides a mechanism
3411 that allows programmers to specify dependencies between the parameters of a
3412 multiple parameter class (For readers with an interest in theoretical
3413 foundations and previous work: The use of dependency information can be seen
3414 both as a generalization of the proposal for `parametric type classes' that was
3415 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3416 later framework for "improvement" of qualified types. The
3417 underlying ideas are also discussed in a more theoretical and abstract setting
3418 in a manuscript [implparam], where they are identified as one point in a
3419 general design space for systems of implicit parameterization.).
3421 To start with an abstract example, consider a declaration such as:
3423 class C a b where ...
3425 which tells us simply that C can be thought of as a binary relation on types
3426 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3427 included in the definition of classes to add information about dependencies
3428 between parameters, as in the following examples:
3430 class D a b | a -> b where ...
3431 class E a b | a -> b, b -> a where ...
3433 The notation <literal>a -> b</literal> used here between the | and where
3434 symbols --- not to be
3435 confused with a function type --- indicates that the a parameter uniquely
3436 determines the b parameter, and might be read as "a determines b." Thus D is
3437 not just a relation, but actually a (partial) function. Similarly, from the two
3438 dependencies that are included in the definition of E, we can see that E
3439 represents a (partial) one-one mapping between types.
3442 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3443 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3444 m>=0, meaning that the y parameters are uniquely determined by the x
3445 parameters. Spaces can be used as separators if more than one variable appears
3446 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3447 annotated with multiple dependencies using commas as separators, as in the
3448 definition of E above. Some dependencies that we can write in this notation are
3449 redundant, and will be rejected because they don't serve any useful
3450 purpose, and may instead indicate an error in the program. Examples of
3451 dependencies like this include <literal>a -> a </literal>,
3452 <literal>a -> a a </literal>,
3453 <literal>a -> </literal>, etc. There can also be
3454 some redundancy if multiple dependencies are given, as in
3455 <literal>a->b</literal>,
3456 <literal>b->c </literal>, <literal>a->c </literal>, and
3457 in which some subset implies the remaining dependencies. Examples like this are
3458 not treated as errors. Note that dependencies appear only in class
3459 declarations, and not in any other part of the language. In particular, the
3460 syntax for instance declarations, class constraints, and types is completely
3464 By including dependencies in a class declaration, we provide a mechanism for
3465 the programmer to specify each multiple parameter class more precisely. The
3466 compiler, on the other hand, is responsible for ensuring that the set of
3467 instances that are in scope at any given point in the program is consistent
3468 with any declared dependencies. For example, the following pair of instance
3469 declarations cannot appear together in the same scope because they violate the
3470 dependency for D, even though either one on its own would be acceptable:
3472 instance D Bool Int where ...
3473 instance D Bool Char where ...
3475 Note also that the following declaration is not allowed, even by itself:
3477 instance D [a] b where ...
3479 The problem here is that this instance would allow one particular choice of [a]
3480 to be associated with more than one choice for b, which contradicts the
3481 dependency specified in the definition of D. More generally, this means that,
3482 in any instance of the form:
3484 instance D t s where ...
3486 for some particular types t and s, the only variables that can appear in s are
3487 the ones that appear in t, and hence, if the type t is known, then s will be
3488 uniquely determined.
3491 The benefit of including dependency information is that it allows us to define
3492 more general multiple parameter classes, without ambiguity problems, and with
3493 the benefit of more accurate types. To illustrate this, we return to the
3494 collection class example, and annotate the original definition of <literal>Collects</literal>
3495 with a simple dependency:
3497 class Collects e ce | ce -> e where
3499 insert :: e -> ce -> ce
3500 member :: e -> ce -> Bool
3502 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3503 determined by the type of the collection ce. Note that both parameters of
3504 Collects are of kind *; there are no constructor classes here. Note too that
3505 all of the instances of Collects that we gave earlier can be used
3506 together with this new definition.
3509 What about the ambiguity problems that we encountered with the original
3510 definition? The empty function still has type Collects e ce => ce, but it is no
3511 longer necessary to regard that as an ambiguous type: Although the variable e
3512 does not appear on the right of the => symbol, the dependency for class
3513 Collects tells us that it is uniquely determined by ce, which does appear on
3514 the right of the => symbol. Hence the context in which empty is used can still
3515 give enough information to determine types for both ce and e, without
3516 ambiguity. More generally, we need only regard a type as ambiguous if it
3517 contains a variable on the left of the => that is not uniquely determined
3518 (either directly or indirectly) by the variables on the right.
3521 Dependencies also help to produce more accurate types for user defined
3522 functions, and hence to provide earlier detection of errors, and less cluttered
3523 types for programmers to work with. Recall the previous definition for a
3526 f x y = insert x y = insert x . insert y
3528 for which we originally obtained a type:
3530 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3532 Given the dependency information that we have for Collects, however, we can
3533 deduce that a and b must be equal because they both appear as the second
3534 parameter in a Collects constraint with the same first parameter c. Hence we
3535 can infer a shorter and more accurate type for f:
3537 f :: (Collects a c) => a -> a -> c -> c
3539 In a similar way, the earlier definition of g will now be flagged as a type error.
3542 Although we have given only a few examples here, it should be clear that the
3543 addition of dependency information can help to make multiple parameter classes
3544 more useful in practice, avoiding ambiguity problems, and allowing more general
3545 sets of instance declarations.
3551 <sect2 id="instance-decls">
3552 <title>Instance declarations</title>
3554 <para>An instance declaration has the form
3556 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 ...
3558 The part before the "<literal>=></literal>" is the
3559 <emphasis>context</emphasis>, while the part after the
3560 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3563 <sect3 id="flexible-instance-head">
3564 <title>Relaxed rules for the instance head</title>
3567 In Haskell 98 the head of an instance declaration
3568 must be of the form <literal>C (T a1 ... an)</literal>, where
3569 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3570 and the <literal>a1 ... an</literal> are distinct type variables.
3571 GHC relaxes these rules in two ways.
3575 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3576 declaration to mention arbitrary nested types.
3577 For example, this becomes a legal instance declaration
3579 instance C (Maybe Int) where ...
3581 See also the <link linkend="instance-overlap">rules on overlap</link>.
3584 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3585 synonyms. As always, using a type synonym is just shorthand for
3586 writing the RHS of the type synonym definition. For example:
3590 type Point = (Int,Int)
3591 instance C Point where ...
3592 instance C [Point] where ...
3596 is legal. However, if you added
3600 instance C (Int,Int) where ...
3604 as well, then the compiler will complain about the overlapping
3605 (actually, identical) instance declarations. As always, type synonyms
3606 must be fully applied. You cannot, for example, write:
3610 instance Monad P where ...
3618 <sect3 id="instance-rules">
3619 <title>Relaxed rules for instance contexts</title>
3621 <para>In Haskell 98, the assertions in the context of the instance declaration
3622 must be of the form <literal>C a</literal> where <literal>a</literal>
3623 is a type variable that occurs in the head.
3627 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3628 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3629 With this flag the context of the instance declaration can each consist of arbitrary
3630 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3634 The Paterson Conditions: for each assertion in the context
3636 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3637 <listitem><para>The assertion has fewer constructors and variables (taken together
3638 and counting repetitions) than the head</para></listitem>
3642 <listitem><para>The Coverage Condition. For each functional dependency,
3643 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3644 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3645 every type variable in
3646 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3647 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3648 substitution mapping each type variable in the class declaration to the
3649 corresponding type in the instance declaration.
3652 These restrictions ensure that context reduction terminates: each reduction
3653 step makes the problem smaller by at least one
3654 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3655 if you give the <option>-XUndecidableInstances</option>
3656 flag (<xref linkend="undecidable-instances"/>).
3657 You can find lots of background material about the reason for these
3658 restrictions in the paper <ulink
3659 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3660 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3663 For example, these are OK:
3665 instance C Int [a] -- Multiple parameters
3666 instance Eq (S [a]) -- Structured type in head
3668 -- Repeated type variable in head
3669 instance C4 a a => C4 [a] [a]
3670 instance Stateful (ST s) (MutVar s)
3672 -- Head can consist of type variables only
3674 instance (Eq a, Show b) => C2 a b
3676 -- Non-type variables in context
3677 instance Show (s a) => Show (Sized s a)
3678 instance C2 Int a => C3 Bool [a]
3679 instance C2 Int a => C3 [a] b
3683 -- Context assertion no smaller than head
3684 instance C a => C a where ...
3685 -- (C b b) has more more occurrences of b than the head
3686 instance C b b => Foo [b] where ...
3691 The same restrictions apply to instances generated by
3692 <literal>deriving</literal> clauses. Thus the following is accepted:
3694 data MinHeap h a = H a (h a)
3697 because the derived instance
3699 instance (Show a, Show (h a)) => Show (MinHeap h a)
3701 conforms to the above rules.
3705 A useful idiom permitted by the above rules is as follows.
3706 If one allows overlapping instance declarations then it's quite
3707 convenient to have a "default instance" declaration that applies if
3708 something more specific does not:
3716 <sect3 id="undecidable-instances">
3717 <title>Undecidable instances</title>
3720 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3721 For example, sometimes you might want to use the following to get the
3722 effect of a "class synonym":
3724 class (C1 a, C2 a, C3 a) => C a where { }
3726 instance (C1 a, C2 a, C3 a) => C a where { }
3728 This allows you to write shorter signatures:
3734 f :: (C1 a, C2 a, C3 a) => ...
3736 The restrictions on functional dependencies (<xref
3737 linkend="functional-dependencies"/>) are particularly troublesome.
3738 It is tempting to introduce type variables in the context that do not appear in
3739 the head, something that is excluded by the normal rules. For example:
3741 class HasConverter a b | a -> b where
3744 data Foo a = MkFoo a
3746 instance (HasConverter a b,Show b) => Show (Foo a) where
3747 show (MkFoo value) = show (convert value)
3749 This is dangerous territory, however. Here, for example, is a program that would make the
3754 instance F [a] [[a]]
3755 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3757 Similarly, it can be tempting to lift the coverage condition:
3759 class Mul a b c | a b -> c where
3760 (.*.) :: a -> b -> c
3762 instance Mul Int Int Int where (.*.) = (*)
3763 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3764 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3766 The third instance declaration does not obey the coverage condition;
3767 and indeed the (somewhat strange) definition:
3769 f = \ b x y -> if b then x .*. [y] else y
3771 makes instance inference go into a loop, because it requires the constraint
3772 <literal>(Mul a [b] b)</literal>.
3775 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3776 the experimental flag <option>-XUndecidableInstances</option>
3777 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3778 both the Paterson Conditions and the Coverage Condition
3779 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3780 fixed-depth recursion stack. If you exceed the stack depth you get a
3781 sort of backtrace, and the opportunity to increase the stack depth
3782 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3788 <sect3 id="instance-overlap">
3789 <title>Overlapping instances</title>
3791 In general, <emphasis>GHC requires that that it be unambiguous which instance
3793 should be used to resolve a type-class constraint</emphasis>. This behaviour
3794 can be modified by two flags: <option>-XOverlappingInstances</option>
3795 <indexterm><primary>-XOverlappingInstances
3796 </primary></indexterm>
3797 and <option>-XIncoherentInstances</option>
3798 <indexterm><primary>-XIncoherentInstances
3799 </primary></indexterm>, as this section discusses. Both these
3800 flags are dynamic flags, and can be set on a per-module basis, using
3801 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3803 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3804 it tries to match every instance declaration against the
3806 by instantiating the head of the instance declaration. For example, consider
3809 instance context1 => C Int a where ... -- (A)
3810 instance context2 => C a Bool where ... -- (B)
3811 instance context3 => C Int [a] where ... -- (C)
3812 instance context4 => C Int [Int] where ... -- (D)
3814 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3815 but (C) and (D) do not. When matching, GHC takes
3816 no account of the context of the instance declaration
3817 (<literal>context1</literal> etc).
3818 GHC's default behaviour is that <emphasis>exactly one instance must match the
3819 constraint it is trying to resolve</emphasis>.
3820 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3821 including both declarations (A) and (B), say); an error is only reported if a
3822 particular constraint matches more than one.
3826 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3827 more than one instance to match, provided there is a most specific one. For
3828 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3829 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3830 most-specific match, the program is rejected.
3833 However, GHC is conservative about committing to an overlapping instance. For example:
3838 Suppose that from the RHS of <literal>f</literal> we get the constraint
3839 <literal>C Int [b]</literal>. But
3840 GHC does not commit to instance (C), because in a particular
3841 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3842 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3843 So GHC rejects the program.
3844 (If you add the flag <option>-XIncoherentInstances</option>,
3845 GHC will instead pick (C), without complaining about
3846 the problem of subsequent instantiations.)
3849 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3850 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3851 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3852 it instead. In this case, GHC will refrain from
3853 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3854 as before) but, rather than rejecting the program, it will infer the type
3856 f :: C Int [b] => [b] -> [b]
3858 That postpones the question of which instance to pick to the
3859 call site for <literal>f</literal>
3860 by which time more is known about the type <literal>b</literal>.
3861 You can write this type signature yourself if you use the
3862 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3866 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3870 instance Foo [b] where
3873 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3874 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3875 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3876 declaration. The solution is to postpone the choice by adding the constraint to the context
3877 of the instance declaration, thus:
3879 instance C Int [b] => Foo [b] where
3882 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3885 The willingness to be overlapped or incoherent is a property of
3886 the <emphasis>instance declaration</emphasis> itself, controlled by the
3887 presence or otherwise of the <option>-XOverlappingInstances</option>
3888 and <option>-XIncoherentInstances</option> flags when that module is
3889 being defined. Neither flag is required in a module that imports and uses the
3890 instance declaration. Specifically, during the lookup process:
3893 An instance declaration is ignored during the lookup process if (a) a more specific
3894 match is found, and (b) the instance declaration was compiled with
3895 <option>-XOverlappingInstances</option>. The flag setting for the
3896 more-specific instance does not matter.
3899 Suppose an instance declaration does not match the constraint being looked up, but
3900 does unify with it, so that it might match when the constraint is further
3901 instantiated. Usually GHC will regard this as a reason for not committing to
3902 some other constraint. But if the instance declaration was compiled with
3903 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3904 check for that declaration.
3907 These rules make it possible for a library author to design a library that relies on
3908 overlapping instances without the library client having to know.
3911 If an instance declaration is compiled without
3912 <option>-XOverlappingInstances</option>,
3913 then that instance can never be overlapped. This could perhaps be
3914 inconvenient. Perhaps the rule should instead say that the
3915 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3916 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3917 at a usage site should be permitted regardless of how the instance declarations
3918 are compiled, if the <option>-XOverlappingInstances</option> flag is
3919 used at the usage site. (Mind you, the exact usage site can occasionally be
3920 hard to pin down.) We are interested to receive feedback on these points.
3922 <para>The <option>-XIncoherentInstances</option> flag implies the
3923 <option>-XOverlappingInstances</option> flag, but not vice versa.
3931 <sect2 id="overloaded-strings">
3932 <title>Overloaded string literals
3936 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3937 string literal has type <literal>String</literal>, but with overloaded string
3938 literals enabled (with <literal>-XOverloadedStrings</literal>)
3939 a string literal has type <literal>(IsString a) => a</literal>.
3942 This means that the usual string syntax can be used, e.g., for packed strings
3943 and other variations of string like types. String literals behave very much
3944 like integer literals, i.e., they can be used in both expressions and patterns.
3945 If used in a pattern the literal with be replaced by an equality test, in the same
3946 way as an integer literal is.
3949 The class <literal>IsString</literal> is defined as:
3951 class IsString a where
3952 fromString :: String -> a
3954 The only predefined instance is the obvious one to make strings work as usual:
3956 instance IsString [Char] where
3959 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3960 it explicitly (for example, to give an instance declaration for it), you can import it
3961 from module <literal>GHC.Exts</literal>.
3964 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3968 Each type in a default declaration must be an
3969 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3973 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3974 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3975 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3976 <emphasis>or</emphasis> <literal>IsString</literal>.
3985 import GHC.Exts( IsString(..) )
3987 newtype MyString = MyString String deriving (Eq, Show)
3988 instance IsString MyString where
3989 fromString = MyString
3991 greet :: MyString -> MyString
3992 greet "hello" = "world"
3996 print $ greet "hello"
3997 print $ greet "fool"
4001 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4002 to work since it gets translated into an equality comparison.
4008 <sect1 id="type-families">
4009 <title>Type families</title>
4012 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4013 facilitate type-level
4014 programming. Type families are a generalisation of <firstterm>associated
4015 data types</firstterm>
4016 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4017 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4018 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4019 Symposium on Principles of Programming Languages (POPL'05)”, pages
4020 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4021 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4022 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4024 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4025 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4026 themselves are described in the paper “<ulink
4027 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4028 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4030 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4031 13th ACM SIGPLAN International Conference on Functional
4032 Programming”, ACM Press, pages 51-62, 2008. Type families
4033 essentially provide type-indexed data types and named functions on types,
4034 which are useful for generic programming and highly parameterised library
4035 interfaces as well as interfaces with enhanced static information, much like
4036 dependent types. They might also be regarded as an alternative to functional
4037 dependencies, but provide a more functional style of type-level programming
4038 than the relational style of functional dependencies.
4041 Indexed type families, or type families for short, are type constructors that
4042 represent sets of types. Set members are denoted by supplying the type family
4043 constructor with type parameters, which are called <firstterm>type
4044 indices</firstterm>. The
4045 difference between vanilla parametrised type constructors and family
4046 constructors is much like between parametrically polymorphic functions and
4047 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4048 behave the same at all type instances, whereas class methods can change their
4049 behaviour in dependence on the class type parameters. Similarly, vanilla type
4050 constructors imply the same data representation for all type instances, but
4051 family constructors can have varying representation types for varying type
4055 Indexed type families come in two flavours: <firstterm>data
4056 families</firstterm> and <firstterm>type synonym
4057 families</firstterm>. They are the indexed family variants of algebraic
4058 data types and type synonyms, respectively. The instances of data families
4059 can be data types and newtypes.
4062 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4063 Additional information on the use of type families in GHC is available on
4064 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4065 Haskell wiki page on type families</ulink>.
4068 <sect2 id="data-families">
4069 <title>Data families</title>
4072 Data families appear in two flavours: (1) they can be defined on the
4074 or (2) they can appear inside type classes (in which case they are known as
4075 associated types). The former is the more general variant, as it lacks the
4076 requirement for the type-indexes to coincide with the class
4077 parameters. However, the latter can lead to more clearly structured code and
4078 compiler warnings if some type instances were - possibly accidentally -
4079 omitted. In the following, we always discuss the general toplevel form first
4080 and then cover the additional constraints placed on associated types.
4083 <sect3 id="data-family-declarations">
4084 <title>Data family declarations</title>
4087 Indexed data families are introduced by a signature, such as
4089 data family GMap k :: * -> *
4091 The special <literal>family</literal> distinguishes family from standard
4092 data declarations. The result kind annotation is optional and, as
4093 usual, defaults to <literal>*</literal> if omitted. An example is
4097 Named arguments can also be given explicit kind signatures if needed.
4099 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4100 declarations] named arguments are entirely optional, so that we can
4101 declare <literal>Array</literal> alternatively with
4103 data family Array :: * -> *
4107 <sect4 id="assoc-data-family-decl">
4108 <title>Associated data family declarations</title>
4110 When a data family is declared as part of a type class, we drop
4111 the <literal>family</literal> special. The <literal>GMap</literal>
4112 declaration takes the following form
4114 class GMapKey k where
4115 data GMap k :: * -> *
4118 In contrast to toplevel declarations, named arguments must be used for
4119 all type parameters that are to be used as type-indexes. Moreover,
4120 the argument names must be class parameters. Each class parameter may
4121 only be used at most once per associated type, but some may be omitted
4122 and they may be in an order other than in the class head. Hence, the
4123 following contrived example is admissible:
4132 <sect3 id="data-instance-declarations">
4133 <title>Data instance declarations</title>
4136 Instance declarations of data and newtype families are very similar to
4137 standard data and newtype declarations. The only two differences are
4138 that the keyword <literal>data</literal> or <literal>newtype</literal>
4139 is followed by <literal>instance</literal> and that some or all of the
4140 type arguments can be non-variable types, but may not contain forall
4141 types or type synonym families. However, data families are generally
4142 allowed in type parameters, and type synonyms are allowed as long as
4143 they are fully applied and expand to a type that is itself admissible -
4144 exactly as this is required for occurrences of type synonyms in class
4145 instance parameters. For example, the <literal>Either</literal>
4146 instance for <literal>GMap</literal> is
4148 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4150 In this example, the declaration has only one variant. In general, it
4154 Data and newtype instance declarations are only permitted when an
4155 appropriate family declaration is in scope - just as a class instance declaratoin
4156 requires the class declaration to be visible. Moreover, each instance
4157 declaration has to conform to the kind determined by its family
4158 declaration. This implies that the number of parameters of an instance
4159 declaration matches the arity determined by the kind of the family.
4162 A data family instance declaration can use the full exprssiveness of
4163 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4165 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4166 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4167 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4170 data instance T Int = T1 Int | T2 Bool
4171 newtype instance T Char = TC Bool
4174 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4175 and indeed can define a GADT. For example:
4178 data instance G [a] b where
4179 G1 :: c -> G [Int] b
4183 <listitem><para> You can use a <literal>deriving</literal> clause on a
4184 <literal>data instance</literal> or <literal>newtype instance</literal>
4191 Even if type families are defined as toplevel declarations, functions
4192 that perform different computations for different family instances may still
4193 need to be defined as methods of type classes. In particular, the
4194 following is not possible:
4197 data instance T Int = A
4198 data instance T Char = B
4200 foo A = 1 -- WRONG: These two equations together...
4201 foo B = 2 -- ...will produce a type error.
4203 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4207 instance Foo Int where
4209 instance Foo Char where
4212 (Given the functionality provided by GADTs (Generalised Algebraic Data
4213 Types), it might seem as if a definition, such as the above, should be
4214 feasible. However, type families are - in contrast to GADTs - are
4215 <emphasis>open;</emphasis> i.e., new instances can always be added,
4217 modules. Supporting pattern matching across different data instances
4218 would require a form of extensible case construct.)
4221 <sect4 id="assoc-data-inst">
4222 <title>Associated data instances</title>
4224 When an associated data family instance is declared within a type
4225 class instance, we drop the <literal>instance</literal> keyword in the
4226 family instance. So, the <literal>Either</literal> instance
4227 for <literal>GMap</literal> becomes:
4229 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4230 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4233 The most important point about associated family instances is that the
4234 type indexes corresponding to class parameters must be identical to
4235 the type given in the instance head; here this is the first argument
4236 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4237 which coincides with the only class parameter. Any parameters to the
4238 family constructor that do not correspond to class parameters, need to
4239 be variables in every instance; here this is the
4240 variable <literal>v</literal>.
4243 Instances for an associated family can only appear as part of
4244 instances declarations of the class in which the family was declared -
4245 just as with the equations of the methods of a class. Also in
4246 correspondence to how methods are handled, declarations of associated
4247 types can be omitted in class instances. If an associated family
4248 instance is omitted, the corresponding instance type is not inhabited;
4249 i.e., only diverging expressions, such
4250 as <literal>undefined</literal>, can assume the type.
4254 <sect4 id="scoping-class-params">
4255 <title>Scoping of class parameters</title>
4257 In the case of multi-parameter type classes, the visibility of class
4258 parameters in the right-hand side of associated family instances
4259 depends <emphasis>solely</emphasis> on the parameters of the data
4260 family. As an example, consider the simple class declaration
4265 Only one of the two class parameters is a parameter to the data
4266 family. Hence, the following instance declaration is invalid:
4268 instance C [c] d where
4269 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4271 Here, the right-hand side of the data instance mentions the type
4272 variable <literal>d</literal> that does not occur in its left-hand
4273 side. We cannot admit such data instances as they would compromise
4278 <sect4 id="family-class-inst">
4279 <title>Type class instances of family instances</title>
4281 Type class instances of instances of data families can be defined as
4282 usual, and in particular data instance declarations can
4283 have <literal>deriving</literal> clauses. For example, we can write
4285 data GMap () v = GMapUnit (Maybe v)
4288 which implicitly defines an instance of the form
4290 instance Show v => Show (GMap () v) where ...
4294 Note that class instances are always for
4295 particular <emphasis>instances</emphasis> of a data family and never
4296 for an entire family as a whole. This is for essentially the same
4297 reasons that we cannot define a toplevel function that performs
4298 pattern matching on the data constructors
4299 of <emphasis>different</emphasis> instances of a single type family.
4300 It would require a form of extensible case construct.
4304 <sect4 id="data-family-overlap">
4305 <title>Overlap of data instances</title>
4307 The instance declarations of a data family used in a single program
4308 may not overlap at all, independent of whether they are associated or
4309 not. In contrast to type class instances, this is not only a matter
4310 of consistency, but one of type safety.
4316 <sect3 id="data-family-import-export">
4317 <title>Import and export</title>
4320 The association of data constructors with type families is more dynamic
4321 than that is the case with standard data and newtype declarations. In
4322 the standard case, the notation <literal>T(..)</literal> in an import or
4323 export list denotes the type constructor and all the data constructors
4324 introduced in its declaration. However, a family declaration never
4325 introduces any data constructors; instead, data constructors are
4326 introduced by family instances. As a result, which data constructors
4327 are associated with a type family depends on the currently visible
4328 instance declarations for that family. Consequently, an import or
4329 export item of the form <literal>T(..)</literal> denotes the family
4330 constructor and all currently visible data constructors - in the case of
4331 an export item, these may be either imported or defined in the current
4332 module. The treatment of import and export items that explicitly list
4333 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4337 <sect4 id="data-family-impexp-assoc">
4338 <title>Associated families</title>
4340 As expected, an import or export item of the
4341 form <literal>C(..)</literal> denotes all of the class' methods and
4342 associated types. However, when associated types are explicitly
4343 listed as subitems of a class, we need some new syntax, as uppercase
4344 identifiers as subitems are usually data constructors, not type
4345 constructors. To clarify that we denote types here, each associated
4346 type name needs to be prefixed by the keyword <literal>type</literal>.
4347 So for example, when explicitly listing the components of
4348 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4349 GMap, empty, lookup, insert)</literal>.
4353 <sect4 id="data-family-impexp-examples">
4354 <title>Examples</title>
4356 Assuming our running <literal>GMapKey</literal> class example, let us
4357 look at some export lists and their meaning:
4360 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4361 just the class name.</para>
4364 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4365 Exports the class, the associated type <literal>GMap</literal>
4367 functions <literal>empty</literal>, <literal>lookup</literal>,
4368 and <literal>insert</literal>. None of the data constructors is
4372 <para><literal>module GMap (GMapKey(..), GMap(..))
4373 where...</literal>: As before, but also exports all the data
4374 constructors <literal>GMapInt</literal>,
4375 <literal>GMapChar</literal>,
4376 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4377 and <literal>GMapUnit</literal>.</para>
4380 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4381 GMap(..)) where...</literal>: As before.</para>
4384 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4385 where...</literal>: As before.</para>
4390 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4391 both the class <literal>GMapKey</literal> as well as its associated
4392 type <literal>GMap</literal>. However, you cannot
4393 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4394 sub-component specifications cannot be nested. To
4395 specify <literal>GMap</literal>'s data constructors, you have to list
4400 <sect4 id="data-family-impexp-instances">
4401 <title>Instances</title>
4403 Family instances are implicitly exported, just like class instances.
4404 However, this applies only to the heads of instances, not to the data
4405 constructors an instance defines.
4413 <sect2 id="synonym-families">
4414 <title>Synonym families</title>
4417 Type families appear in two flavours: (1) they can be defined on the
4418 toplevel or (2) they can appear inside type classes (in which case they
4419 are known as associated type synonyms). The former is the more general
4420 variant, as it lacks the requirement for the type-indexes to coincide with
4421 the class parameters. However, the latter can lead to more clearly
4422 structured code and compiler warnings if some type instances were -
4423 possibly accidentally - omitted. In the following, we always discuss the
4424 general toplevel form first and then cover the additional constraints
4425 placed on associated types.
4428 <sect3 id="type-family-declarations">
4429 <title>Type family declarations</title>
4432 Indexed type families are introduced by a signature, such as
4434 type family Elem c :: *
4436 The special <literal>family</literal> distinguishes family from standard
4437 type declarations. The result kind annotation is optional and, as
4438 usual, defaults to <literal>*</literal> if omitted. An example is
4442 Parameters can also be given explicit kind signatures if needed. We
4443 call the number of parameters in a type family declaration, the family's
4444 arity, and all applications of a type family must be fully saturated
4445 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4446 and it implies that the kind of a type family is not sufficient to
4447 determine a family's arity, and hence in general, also insufficient to
4448 determine whether a type family application is well formed. As an
4449 example, consider the following declaration:
4451 type family F a b :: * -> * -- F's arity is 2,
4452 -- although its overall kind is * -> * -> * -> *
4454 Given this declaration the following are examples of well-formed and
4457 F Char [Int] -- OK! Kind: * -> *
4458 F Char [Int] Bool -- OK! Kind: *
4459 F IO Bool -- WRONG: kind mismatch in the first argument
4460 F Bool -- WRONG: unsaturated application
4464 <sect4 id="assoc-type-family-decl">
4465 <title>Associated type family declarations</title>
4467 When a type family is declared as part of a type class, we drop
4468 the <literal>family</literal> special. The <literal>Elem</literal>
4469 declaration takes the following form
4471 class Collects ce where
4475 The argument names of the type family must be class parameters. Each
4476 class parameter may only be used at most once per associated type, but
4477 some may be omitted and they may be in an order other than in the
4478 class head. Hence, the following contrived example is admissible:
4483 These rules are exactly as for associated data families.
4488 <sect3 id="type-instance-declarations">
4489 <title>Type instance declarations</title>
4491 Instance declarations of type families are very similar to standard type
4492 synonym declarations. The only two differences are that the
4493 keyword <literal>type</literal> is followed
4494 by <literal>instance</literal> and that some or all of the type
4495 arguments can be non-variable types, but may not contain forall types or
4496 type synonym families. However, data families are generally allowed, and
4497 type synonyms are allowed as long as they are fully applied and expand
4498 to a type that is admissible - these are the exact same requirements as
4499 for data instances. For example, the <literal>[e]</literal> instance
4500 for <literal>Elem</literal> is
4502 type instance Elem [e] = e
4506 Type family instance declarations are only legitimate when an
4507 appropriate family declaration is in scope - just like class instances
4508 require the class declaration to be visible. Moreover, each instance
4509 declaration has to conform to the kind determined by its family
4510 declaration, and the number of type parameters in an instance
4511 declaration must match the number of type parameters in the family
4512 declaration. Finally, the right-hand side of a type instance must be a
4513 monotype (i.e., it may not include foralls) and after the expansion of
4514 all saturated vanilla type synonyms, no synonyms, except family synonyms
4515 may remain. Here are some examples of admissible and illegal type
4518 type family F a :: *
4519 type instance F [Int] = Int -- OK!
4520 type instance F String = Char -- OK!
4521 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4522 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4523 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4525 type family G a b :: * -> *
4526 type instance G Int = (,) -- WRONG: must be two type parameters
4527 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4531 <sect4 id="assoc-type-instance">
4532 <title>Associated type instance declarations</title>
4534 When an associated family instance is declared within a type class
4535 instance, we drop the <literal>instance</literal> keyword in the family
4536 instance. So, the <literal>[e]</literal> instance
4537 for <literal>Elem</literal> becomes:
4539 instance (Eq (Elem [e])) => Collects ([e]) where
4543 The most important point about associated family instances is that the
4544 type indexes corresponding to class parameters must be identical to the
4545 type given in the instance head; here this is <literal>[e]</literal>,
4546 which coincides with the only class parameter.
4549 Instances for an associated family can only appear as part of instances
4550 declarations of the class in which the family was declared - just as
4551 with the equations of the methods of a class. Also in correspondence to
4552 how methods are handled, declarations of associated types can be omitted
4553 in class instances. If an associated family instance is omitted, the
4554 corresponding instance type is not inhabited; i.e., only diverging
4555 expressions, such as <literal>undefined</literal>, can assume the type.
4559 <sect4 id="type-family-overlap">
4560 <title>Overlap of type synonym instances</title>
4562 The instance declarations of a type family used in a single program
4563 may only overlap if the right-hand sides of the overlapping instances
4564 coincide for the overlapping types. More formally, two instance
4565 declarations overlap if there is a substitution that makes the
4566 left-hand sides of the instances syntactically the same. Whenever
4567 that is the case, the right-hand sides of the instances must also be
4568 syntactically equal under the same substitution. This condition is
4569 independent of whether the type family is associated or not, and it is
4570 not only a matter of consistency, but one of type safety.
4573 Here are two example to illustrate the condition under which overlap
4576 type instance F (a, Int) = [a]
4577 type instance F (Int, b) = [b] -- overlap permitted
4579 type instance G (a, Int) = [a]
4580 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4585 <sect4 id="type-family-decidability">
4586 <title>Decidability of type synonym instances</title>
4588 In order to guarantee that type inference in the presence of type
4589 families decidable, we need to place a number of additional
4590 restrictions on the formation of type instance declarations (c.f.,
4591 Definition 5 (Relaxed Conditions) of “<ulink
4592 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4593 Checking with Open Type Functions</ulink>”). Instance
4594 declarations have the general form
4596 type instance F t1 .. tn = t
4598 where we require that for every type family application <literal>(G s1
4599 .. sm)</literal> in <literal>t</literal>,
4602 <para><literal>s1 .. sm</literal> do not contain any type family
4603 constructors,</para>
4606 <para>the total number of symbols (data type constructors and type
4607 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4608 in <literal>t1 .. tn</literal>, and</para>
4611 <para>for every type
4612 variable <literal>a</literal>, <literal>a</literal> occurs
4613 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4614 .. tn</literal>.</para>
4617 These restrictions are easily verified and ensure termination of type
4618 inference. However, they are not sufficient to guarantee completeness
4619 of type inference in the presence of, so called, ''loopy equalities'',
4620 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4621 a type variable is underneath a family application and data
4622 constructor application - see the above mentioned paper for details.
4625 If the option <option>-XUndecidableInstances</option> is passed to the
4626 compiler, the above restrictions are not enforced and it is on the
4627 programmer to ensure termination of the normalisation of type families
4628 during type inference.
4633 <sect3 id-="equality-constraints">
4634 <title>Equality constraints</title>
4636 Type context can include equality constraints of the form <literal>t1 ~
4637 t2</literal>, which denote that the types <literal>t1</literal>
4638 and <literal>t2</literal> need to be the same. In the presence of type
4639 families, whether two types are equal cannot generally be decided
4640 locally. Hence, the contexts of function signatures may include
4641 equality constraints, as in the following example:
4643 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4645 where we require that the element type of <literal>c1</literal>
4646 and <literal>c2</literal> are the same. In general, the
4647 types <literal>t1</literal> and <literal>t2</literal> of an equality
4648 constraint may be arbitrary monotypes; i.e., they may not contain any
4649 quantifiers, independent of whether higher-rank types are otherwise
4653 Equality constraints can also appear in class and instance contexts.
4654 The former enable a simple translation of programs using functional
4655 dependencies into programs using family synonyms instead. The general
4656 idea is to rewrite a class declaration of the form
4658 class C a b | a -> b
4662 class (F a ~ b) => C a b where
4665 That is, we represent every functional dependency (FD) <literal>a1 .. an
4666 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4667 superclass context equality <literal>F a1 .. an ~ b</literal>,
4668 essentially giving a name to the functional dependency. In class
4669 instances, we define the type instances of FD families in accordance
4670 with the class head. Method signatures are not affected by that
4674 NB: Equalities in superclass contexts are not fully implemented in
4679 <sect3 id-="ty-fams-in-instances">
4680 <title>Type families and instance declarations</title>
4681 <para>Type families require us to extend the rules for
4682 the form of instance heads, which are given
4683 in <xref linkend="flexible-instance-head"/>.
4686 <listitem><para>Data type families may appear in an instance head</para></listitem>
4687 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4689 The reason for the latter restriction is that there is no way to check for. Consider
4692 type instance F Bool = Int
4699 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4700 The situation is especially bad because the type instance for <literal>F Bool</literal>
4701 might be in another module, or even in a module that is not yet written.
4708 <sect1 id="other-type-extensions">
4709 <title>Other type system extensions</title>
4711 <sect2 id="type-restrictions">
4712 <title>Type signatures</title>
4714 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4716 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4717 that the type-class constraints in a type signature must have the
4718 form <emphasis>(class type-variable)</emphasis> or
4719 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4720 With <option>-XFlexibleContexts</option>
4721 these type signatures are perfectly OK
4724 g :: Ord (T a ()) => ...
4728 GHC imposes the following restrictions on the constraints in a type signature.
4732 forall tv1..tvn (c1, ...,cn) => type
4735 (Here, we write the "foralls" explicitly, although the Haskell source
4736 language omits them; in Haskell 98, all the free type variables of an
4737 explicit source-language type signature are universally quantified,
4738 except for the class type variables in a class declaration. However,
4739 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4748 <emphasis>Each universally quantified type variable
4749 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4751 A type variable <literal>a</literal> is "reachable" if it appears
4752 in the same constraint as either a type variable free in
4753 <literal>type</literal>, or another reachable type variable.
4754 A value with a type that does not obey
4755 this reachability restriction cannot be used without introducing
4756 ambiguity; that is why the type is rejected.
4757 Here, for example, is an illegal type:
4761 forall a. Eq a => Int
4765 When a value with this type was used, the constraint <literal>Eq tv</literal>
4766 would be introduced where <literal>tv</literal> is a fresh type variable, and
4767 (in the dictionary-translation implementation) the value would be
4768 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4769 can never know which instance of <literal>Eq</literal> to use because we never
4770 get any more information about <literal>tv</literal>.
4774 that the reachability condition is weaker than saying that <literal>a</literal> is
4775 functionally dependent on a type variable free in
4776 <literal>type</literal> (see <xref
4777 linkend="functional-dependencies"/>). The reason for this is there
4778 might be a "hidden" dependency, in a superclass perhaps. So
4779 "reachable" is a conservative approximation to "functionally dependent".
4780 For example, consider:
4782 class C a b | a -> b where ...
4783 class C a b => D a b where ...
4784 f :: forall a b. D a b => a -> a
4786 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4787 but that is not immediately apparent from <literal>f</literal>'s type.
4793 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4794 universally quantified type variables <literal>tvi</literal></emphasis>.
4796 For example, this type is OK because <literal>C a b</literal> mentions the
4797 universally quantified type variable <literal>b</literal>:
4801 forall a. C a b => burble
4805 The next type is illegal because the constraint <literal>Eq b</literal> does not
4806 mention <literal>a</literal>:
4810 forall a. Eq b => burble
4814 The reason for this restriction is milder than the other one. The
4815 excluded types are never useful or necessary (because the offending
4816 context doesn't need to be witnessed at this point; it can be floated
4817 out). Furthermore, floating them out increases sharing. Lastly,
4818 excluding them is a conservative choice; it leaves a patch of
4819 territory free in case we need it later.
4833 <sect2 id="implicit-parameters">
4834 <title>Implicit parameters</title>
4836 <para> Implicit parameters are implemented as described in
4837 "Implicit parameters: dynamic scoping with static types",
4838 J Lewis, MB Shields, E Meijer, J Launchbury,
4839 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4843 <para>(Most of the following, still rather incomplete, documentation is
4844 due to Jeff Lewis.)</para>
4846 <para>Implicit parameter support is enabled with the option
4847 <option>-XImplicitParams</option>.</para>
4850 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4851 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4852 context. In Haskell, all variables are statically bound. Dynamic
4853 binding of variables is a notion that goes back to Lisp, but was later
4854 discarded in more modern incarnations, such as Scheme. Dynamic binding
4855 can be very confusing in an untyped language, and unfortunately, typed
4856 languages, in particular Hindley-Milner typed languages like Haskell,
4857 only support static scoping of variables.
4860 However, by a simple extension to the type class system of Haskell, we
4861 can support dynamic binding. Basically, we express the use of a
4862 dynamically bound variable as a constraint on the type. These
4863 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4864 function uses a dynamically-bound variable <literal>?x</literal>
4865 of type <literal>t'</literal>". For
4866 example, the following expresses the type of a sort function,
4867 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4869 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4871 The dynamic binding constraints are just a new form of predicate in the type class system.
4874 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4875 where <literal>x</literal> is
4876 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4877 Use of this construct also introduces a new
4878 dynamic-binding constraint in the type of the expression.
4879 For example, the following definition
4880 shows how we can define an implicitly parameterized sort function in
4881 terms of an explicitly parameterized <literal>sortBy</literal> function:
4883 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4885 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4891 <title>Implicit-parameter type constraints</title>
4893 Dynamic binding constraints behave just like other type class
4894 constraints in that they are automatically propagated. Thus, when a
4895 function is used, its implicit parameters are inherited by the
4896 function that called it. For example, our <literal>sort</literal> function might be used
4897 to pick out the least value in a list:
4899 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4900 least xs = head (sort xs)
4902 Without lifting a finger, the <literal>?cmp</literal> parameter is
4903 propagated to become a parameter of <literal>least</literal> as well. With explicit
4904 parameters, the default is that parameters must always be explicit
4905 propagated. With implicit parameters, the default is to always
4909 An implicit-parameter type constraint differs from other type class constraints in the
4910 following way: All uses of a particular implicit parameter must have
4911 the same type. This means that the type of <literal>(?x, ?x)</literal>
4912 is <literal>(?x::a) => (a,a)</literal>, and not
4913 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4917 <para> You can't have an implicit parameter in the context of a class or instance
4918 declaration. For example, both these declarations are illegal:
4920 class (?x::Int) => C a where ...
4921 instance (?x::a) => Foo [a] where ...
4923 Reason: exactly which implicit parameter you pick up depends on exactly where
4924 you invoke a function. But the ``invocation'' of instance declarations is done
4925 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4926 Easiest thing is to outlaw the offending types.</para>
4928 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4930 f :: (?x :: [a]) => Int -> Int
4933 g :: (Read a, Show a) => String -> String
4936 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4937 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4938 quite unambiguous, and fixes the type <literal>a</literal>.
4943 <title>Implicit-parameter bindings</title>
4946 An implicit parameter is <emphasis>bound</emphasis> using the standard
4947 <literal>let</literal> or <literal>where</literal> binding forms.
4948 For example, we define the <literal>min</literal> function by binding
4949 <literal>cmp</literal>.
4952 min = let ?cmp = (<=) in least
4956 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4957 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4958 (including in a list comprehension, or do-notation, or pattern guards),
4959 or a <literal>where</literal> clause.
4960 Note the following points:
4963 An implicit-parameter binding group must be a
4964 collection of simple bindings to implicit-style variables (no
4965 function-style bindings, and no type signatures); these bindings are
4966 neither polymorphic or recursive.
4969 You may not mix implicit-parameter bindings with ordinary bindings in a
4970 single <literal>let</literal>
4971 expression; use two nested <literal>let</literal>s instead.
4972 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4976 You may put multiple implicit-parameter bindings in a
4977 single binding group; but they are <emphasis>not</emphasis> treated
4978 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4979 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4980 parameter. The bindings are not nested, and may be re-ordered without changing
4981 the meaning of the program.
4982 For example, consider:
4984 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4986 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4987 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4989 f :: (?x::Int) => Int -> Int
4997 <sect3><title>Implicit parameters and polymorphic recursion</title>
5000 Consider these two definitions:
5003 len1 xs = let ?acc = 0 in len_acc1 xs
5006 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5011 len2 xs = let ?acc = 0 in len_acc2 xs
5013 len_acc2 :: (?acc :: Int) => [a] -> Int
5015 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5017 The only difference between the two groups is that in the second group
5018 <literal>len_acc</literal> is given a type signature.
5019 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5020 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5021 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5022 has a type signature, the recursive call is made to the
5023 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5024 as an implicit parameter. So we get the following results in GHCi:
5031 Adding a type signature dramatically changes the result! This is a rather
5032 counter-intuitive phenomenon, worth watching out for.
5036 <sect3><title>Implicit parameters and monomorphism</title>
5038 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5039 Haskell Report) to implicit parameters. For example, consider:
5047 Since the binding for <literal>y</literal> falls under the Monomorphism
5048 Restriction it is not generalised, so the type of <literal>y</literal> is
5049 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5050 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5051 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5052 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5053 <literal>y</literal> in the body of the <literal>let</literal> will see the
5054 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5055 <literal>14</literal>.
5060 <!-- ======================= COMMENTED OUT ========================
5062 We intend to remove linear implicit parameters, so I'm at least removing
5063 them from the 6.6 user manual
5065 <sect2 id="linear-implicit-parameters">
5066 <title>Linear implicit parameters</title>
5068 Linear implicit parameters are an idea developed by Koen Claessen,
5069 Mark Shields, and Simon PJ. They address the long-standing
5070 problem that monads seem over-kill for certain sorts of problem, notably:
5073 <listitem> <para> distributing a supply of unique names </para> </listitem>
5074 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5075 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5079 Linear implicit parameters are just like ordinary implicit parameters,
5080 except that they are "linear"; that is, they cannot be copied, and
5081 must be explicitly "split" instead. Linear implicit parameters are
5082 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5083 (The '/' in the '%' suggests the split!)
5088 import GHC.Exts( Splittable )
5090 data NameSupply = ...
5092 splitNS :: NameSupply -> (NameSupply, NameSupply)
5093 newName :: NameSupply -> Name
5095 instance Splittable NameSupply where
5099 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5100 f env (Lam x e) = Lam x' (f env e)
5103 env' = extend env x x'
5104 ...more equations for f...
5106 Notice that the implicit parameter %ns is consumed
5108 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5109 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5113 So the translation done by the type checker makes
5114 the parameter explicit:
5116 f :: NameSupply -> Env -> Expr -> Expr
5117 f ns env (Lam x e) = Lam x' (f ns1 env e)
5119 (ns1,ns2) = splitNS ns
5121 env = extend env x x'
5123 Notice the call to 'split' introduced by the type checker.
5124 How did it know to use 'splitNS'? Because what it really did
5125 was to introduce a call to the overloaded function 'split',
5126 defined by the class <literal>Splittable</literal>:
5128 class Splittable a where
5131 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5132 split for name supplies. But we can simply write
5138 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5140 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5141 <literal>GHC.Exts</literal>.
5146 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5147 are entirely distinct implicit parameters: you
5148 can use them together and they won't interfere with each other. </para>
5151 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5153 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5154 in the context of a class or instance declaration. </para></listitem>
5158 <sect3><title>Warnings</title>
5161 The monomorphism restriction is even more important than usual.
5162 Consider the example above:
5164 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5165 f env (Lam x e) = Lam x' (f env e)
5168 env' = extend env x x'
5170 If we replaced the two occurrences of x' by (newName %ns), which is
5171 usually a harmless thing to do, we get:
5173 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5174 f env (Lam x e) = Lam (newName %ns) (f env e)
5176 env' = extend env x (newName %ns)
5178 But now the name supply is consumed in <emphasis>three</emphasis> places
5179 (the two calls to newName,and the recursive call to f), so
5180 the result is utterly different. Urk! We don't even have
5184 Well, this is an experimental change. With implicit
5185 parameters we have already lost beta reduction anyway, and
5186 (as John Launchbury puts it) we can't sensibly reason about
5187 Haskell programs without knowing their typing.
5192 <sect3><title>Recursive functions</title>
5193 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5196 foo :: %x::T => Int -> [Int]
5198 foo n = %x : foo (n-1)
5200 where T is some type in class Splittable.</para>
5202 Do you get a list of all the same T's or all different T's
5203 (assuming that split gives two distinct T's back)?
5205 If you supply the type signature, taking advantage of polymorphic
5206 recursion, you get what you'd probably expect. Here's the
5207 translated term, where the implicit param is made explicit:
5210 foo x n = let (x1,x2) = split x
5211 in x1 : foo x2 (n-1)
5213 But if you don't supply a type signature, GHC uses the Hindley
5214 Milner trick of using a single monomorphic instance of the function
5215 for the recursive calls. That is what makes Hindley Milner type inference
5216 work. So the translation becomes
5220 foom n = x : foom (n-1)
5224 Result: 'x' is not split, and you get a list of identical T's. So the
5225 semantics of the program depends on whether or not foo has a type signature.
5228 You may say that this is a good reason to dislike linear implicit parameters
5229 and you'd be right. That is why they are an experimental feature.
5235 ================ END OF Linear Implicit Parameters commented out -->
5237 <sect2 id="kinding">
5238 <title>Explicitly-kinded quantification</title>
5241 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5242 to give the kind explicitly as (machine-checked) documentation,
5243 just as it is nice to give a type signature for a function. On some occasions,
5244 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5245 John Hughes had to define the data type:
5247 data Set cxt a = Set [a]
5248 | Unused (cxt a -> ())
5250 The only use for the <literal>Unused</literal> constructor was to force the correct
5251 kind for the type variable <literal>cxt</literal>.
5254 GHC now instead allows you to specify the kind of a type variable directly, wherever
5255 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5258 This flag enables kind signatures in the following places:
5260 <listitem><para><literal>data</literal> declarations:
5262 data Set (cxt :: * -> *) a = Set [a]
5263 </screen></para></listitem>
5264 <listitem><para><literal>type</literal> declarations:
5266 type T (f :: * -> *) = f Int
5267 </screen></para></listitem>
5268 <listitem><para><literal>class</literal> declarations:
5270 class (Eq a) => C (f :: * -> *) a where ...
5271 </screen></para></listitem>
5272 <listitem><para><literal>forall</literal>'s in type signatures:
5274 f :: forall (cxt :: * -> *). Set cxt Int
5275 </screen></para></listitem>
5280 The parentheses are required. Some of the spaces are required too, to
5281 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5282 will get a parse error, because "<literal>::*->*</literal>" is a
5283 single lexeme in Haskell.
5287 As part of the same extension, you can put kind annotations in types
5290 f :: (Int :: *) -> Int
5291 g :: forall a. a -> (a :: *)
5295 atype ::= '(' ctype '::' kind ')
5297 The parentheses are required.
5302 <sect2 id="universal-quantification">
5303 <title>Arbitrary-rank polymorphism
5307 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5308 allows us to say exactly what this means. For example:
5316 g :: forall b. (b -> b)
5318 The two are treated identically.
5322 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5323 explicit universal quantification in
5325 For example, all the following types are legal:
5327 f1 :: forall a b. a -> b -> a
5328 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5330 f2 :: (forall a. a->a) -> Int -> Int
5331 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5333 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5335 f4 :: Int -> (forall a. a -> a)
5337 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5338 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5339 The <literal>forall</literal> makes explicit the universal quantification that
5340 is implicitly added by Haskell.
5343 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5344 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5345 shows, the polymorphic type on the left of the function arrow can be overloaded.
5348 The function <literal>f3</literal> has a rank-3 type;
5349 it has rank-2 types on the left of a function arrow.
5352 GHC has three flags to control higher-rank types:
5355 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5358 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5361 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5362 That is, you can nest <literal>forall</literal>s
5363 arbitrarily deep in function arrows.
5364 In particular, a forall-type (also called a "type scheme"),
5365 including an operational type class context, is legal:
5367 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5368 of a function arrow </para> </listitem>
5369 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5370 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5371 field type signatures.</para> </listitem>
5372 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5373 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5377 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5378 a type variable any more!
5387 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5388 the types of the constructor arguments. Here are several examples:
5394 data T a = T1 (forall b. b -> b -> b) a
5396 data MonadT m = MkMonad { return :: forall a. a -> m a,
5397 bind :: forall a b. m a -> (a -> m b) -> m b
5400 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5406 The constructors have rank-2 types:
5412 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5413 MkMonad :: forall m. (forall a. a -> m a)
5414 -> (forall a b. m a -> (a -> m b) -> m b)
5416 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5422 Notice that you don't need to use a <literal>forall</literal> if there's an
5423 explicit context. For example in the first argument of the
5424 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5425 prefixed to the argument type. The implicit <literal>forall</literal>
5426 quantifies all type variables that are not already in scope, and are
5427 mentioned in the type quantified over.
5431 As for type signatures, implicit quantification happens for non-overloaded
5432 types too. So if you write this:
5435 data T a = MkT (Either a b) (b -> b)
5438 it's just as if you had written this:
5441 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5444 That is, since the type variable <literal>b</literal> isn't in scope, it's
5445 implicitly universally quantified. (Arguably, it would be better
5446 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5447 where that is what is wanted. Feedback welcomed.)
5451 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5452 the constructor to suitable values, just as usual. For example,
5463 a3 = MkSwizzle reverse
5466 a4 = let r x = Just x
5473 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5474 mkTs f x y = [T1 f x, T1 f y]
5480 The type of the argument can, as usual, be more general than the type
5481 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5482 does not need the <literal>Ord</literal> constraint.)
5486 When you use pattern matching, the bound variables may now have
5487 polymorphic types. For example:
5493 f :: T a -> a -> (a, Char)
5494 f (T1 w k) x = (w k x, w 'c' 'd')
5496 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5497 g (MkSwizzle s) xs f = s (map f (s xs))
5499 h :: MonadT m -> [m a] -> m [a]
5500 h m [] = return m []
5501 h m (x:xs) = bind m x $ \y ->
5502 bind m (h m xs) $ \ys ->
5509 In the function <function>h</function> we use the record selectors <literal>return</literal>
5510 and <literal>bind</literal> to extract the polymorphic bind and return functions
5511 from the <literal>MonadT</literal> data structure, rather than using pattern
5517 <title>Type inference</title>
5520 In general, type inference for arbitrary-rank types is undecidable.
5521 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5522 to get a decidable algorithm by requiring some help from the programmer.
5523 We do not yet have a formal specification of "some help" but the rule is this:
5526 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5527 provides an explicit polymorphic type for x, or GHC's type inference will assume
5528 that x's type has no foralls in it</emphasis>.
5531 What does it mean to "provide" an explicit type for x? You can do that by
5532 giving a type signature for x directly, using a pattern type signature
5533 (<xref linkend="scoped-type-variables"/>), thus:
5535 \ f :: (forall a. a->a) -> (f True, f 'c')
5537 Alternatively, you can give a type signature to the enclosing
5538 context, which GHC can "push down" to find the type for the variable:
5540 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5542 Here the type signature on the expression can be pushed inwards
5543 to give a type signature for f. Similarly, and more commonly,
5544 one can give a type signature for the function itself:
5546 h :: (forall a. a->a) -> (Bool,Char)
5547 h f = (f True, f 'c')
5549 You don't need to give a type signature if the lambda bound variable
5550 is a constructor argument. Here is an example we saw earlier:
5552 f :: T a -> a -> (a, Char)
5553 f (T1 w k) x = (w k x, w 'c' 'd')
5555 Here we do not need to give a type signature to <literal>w</literal>, because
5556 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5563 <sect3 id="implicit-quant">
5564 <title>Implicit quantification</title>
5567 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5568 user-written types, if and only if there is no explicit <literal>forall</literal>,
5569 GHC finds all the type variables mentioned in the type that are not already
5570 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5574 f :: forall a. a -> a
5581 h :: forall b. a -> b -> b
5587 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5590 f :: (a -> a) -> Int
5592 f :: forall a. (a -> a) -> Int
5594 f :: (forall a. a -> a) -> Int
5597 g :: (Ord a => a -> a) -> Int
5598 -- MEANS the illegal type
5599 g :: forall a. (Ord a => a -> a) -> Int
5601 g :: (forall a. Ord a => a -> a) -> Int
5603 The latter produces an illegal type, which you might think is silly,
5604 but at least the rule is simple. If you want the latter type, you
5605 can write your for-alls explicitly. Indeed, doing so is strongly advised
5612 <sect2 id="impredicative-polymorphism">
5613 <title>Impredicative polymorphism
5615 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5616 enabled with <option>-XImpredicativeTypes</option>.
5618 that you can call a polymorphic function at a polymorphic type, and
5619 parameterise data structures over polymorphic types. For example:
5621 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5622 f (Just g) = Just (g [3], g "hello")
5625 Notice here that the <literal>Maybe</literal> type is parameterised by the
5626 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5629 <para>The technical details of this extension are described in the paper
5630 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5631 type inference for higher-rank types and impredicativity</ulink>,
5632 which appeared at ICFP 2006.
5636 <sect2 id="scoped-type-variables">
5637 <title>Lexically scoped type variables
5641 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5642 which some type signatures are simply impossible to write. For example:
5644 f :: forall a. [a] -> [a]
5650 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5651 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5652 The type variables bound by a <literal>forall</literal> scope over
5653 the entire definition of the accompanying value declaration.
5654 In this example, the type variable <literal>a</literal> scopes over the whole
5655 definition of <literal>f</literal>, including over
5656 the type signature for <varname>ys</varname>.
5657 In Haskell 98 it is not possible to declare
5658 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5659 it becomes possible to do so.
5661 <para>Lexically-scoped type variables are enabled by
5662 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5664 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5665 variables work, compared to earlier releases. Read this section
5669 <title>Overview</title>
5671 <para>The design follows the following principles
5673 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5674 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5675 design.)</para></listitem>
5676 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5677 type variables. This means that every programmer-written type signature
5678 (including one that contains free scoped type variables) denotes a
5679 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5680 checker, and no inference is involved.</para></listitem>
5681 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5682 changing the program.</para></listitem>
5686 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5688 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5689 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5690 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5691 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5695 In Haskell, a programmer-written type signature is implicitly quantified over
5696 its free type variables (<ulink
5697 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5699 of the Haskell Report).
5700 Lexically scoped type variables affect this implicit quantification rules
5701 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5702 quantified. For example, if type variable <literal>a</literal> is in scope,
5705 (e :: a -> a) means (e :: a -> a)
5706 (e :: b -> b) means (e :: forall b. b->b)
5707 (e :: a -> b) means (e :: forall b. a->b)
5715 <sect3 id="decl-type-sigs">
5716 <title>Declaration type signatures</title>
5717 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5718 quantification (using <literal>forall</literal>) brings into scope the
5719 explicitly-quantified
5720 type variables, in the definition of the named function. For example:
5722 f :: forall a. [a] -> [a]
5723 f (x:xs) = xs ++ [ x :: a ]
5725 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5726 the definition of "<literal>f</literal>".
5728 <para>This only happens if:
5730 <listitem><para> The quantification in <literal>f</literal>'s type
5731 signature is explicit. For example:
5734 g (x:xs) = xs ++ [ x :: a ]
5736 This program will be rejected, because "<literal>a</literal>" does not scope
5737 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5738 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5739 quantification rules.
5741 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5742 not a pattern binding.
5745 f1 :: forall a. [a] -> [a]
5746 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5748 f2 :: forall a. [a] -> [a]
5749 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5751 f3 :: forall a. [a] -> [a]
5752 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5754 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5755 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5756 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5757 the type signature brings <literal>a</literal> into scope.
5763 <sect3 id="exp-type-sigs">
5764 <title>Expression type signatures</title>
5766 <para>An expression type signature that has <emphasis>explicit</emphasis>
5767 quantification (using <literal>forall</literal>) brings into scope the
5768 explicitly-quantified
5769 type variables, in the annotated expression. For example:
5771 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5773 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5774 type variable <literal>s</literal> into scope, in the annotated expression
5775 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5780 <sect3 id="pattern-type-sigs">
5781 <title>Pattern type signatures</title>
5783 A type signature may occur in any pattern; this is a <emphasis>pattern type
5784 signature</emphasis>.
5787 -- f and g assume that 'a' is already in scope
5788 f = \(x::Int, y::a) -> x
5790 h ((x,y) :: (Int,Bool)) = (y,x)
5792 In the case where all the type variables in the pattern type signature are
5793 already in scope (i.e. bound by the enclosing context), matters are simple: the
5794 signature simply constrains the type of the pattern in the obvious way.
5797 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5798 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5799 that are already in scope. For example:
5801 f :: forall a. [a] -> (Int, [a])
5804 (ys::[a], n) = (reverse xs, length xs) -- OK
5805 zs::[a] = xs ++ ys -- OK
5807 Just (v::b) = ... -- Not OK; b is not in scope
5809 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5810 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5814 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5815 type signature may mention a type variable that is not in scope; in this case,
5816 <emphasis>the signature brings that type variable into scope</emphasis>.
5817 This is particularly important for existential data constructors. For example:
5819 data T = forall a. MkT [a]
5822 k (MkT [t::a]) = MkT t3
5826 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5827 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5828 because it is bound by the pattern match. GHC's rule is that in this situation
5829 (and only then), a pattern type signature can mention a type variable that is
5830 not already in scope; the effect is to bring it into scope, standing for the
5831 existentially-bound type variable.
5834 When a pattern type signature binds a type variable in this way, GHC insists that the
5835 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5836 This means that any user-written type signature always stands for a completely known type.
5839 If all this seems a little odd, we think so too. But we must have
5840 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5841 could not name existentially-bound type variables in subsequent type signatures.
5844 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5845 signature is allowed to mention a lexical variable that is not already in
5847 For example, both <literal>f</literal> and <literal>g</literal> would be
5848 illegal if <literal>a</literal> was not already in scope.
5854 <!-- ==================== Commented out part about result type signatures
5856 <sect3 id="result-type-sigs">
5857 <title>Result type signatures</title>
5860 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5863 {- f assumes that 'a' is already in scope -}
5864 f x y :: [a] = [x,y,x]
5866 g = \ x :: [Int] -> [3,4]
5868 h :: forall a. [a] -> a
5872 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5873 the result of the function. Similarly, the body of the lambda in the RHS of
5874 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5875 alternative in <literal>h</literal> is <literal>a</literal>.
5877 <para> A result type signature never brings new type variables into scope.</para>
5879 There are a couple of syntactic wrinkles. First, notice that all three
5880 examples would parse quite differently with parentheses:
5882 {- f assumes that 'a' is already in scope -}
5883 f x (y :: [a]) = [x,y,x]
5885 g = \ (x :: [Int]) -> [3,4]
5887 h :: forall a. [a] -> a
5891 Now the signature is on the <emphasis>pattern</emphasis>; and
5892 <literal>h</literal> would certainly be ill-typed (since the pattern
5893 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5895 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5896 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5897 token or a parenthesised type of some sort). To see why,
5898 consider how one would parse this:
5907 <sect3 id="cls-inst-scoped-tyvars">
5908 <title>Class and instance declarations</title>
5911 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5912 scope over the methods defined in the <literal>where</literal> part. For example:
5930 <sect2 id="typing-binds">
5931 <title>Generalised typing of mutually recursive bindings</title>
5934 The Haskell Report specifies that a group of bindings (at top level, or in a
5935 <literal>let</literal> or <literal>where</literal>) should be sorted into
5936 strongly-connected components, and then type-checked in dependency order
5937 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5938 Report, Section 4.5.1</ulink>).
5939 As each group is type-checked, any binders of the group that
5941 an explicit type signature are put in the type environment with the specified
5943 and all others are monomorphic until the group is generalised
5944 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5947 <para>Following a suggestion of Mark Jones, in his paper
5948 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5950 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5952 <emphasis>the dependency analysis ignores references to variables that have an explicit
5953 type signature</emphasis>.
5954 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5955 typecheck. For example, consider:
5957 f :: Eq a => a -> Bool
5958 f x = (x == x) || g True || g "Yes"
5960 g y = (y <= y) || f True
5962 This is rejected by Haskell 98, but under Jones's scheme the definition for
5963 <literal>g</literal> is typechecked first, separately from that for
5964 <literal>f</literal>,
5965 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5966 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5967 type is generalised, to get
5969 g :: Ord a => a -> Bool
5971 Now, the definition for <literal>f</literal> is typechecked, with this type for
5972 <literal>g</literal> in the type environment.
5976 The same refined dependency analysis also allows the type signatures of
5977 mutually-recursive functions to have different contexts, something that is illegal in
5978 Haskell 98 (Section 4.5.2, last sentence). With
5979 <option>-XRelaxedPolyRec</option>
5980 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5981 type signatures; in practice this means that only variables bound by the same
5982 pattern binding must have the same context. For example, this is fine:
5984 f :: Eq a => a -> Bool
5985 f x = (x == x) || g True
5987 g :: Ord a => a -> Bool
5988 g y = (y <= y) || f True
5994 <!-- ==================== End of type system extensions ================= -->
5996 <!-- ====================== TEMPLATE HASKELL ======================= -->
5998 <sect1 id="template-haskell">
5999 <title>Template Haskell</title>
6001 <para>Template Haskell allows you to do compile-time meta-programming in
6004 the main technical innovations is discussed in "<ulink
6005 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6006 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6009 There is a Wiki page about
6010 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6011 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6015 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6016 Haskell library reference material</ulink>
6017 (look for module <literal>Language.Haskell.TH</literal>).
6018 Many changes to the original design are described in
6019 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6020 Notes on Template Haskell version 2</ulink>.
6021 Not all of these changes are in GHC, however.
6024 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6025 as a worked example to help get you started.
6029 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6030 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6035 <title>Syntax</title>
6037 <para> Template Haskell has the following new syntactic
6038 constructions. You need to use the flag
6039 <option>-XTemplateHaskell</option>
6040 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6041 </indexterm>to switch these syntactic extensions on
6042 (<option>-XTemplateHaskell</option> is no longer implied by
6043 <option>-fglasgow-exts</option>).</para>
6047 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6048 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6049 There must be no space between the "$" and the identifier or parenthesis. This use
6050 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6051 of "." as an infix operator. If you want the infix operator, put spaces around it.
6053 <para> A splice can occur in place of
6055 <listitem><para> an expression; the spliced expression must
6056 have type <literal>Q Exp</literal></para></listitem>
6057 <listitem><para> an type; the spliced expression must
6058 have type <literal>Q Typ</literal></para></listitem>
6059 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
6062 Inside a splice you can can only call functions defined in imported modules,
6063 not functions defined elsewhere in the same module.</listitem>
6067 A expression quotation is written in Oxford brackets, thus:
6069 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
6070 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6071 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6072 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6073 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6074 the quotation has type <literal>Q Typ</literal>.</para></listitem>
6075 </itemizedlist></para></listitem>
6078 A quasi-quotation can appear in either a pattern context or an
6079 expression context and is also written in Oxford brackets:
6081 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
6082 where the "..." is an arbitrary string; a full description of the
6083 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6084 </itemizedlist></para></listitem>
6087 A name can be quoted with either one or two prefix single quotes:
6089 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6090 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6091 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6093 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6094 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6097 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6098 may also be given as an argument to the <literal>reify</literal> function.
6104 (Compared to the original paper, there are many differences of detail.
6105 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6106 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6107 Pattern splices and quotations are not implemented.)
6111 <sect2> <title> Using Template Haskell </title>
6115 The data types and monadic constructor functions for Template Haskell are in the library
6116 <literal>Language.Haskell.THSyntax</literal>.
6120 You can only run a function at compile time if it is imported from another module. That is,
6121 you can't define a function in a module, and call it from within a splice in the same module.
6122 (It would make sense to do so, but it's hard to implement.)
6126 You can only run a function at compile time if it is imported
6127 from another module <emphasis>that is not part of a mutually-recursive group of modules
6128 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6129 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6130 splice is to be run.</para>
6132 For example, when compiling module A,
6133 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6134 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6138 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6141 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6142 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6143 compiles and runs a program, and then looks at the result. So it's important that
6144 the program it compiles produces results whose representations are identical to
6145 those of the compiler itself.
6149 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6150 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6155 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6156 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6157 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6164 -- Import our template "pr"
6165 import Printf ( pr )
6167 -- The splice operator $ takes the Haskell source code
6168 -- generated at compile time by "pr" and splices it into
6169 -- the argument of "putStrLn".
6170 main = putStrLn ( $(pr "Hello") )
6176 -- Skeletal printf from the paper.
6177 -- It needs to be in a separate module to the one where
6178 -- you intend to use it.
6180 -- Import some Template Haskell syntax
6181 import Language.Haskell.TH
6183 -- Describe a format string
6184 data Format = D | S | L String
6186 -- Parse a format string. This is left largely to you
6187 -- as we are here interested in building our first ever
6188 -- Template Haskell program and not in building printf.
6189 parse :: String -> [Format]
6192 -- Generate Haskell source code from a parsed representation
6193 -- of the format string. This code will be spliced into
6194 -- the module which calls "pr", at compile time.
6195 gen :: [Format] -> Q Exp
6196 gen [D] = [| \n -> show n |]
6197 gen [S] = [| \s -> s |]
6198 gen [L s] = stringE s
6200 -- Here we generate the Haskell code for the splice
6201 -- from an input format string.
6202 pr :: String -> Q Exp
6203 pr s = gen (parse s)
6206 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6209 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6212 <para>Run "main.exe" and here is your output:</para>
6222 <title>Using Template Haskell with Profiling</title>
6223 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6225 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6226 interpreter to run the splice expressions. The bytecode interpreter
6227 runs the compiled expression on top of the same runtime on which GHC
6228 itself is running; this means that the compiled code referred to by
6229 the interpreted expression must be compatible with this runtime, and
6230 in particular this means that object code that is compiled for
6231 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6232 expression, because profiled object code is only compatible with the
6233 profiling version of the runtime.</para>
6235 <para>This causes difficulties if you have a multi-module program
6236 containing Template Haskell code and you need to compile it for
6237 profiling, because GHC cannot load the profiled object code and use it
6238 when executing the splices. Fortunately GHC provides a workaround.
6239 The basic idea is to compile the program twice:</para>
6243 <para>Compile the program or library first the normal way, without
6244 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6247 <para>Then compile it again with <option>-prof</option>, and
6248 additionally use <option>-osuf
6249 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6250 to name the object files differently (you can choose any suffix
6251 that isn't the normal object suffix here). GHC will automatically
6252 load the object files built in the first step when executing splice
6253 expressions. If you omit the <option>-osuf</option> flag when
6254 building with <option>-prof</option> and Template Haskell is used,
6255 GHC will emit an error message. </para>
6260 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6261 <para>Quasi-quotation allows patterns and expressions to be written using
6262 programmer-defined concrete syntax; the motivation behind the extension and
6263 several examples are documented in
6264 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6265 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6266 2007). The example below shows how to write a quasiquoter for a simple
6267 expression language.</para>
6270 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6271 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6272 functions for quoting expressions and patterns, respectively. The first argument
6273 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6274 context of the quasi-quotation statement determines which of the two parsers is
6275 called: if the quasi-quotation occurs in an expression context, the expression
6276 parser is called, and if it occurs in a pattern context, the pattern parser is
6280 Note that in the example we make use of an antiquoted
6281 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6282 (this syntax for anti-quotation was defined by the parser's
6283 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6284 integer value argument of the constructor <literal>IntExpr</literal> when
6285 pattern matching. Please see the referenced paper for further details regarding
6286 anti-quotation as well as the description of a technique that uses SYB to
6287 leverage a single parser of type <literal>String -> a</literal> to generate both
6288 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6289 pattern parser that returns a value of type <literal>Q Pat</literal>.
6292 <para>In general, a quasi-quote has the form
6293 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6294 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6295 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6296 can be arbitrary, and may contain newlines.
6299 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6300 the example, <literal>expr</literal> cannot be defined
6301 in <literal>Main.hs</literal> where it is used, but must be imported.
6312 main = do { print $ eval [$expr|1 + 2|]
6314 { [$expr|'int:n|] -> print n
6323 import qualified Language.Haskell.TH as TH
6324 import Language.Haskell.TH.Quote
6326 data Expr = IntExpr Integer
6327 | AntiIntExpr String
6328 | BinopExpr BinOp Expr Expr
6330 deriving(Show, Typeable, Data)
6336 deriving(Show, Typeable, Data)
6338 eval :: Expr -> Integer
6339 eval (IntExpr n) = n
6340 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6347 expr = QuasiQuoter parseExprExp parseExprPat
6349 -- Parse an Expr, returning its representation as
6350 -- either a Q Exp or a Q Pat. See the referenced paper
6351 -- for how to use SYB to do this by writing a single
6352 -- parser of type String -> Expr instead of two
6353 -- separate parsers.
6355 parseExprExp :: String -> Q Exp
6358 parseExprPat :: String -> Q Pat
6362 <para>Now run the compiler:
6365 $ ghc --make -XQuasiQuotes Main.hs -o main
6368 <para>Run "main" and here is your output:</para>
6380 <!-- ===================== Arrow notation =================== -->
6382 <sect1 id="arrow-notation">
6383 <title>Arrow notation
6386 <para>Arrows are a generalization of monads introduced by John Hughes.
6387 For more details, see
6392 “Generalising Monads to Arrows”,
6393 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6394 pp67–111, May 2000.
6395 The paper that introduced arrows: a friendly introduction, motivated with
6396 programming examples.
6402 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6403 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6404 Introduced the notation described here.
6410 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6411 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6418 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6419 John Hughes, in <citetitle>5th International Summer School on
6420 Advanced Functional Programming</citetitle>,
6421 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6423 This paper includes another introduction to the notation,
6424 with practical examples.
6430 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6431 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6432 A terse enumeration of the formal rules used
6433 (extracted from comments in the source code).
6439 The arrows web page at
6440 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6445 With the <option>-XArrows</option> flag, GHC supports the arrow
6446 notation described in the second of these papers,
6447 translating it using combinators from the
6448 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6450 What follows is a brief introduction to the notation;
6451 it won't make much sense unless you've read Hughes's paper.
6454 <para>The extension adds a new kind of expression for defining arrows:
6456 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6457 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6459 where <literal>proc</literal> is a new keyword.
6460 The variables of the pattern are bound in the body of the
6461 <literal>proc</literal>-expression,
6462 which is a new sort of thing called a <firstterm>command</firstterm>.
6463 The syntax of commands is as follows:
6465 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6466 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6467 | <replaceable>cmd</replaceable><superscript>0</superscript>
6469 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6470 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6471 infix operators as for expressions, and
6473 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6474 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6475 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6476 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6477 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6478 | <replaceable>fcmd</replaceable>
6480 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6481 | ( <replaceable>cmd</replaceable> )
6482 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6484 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6485 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6486 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6487 | <replaceable>cmd</replaceable>
6489 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6490 except that the bodies are commands instead of expressions.
6494 Commands produce values, but (like monadic computations)
6495 may yield more than one value,
6496 or none, and may do other things as well.
6497 For the most part, familiarity with monadic notation is a good guide to
6499 However the values of expressions, even monadic ones,
6500 are determined by the values of the variables they contain;
6501 this is not necessarily the case for commands.
6505 A simple example of the new notation is the expression
6507 proc x -> f -< x+1
6509 We call this a <firstterm>procedure</firstterm> or
6510 <firstterm>arrow abstraction</firstterm>.
6511 As with a lambda expression, the variable <literal>x</literal>
6512 is a new variable bound within the <literal>proc</literal>-expression.
6513 It refers to the input to the arrow.
6514 In the above example, <literal>-<</literal> is not an identifier but an
6515 new reserved symbol used for building commands from an expression of arrow
6516 type and an expression to be fed as input to that arrow.
6517 (The weird look will make more sense later.)
6518 It may be read as analogue of application for arrows.
6519 The above example is equivalent to the Haskell expression
6521 arr (\ x -> x+1) >>> f
6523 That would make no sense if the expression to the left of
6524 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6525 More generally, the expression to the left of <literal>-<</literal>
6526 may not involve any <firstterm>local variable</firstterm>,
6527 i.e. a variable bound in the current arrow abstraction.
6528 For such a situation there is a variant <literal>-<<</literal>, as in
6530 proc x -> f x -<< x+1
6532 which is equivalent to
6534 arr (\ x -> (f x, x+1)) >>> app
6536 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6538 Such an arrow is equivalent to a monad, so if you're using this form
6539 you may find a monadic formulation more convenient.
6543 <title>do-notation for commands</title>
6546 Another form of command is a form of <literal>do</literal>-notation.
6547 For example, you can write
6556 You can read this much like ordinary <literal>do</literal>-notation,
6557 but with commands in place of monadic expressions.
6558 The first line sends the value of <literal>x+1</literal> as an input to
6559 the arrow <literal>f</literal>, and matches its output against
6560 <literal>y</literal>.
6561 In the next line, the output is discarded.
6562 The arrow <function>returnA</function> is defined in the
6563 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6564 module as <literal>arr id</literal>.
6565 The above example is treated as an abbreviation for
6567 arr (\ x -> (x, x)) >>>
6568 first (arr (\ x -> x+1) >>> f) >>>
6569 arr (\ (y, x) -> (y, (x, y))) >>>
6570 first (arr (\ y -> 2*y) >>> g) >>>
6572 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6573 first (arr (\ (x, z) -> x*z) >>> h) >>>
6574 arr (\ (t, z) -> t+z) >>>
6577 Note that variables not used later in the composition are projected out.
6578 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6580 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6581 module, this reduces to
6583 arr (\ x -> (x+1, x)) >>>
6585 arr (\ (y, x) -> (2*y, (x, y))) >>>
6587 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6589 arr (\ (t, z) -> t+z)
6591 which is what you might have written by hand.
6592 With arrow notation, GHC keeps track of all those tuples of variables for you.
6596 Note that although the above translation suggests that
6597 <literal>let</literal>-bound variables like <literal>z</literal> must be
6598 monomorphic, the actual translation produces Core,
6599 so polymorphic variables are allowed.
6603 It's also possible to have mutually recursive bindings,
6604 using the new <literal>rec</literal> keyword, as in the following example:
6606 counter :: ArrowCircuit a => a Bool Int
6607 counter = proc reset -> do
6608 rec output <- returnA -< if reset then 0 else next
6609 next <- delay 0 -< output+1
6610 returnA -< output
6612 The translation of such forms uses the <function>loop</function> combinator,
6613 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6619 <title>Conditional commands</title>
6622 In the previous example, we used a conditional expression to construct the
6624 Sometimes we want to conditionally execute different commands, as in
6631 which is translated to
6633 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6634 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6636 Since the translation uses <function>|||</function>,
6637 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6641 There are also <literal>case</literal> commands, like
6647 y <- h -< (x1, x2)
6651 The syntax is the same as for <literal>case</literal> expressions,
6652 except that the bodies of the alternatives are commands rather than expressions.
6653 The translation is similar to that of <literal>if</literal> commands.
6659 <title>Defining your own control structures</title>
6662 As we're seen, arrow notation provides constructs,
6663 modelled on those for expressions,
6664 for sequencing, value recursion and conditionals.
6665 But suitable combinators,
6666 which you can define in ordinary Haskell,
6667 may also be used to build new commands out of existing ones.
6668 The basic idea is that a command defines an arrow from environments to values.
6669 These environments assign values to the free local variables of the command.
6670 Thus combinators that produce arrows from arrows
6671 may also be used to build commands from commands.
6672 For example, the <literal>ArrowChoice</literal> class includes a combinator
6674 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6676 so we can use it to build commands:
6678 expr' = proc x -> do
6681 symbol Plus -< ()
6682 y <- term -< ()
6685 symbol Minus -< ()
6686 y <- term -< ()
6689 (The <literal>do</literal> on the first line is needed to prevent the first
6690 <literal><+> ...</literal> from being interpreted as part of the
6691 expression on the previous line.)
6692 This is equivalent to
6694 expr' = (proc x -> returnA -< x)
6695 <+> (proc x -> do
6696 symbol Plus -< ()
6697 y <- term -< ()
6699 <+> (proc x -> do
6700 symbol Minus -< ()
6701 y <- term -< ()
6704 It is essential that this operator be polymorphic in <literal>e</literal>
6705 (representing the environment input to the command
6706 and thence to its subcommands)
6707 and satisfy the corresponding naturality property
6709 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6711 at least for strict <literal>k</literal>.
6712 (This should be automatic if you're not using <function>seq</function>.)
6713 This ensures that environments seen by the subcommands are environments
6714 of the whole command,
6715 and also allows the translation to safely trim these environments.
6716 The operator must also not use any variable defined within the current
6721 We could define our own operator
6723 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6724 untilA body cond = proc x ->
6725 b <- cond -< x
6726 if b then returnA -< ()
6729 untilA body cond -< x
6731 and use it in the same way.
6732 Of course this infix syntax only makes sense for binary operators;
6733 there is also a more general syntax involving special brackets:
6737 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6744 <title>Primitive constructs</title>
6747 Some operators will need to pass additional inputs to their subcommands.
6748 For example, in an arrow type supporting exceptions,
6749 the operator that attaches an exception handler will wish to pass the
6750 exception that occurred to the handler.
6751 Such an operator might have a type
6753 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6755 where <literal>Ex</literal> is the type of exceptions handled.
6756 You could then use this with arrow notation by writing a command
6758 body `handleA` \ ex -> handler
6760 so that if an exception is raised in the command <literal>body</literal>,
6761 the variable <literal>ex</literal> is bound to the value of the exception
6762 and the command <literal>handler</literal>,
6763 which typically refers to <literal>ex</literal>, is entered.
6764 Though the syntax here looks like a functional lambda,
6765 we are talking about commands, and something different is going on.
6766 The input to the arrow represented by a command consists of values for
6767 the free local variables in the command, plus a stack of anonymous values.
6768 In all the prior examples, this stack was empty.
6769 In the second argument to <function>handleA</function>,
6770 this stack consists of one value, the value of the exception.
6771 The command form of lambda merely gives this value a name.
6776 the values on the stack are paired to the right of the environment.
6777 So operators like <function>handleA</function> that pass
6778 extra inputs to their subcommands can be designed for use with the notation
6779 by pairing the values with the environment in this way.
6780 More precisely, the type of each argument of the operator (and its result)
6781 should have the form
6783 a (...(e,t1), ... tn) t
6785 where <replaceable>e</replaceable> is a polymorphic variable
6786 (representing the environment)
6787 and <replaceable>ti</replaceable> are the types of the values on the stack,
6788 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6789 The polymorphic variable <replaceable>e</replaceable> must not occur in
6790 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6791 <replaceable>t</replaceable>.
6792 However the arrows involved need not be the same.
6793 Here are some more examples of suitable operators:
6795 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6796 runReader :: ... => a e c -> a' (e,State) c
6797 runState :: ... => a e c -> a' (e,State) (c,State)
6799 We can supply the extra input required by commands built with the last two
6800 by applying them to ordinary expressions, as in
6804 (|runReader (do { ... })|) s
6806 which adds <literal>s</literal> to the stack of inputs to the command
6807 built using <function>runReader</function>.
6811 The command versions of lambda abstraction and application are analogous to
6812 the expression versions.
6813 In particular, the beta and eta rules describe equivalences of commands.
6814 These three features (operators, lambda abstraction and application)
6815 are the core of the notation; everything else can be built using them,
6816 though the results would be somewhat clumsy.
6817 For example, we could simulate <literal>do</literal>-notation by defining
6819 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6820 u `bind` f = returnA &&& u >>> f
6822 bind_ :: Arrow a => a e b -> a e c -> a e c
6823 u `bind_` f = u `bind` (arr fst >>> f)
6825 We could simulate <literal>if</literal> by defining
6827 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6828 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6835 <title>Differences with the paper</title>
6840 <para>Instead of a single form of arrow application (arrow tail) with two
6841 translations, the implementation provides two forms
6842 <quote><literal>-<</literal></quote> (first-order)
6843 and <quote><literal>-<<</literal></quote> (higher-order).
6848 <para>User-defined operators are flagged with banana brackets instead of
6849 a new <literal>form</literal> keyword.
6858 <title>Portability</title>
6861 Although only GHC implements arrow notation directly,
6862 there is also a preprocessor
6864 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6865 that translates arrow notation into Haskell 98
6866 for use with other Haskell systems.
6867 You would still want to check arrow programs with GHC;
6868 tracing type errors in the preprocessor output is not easy.
6869 Modules intended for both GHC and the preprocessor must observe some
6870 additional restrictions:
6875 The module must import
6876 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6882 The preprocessor cannot cope with other Haskell extensions.
6883 These would have to go in separate modules.
6889 Because the preprocessor targets Haskell (rather than Core),
6890 <literal>let</literal>-bound variables are monomorphic.
6901 <!-- ==================== BANG PATTERNS ================= -->
6903 <sect1 id="bang-patterns">
6904 <title>Bang patterns
6905 <indexterm><primary>Bang patterns</primary></indexterm>
6907 <para>GHC supports an extension of pattern matching called <emphasis>bang
6908 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6909 Bang patterns are under consideration for Haskell Prime.
6911 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6912 prime feature description</ulink> contains more discussion and examples
6913 than the material below.
6916 The key change is the addition of a new rule to the
6917 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6918 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6919 against a value <replaceable>v</replaceable> behaves as follows:
6921 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6922 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6926 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6929 <sect2 id="bang-patterns-informal">
6930 <title>Informal description of bang patterns
6933 The main idea is to add a single new production to the syntax of patterns:
6937 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6938 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6943 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6944 whereas without the bang it would be lazy.
6945 Bang patterns can be nested of course:
6949 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6950 <literal>y</literal>.
6951 A bang only really has an effect if it precedes a variable or wild-card pattern:
6956 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6957 putting a bang before a pattern that
6958 forces evaluation anyway does nothing.
6961 There is one (apparent) exception to this general rule that a bang only
6962 makes a difference when it precedes a variable or wild-card: a bang at the
6963 top level of a <literal>let</literal> or <literal>where</literal>
6964 binding makes the binding strict, regardless of the pattern. For example:
6968 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6969 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6970 (We say "apparent" exception because the Right Way to think of it is that the bang
6971 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6972 is part of the syntax of the <emphasis>binding</emphasis>.)
6973 Nested bangs in a pattern binding behave uniformly with all other forms of
6974 pattern matching. For example
6976 let (!x,[y]) = e in b
6978 is equivalent to this:
6980 let { t = case e of (x,[y]) -> x `seq` (x,y)
6985 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6986 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6987 evaluation of <literal>x</literal>.
6990 Bang patterns work in <literal>case</literal> expressions too, of course:
6992 g5 x = let y = f x in body
6993 g6 x = case f x of { y -> body }
6994 g7 x = case f x of { !y -> body }
6996 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6997 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6998 result, and then evaluates <literal>body</literal>.
7003 <sect2 id="bang-patterns-sem">
7004 <title>Syntax and semantics
7008 We add a single new production to the syntax of patterns:
7012 There is one problem with syntactic ambiguity. Consider:
7016 Is this a definition of the infix function "<literal>(!)</literal>",
7017 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7018 ambiguity in favour of the latter. If you want to define
7019 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7024 The semantics of Haskell pattern matching is described in <ulink
7025 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7026 Section 3.17.2</ulink> of the Haskell Report. To this description add
7027 one extra item 10, saying:
7028 <itemizedlist><listitem><para>Matching
7029 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7030 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7031 <listitem><para>otherwise, <literal>pat</literal> is matched against
7032 <literal>v</literal></para></listitem>
7034 </para></listitem></itemizedlist>
7035 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7036 Section 3.17.3</ulink>, add a new case (t):
7038 case v of { !pat -> e; _ -> e' }
7039 = v `seq` case v of { pat -> e; _ -> e' }
7042 That leaves let expressions, whose translation is given in
7043 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7045 of the Haskell Report.
7046 In the translation box, first apply
7047 the following transformation: for each pattern <literal>pi</literal> that is of
7048 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7049 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7050 have a bang at the top, apply the rules in the existing box.
7052 <para>The effect of the let rule is to force complete matching of the pattern
7053 <literal>qi</literal> before evaluation of the body is begun. The bang is
7054 retained in the translated form in case <literal>qi</literal> is a variable,
7062 The let-binding can be recursive. However, it is much more common for
7063 the let-binding to be non-recursive, in which case the following law holds:
7064 <literal>(let !p = rhs in body)</literal>
7066 <literal>(case rhs of !p -> body)</literal>
7069 A pattern with a bang at the outermost level is not allowed at the top level of
7075 <!-- ==================== ASSERTIONS ================= -->
7077 <sect1 id="assertions">
7079 <indexterm><primary>Assertions</primary></indexterm>
7083 If you want to make use of assertions in your standard Haskell code, you
7084 could define a function like the following:
7090 assert :: Bool -> a -> a
7091 assert False x = error "assertion failed!"
7098 which works, but gives you back a less than useful error message --
7099 an assertion failed, but which and where?
7103 One way out is to define an extended <function>assert</function> function which also
7104 takes a descriptive string to include in the error message and
7105 perhaps combine this with the use of a pre-processor which inserts
7106 the source location where <function>assert</function> was used.
7110 Ghc offers a helping hand here, doing all of this for you. For every
7111 use of <function>assert</function> in the user's source:
7117 kelvinToC :: Double -> Double
7118 kelvinToC k = assert (k >= 0.0) (k+273.15)
7124 Ghc will rewrite this to also include the source location where the
7131 assert pred val ==> assertError "Main.hs|15" pred val
7137 The rewrite is only performed by the compiler when it spots
7138 applications of <function>Control.Exception.assert</function>, so you
7139 can still define and use your own versions of
7140 <function>assert</function>, should you so wish. If not, import
7141 <literal>Control.Exception</literal> to make use
7142 <function>assert</function> in your code.
7146 GHC ignores assertions when optimisation is turned on with the
7147 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7148 <literal>assert pred e</literal> will be rewritten to
7149 <literal>e</literal>. You can also disable assertions using the
7150 <option>-fignore-asserts</option>
7151 option<indexterm><primary><option>-fignore-asserts</option></primary>
7152 </indexterm>.</para>
7155 Assertion failures can be caught, see the documentation for the
7156 <literal>Control.Exception</literal> library for the details.
7162 <!-- =============================== PRAGMAS =========================== -->
7164 <sect1 id="pragmas">
7165 <title>Pragmas</title>
7167 <indexterm><primary>pragma</primary></indexterm>
7169 <para>GHC supports several pragmas, or instructions to the
7170 compiler placed in the source code. Pragmas don't normally affect
7171 the meaning of the program, but they might affect the efficiency
7172 of the generated code.</para>
7174 <para>Pragmas all take the form
7176 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7178 where <replaceable>word</replaceable> indicates the type of
7179 pragma, and is followed optionally by information specific to that
7180 type of pragma. Case is ignored in
7181 <replaceable>word</replaceable>. The various values for
7182 <replaceable>word</replaceable> that GHC understands are described
7183 in the following sections; any pragma encountered with an
7184 unrecognised <replaceable>word</replaceable> is
7185 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7186 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7188 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7192 pragma must precede the <literal>module</literal> keyword in the file.
7195 There can be as many file-header pragmas as you please, and they can be
7196 preceded or followed by comments.
7199 File-header pragmas are read once only, before
7200 pre-processing the file (e.g. with cpp).
7203 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7204 <literal>{-# OPTIONS_GHC #-}</literal>, and
7205 <literal>{-# INCLUDE #-}</literal>.
7210 <sect2 id="language-pragma">
7211 <title>LANGUAGE pragma</title>
7213 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7214 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7216 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7218 It is the intention that all Haskell compilers support the
7219 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7220 all extensions are supported by all compilers, of
7221 course. The <literal>LANGUAGE</literal> pragma should be used instead
7222 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7224 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7226 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7228 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7230 <para>Every language extension can also be turned into a command-line flag
7231 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7232 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7235 <para>A list of all supported language extensions can be obtained by invoking
7236 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7238 <para>Any extension from the <literal>Extension</literal> type defined in
7240 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7241 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7245 <sect2 id="options-pragma">
7246 <title>OPTIONS_GHC pragma</title>
7247 <indexterm><primary>OPTIONS_GHC</primary>
7249 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7252 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7253 additional options that are given to the compiler when compiling
7254 this source file. See <xref linkend="source-file-options"/> for
7257 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7258 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7261 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7263 <sect2 id="include-pragma">
7264 <title>INCLUDE pragma</title>
7266 <para>The <literal>INCLUDE</literal> used to be necessary for
7267 specifying header files to be included when using the FFI and
7268 compiling via C. It is no longer required for GHC, but is
7269 accepted (and ignored) for compatibility with other
7273 <sect2 id="warning-deprecated-pragma">
7274 <title>WARNING and DEPRECATED pragmas</title>
7275 <indexterm><primary>WARNING</primary></indexterm>
7276 <indexterm><primary>DEPRECATED</primary></indexterm>
7278 <para>The WARNING pragma allows you to attach an arbitrary warning
7279 to a particular function, class, or type.
7280 A DEPRECATED pragma lets you specify that
7281 a particular function, class, or type is deprecated.
7282 There are two ways of using these pragmas.
7286 <para>You can work on an entire module thus:</para>
7288 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7293 module Wibble {-# WARNING "This is an unstable interface." #-} where
7296 <para>When you compile any module that import
7297 <literal>Wibble</literal>, GHC will print the specified
7302 <para>You can attach a warning to a function, class, type, or data constructor, with the
7303 following top-level declarations:</para>
7305 {-# DEPRECATED f, C, T "Don't use these" #-}
7306 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7308 <para>When you compile any module that imports and uses any
7309 of the specified entities, GHC will print the specified
7311 <para> You can only attach to entities declared at top level in the module
7312 being compiled, and you can only use unqualified names in the list of
7313 entities. A capitalised name, such as <literal>T</literal>
7314 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7315 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7316 both are in scope. If both are in scope, there is currently no way to
7317 specify one without the other (c.f. fixities
7318 <xref linkend="infix-tycons"/>).</para>
7321 Warnings and deprecations are not reported for
7322 (a) uses within the defining module, and
7323 (b) uses in an export list.
7324 The latter reduces spurious complaints within a library
7325 in which one module gathers together and re-exports
7326 the exports of several others.
7328 <para>You can suppress the warnings with the flag
7329 <option>-fno-warn-warnings-deprecations</option>.</para>
7332 <sect2 id="inline-noinline-pragma">
7333 <title>INLINE and NOINLINE pragmas</title>
7335 <para>These pragmas control the inlining of function
7338 <sect3 id="inline-pragma">
7339 <title>INLINE pragma</title>
7340 <indexterm><primary>INLINE</primary></indexterm>
7342 <para>GHC (with <option>-O</option>, as always) tries to
7343 inline (or “unfold”) functions/values that are
7344 “small enough,” thus avoiding the call overhead
7345 and possibly exposing other more-wonderful optimisations.
7346 Normally, if GHC decides a function is “too
7347 expensive” to inline, it will not do so, nor will it
7348 export that unfolding for other modules to use.</para>
7350 <para>The sledgehammer you can bring to bear is the
7351 <literal>INLINE</literal><indexterm><primary>INLINE
7352 pragma</primary></indexterm> pragma, used thusly:</para>
7355 key_function :: Int -> String -> (Bool, Double)
7356 {-# INLINE key_function #-}
7359 <para>The major effect of an <literal>INLINE</literal> pragma
7360 is to declare a function's “cost” to be very low.
7361 The normal unfolding machinery will then be very keen to
7362 inline it. However, an <literal>INLINE</literal> pragma for a
7363 function "<literal>f</literal>" has a number of other effects:
7366 No functions are inlined into <literal>f</literal>. Otherwise
7367 GHC might inline a big function into <literal>f</literal>'s right hand side,
7368 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7371 The float-in, float-out, and common-sub-expression transformations are not
7372 applied to the body of <literal>f</literal>.
7375 An INLINE function is not worker/wrappered by strictness analysis.
7376 It's going to be inlined wholesale instead.
7379 All of these effects are aimed at ensuring that what gets inlined is
7380 exactly what you asked for, no more and no less.
7382 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7383 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7384 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7385 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7386 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7387 when there is no choice even an INLINE function can be selected, in which case
7388 the INLINE pragma is ignored.
7389 For example, for a self-recursive function, the loop breaker can only be the function
7390 itself, so an INLINE pragma is always ignored.</para>
7392 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7393 function can be put anywhere its type signature could be
7396 <para><literal>INLINE</literal> pragmas are a particularly
7398 <literal>then</literal>/<literal>return</literal> (or
7399 <literal>bind</literal>/<literal>unit</literal>) functions in
7400 a monad. For example, in GHC's own
7401 <literal>UniqueSupply</literal> monad code, we have:</para>
7404 {-# INLINE thenUs #-}
7405 {-# INLINE returnUs #-}
7408 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7409 linkend="noinline-pragma"/>).</para>
7411 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7412 so if you want your code to be HBC-compatible you'll have to surround
7413 the pragma with C pre-processor directives
7414 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7418 <sect3 id="noinline-pragma">
7419 <title>NOINLINE pragma</title>
7421 <indexterm><primary>NOINLINE</primary></indexterm>
7422 <indexterm><primary>NOTINLINE</primary></indexterm>
7424 <para>The <literal>NOINLINE</literal> pragma does exactly what
7425 you'd expect: it stops the named function from being inlined
7426 by the compiler. You shouldn't ever need to do this, unless
7427 you're very cautious about code size.</para>
7429 <para><literal>NOTINLINE</literal> is a synonym for
7430 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7431 specified by Haskell 98 as the standard way to disable
7432 inlining, so it should be used if you want your code to be
7436 <sect3 id="phase-control">
7437 <title>Phase control</title>
7439 <para> Sometimes you want to control exactly when in GHC's
7440 pipeline the INLINE pragma is switched on. Inlining happens
7441 only during runs of the <emphasis>simplifier</emphasis>. Each
7442 run of the simplifier has a different <emphasis>phase
7443 number</emphasis>; the phase number decreases towards zero.
7444 If you use <option>-dverbose-core2core</option> you'll see the
7445 sequence of phase numbers for successive runs of the
7446 simplifier. In an INLINE pragma you can optionally specify a
7450 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7451 <literal>f</literal>
7452 until phase <literal>k</literal>, but from phase
7453 <literal>k</literal> onwards be very keen to inline it.
7456 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7457 <literal>f</literal>
7458 until phase <literal>k</literal>, but from phase
7459 <literal>k</literal> onwards do not inline it.
7462 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7463 <literal>f</literal>
7464 until phase <literal>k</literal>, but from phase
7465 <literal>k</literal> onwards be willing to inline it (as if
7466 there was no pragma).
7469 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7470 <literal>f</literal>
7471 until phase <literal>k</literal>, but from phase
7472 <literal>k</literal> onwards do not inline it.
7475 The same information is summarised here:
7477 -- Before phase 2 Phase 2 and later
7478 {-# INLINE [2] f #-} -- No Yes
7479 {-# INLINE [~2] f #-} -- Yes No
7480 {-# NOINLINE [2] f #-} -- No Maybe
7481 {-# NOINLINE [~2] f #-} -- Maybe No
7483 {-# INLINE f #-} -- Yes Yes
7484 {-# NOINLINE f #-} -- No No
7486 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7487 function body is small, or it is applied to interesting-looking arguments etc).
7488 Another way to understand the semantics is this:
7490 <listitem><para>For both INLINE and NOINLINE, the phase number says
7491 when inlining is allowed at all.</para></listitem>
7492 <listitem><para>The INLINE pragma has the additional effect of making the
7493 function body look small, so that when inlining is allowed it is very likely to
7498 <para>The same phase-numbering control is available for RULES
7499 (<xref linkend="rewrite-rules"/>).</para>
7503 <sect2 id="annotation-pragmas">
7504 <title>ANN pragmas</title>
7506 <para>GHC offers the ability to annotate various code constructs with additional
7507 data by using three pragmas. This data can then be inspected at a later date by
7508 using GHC-as-a-library.</para>
7510 <sect3 id="ann-pragma">
7511 <title>Annotating values</title>
7513 <indexterm><primary>ANN</primary></indexterm>
7515 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7516 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7517 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7518 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7519 you would do this:</para>
7522 {-# ANN foo (Just "Hello") #-}
7527 A number of restrictions apply to use of annotations:
7529 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7530 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7531 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7532 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7533 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7535 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7536 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7539 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7540 please give the GHC team a shout</ulink>.
7543 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7544 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7547 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7552 <sect3 id="typeann-pragma">
7553 <title>Annotating types</title>
7555 <indexterm><primary>ANN type</primary></indexterm>
7556 <indexterm><primary>ANN</primary></indexterm>
7558 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7561 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7566 <sect3 id="modann-pragma">
7567 <title>Annotating modules</title>
7569 <indexterm><primary>ANN module</primary></indexterm>
7570 <indexterm><primary>ANN</primary></indexterm>
7572 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7575 {-# ANN module (Just "A `Maybe String' annotation") #-}
7580 <sect2 id="line-pragma">
7581 <title>LINE pragma</title>
7583 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7584 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7585 <para>This pragma is similar to C's <literal>#line</literal>
7586 pragma, and is mainly for use in automatically generated Haskell
7587 code. It lets you specify the line number and filename of the
7588 original code; for example</para>
7590 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7592 <para>if you'd generated the current file from something called
7593 <filename>Foo.vhs</filename> and this line corresponds to line
7594 42 in the original. GHC will adjust its error messages to refer
7595 to the line/file named in the <literal>LINE</literal>
7600 <title>RULES pragma</title>
7602 <para>The RULES pragma lets you specify rewrite rules. It is
7603 described in <xref linkend="rewrite-rules"/>.</para>
7606 <sect2 id="specialize-pragma">
7607 <title>SPECIALIZE pragma</title>
7609 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7610 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7611 <indexterm><primary>overloading, death to</primary></indexterm>
7613 <para>(UK spelling also accepted.) For key overloaded
7614 functions, you can create extra versions (NB: more code space)
7615 specialised to particular types. Thus, if you have an
7616 overloaded function:</para>
7619 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7622 <para>If it is heavily used on lists with
7623 <literal>Widget</literal> keys, you could specialise it as
7627 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7630 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7631 be put anywhere its type signature could be put.</para>
7633 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7634 (a) a specialised version of the function and (b) a rewrite rule
7635 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7636 un-specialised function into a call to the specialised one.</para>
7638 <para>The type in a SPECIALIZE pragma can be any type that is less
7639 polymorphic than the type of the original function. In concrete terms,
7640 if the original function is <literal>f</literal> then the pragma
7642 {-# SPECIALIZE f :: <type> #-}
7644 is valid if and only if the definition
7646 f_spec :: <type>
7649 is valid. Here are some examples (where we only give the type signature
7650 for the original function, not its code):
7652 f :: Eq a => a -> b -> b
7653 {-# SPECIALISE f :: Int -> b -> b #-}
7655 g :: (Eq a, Ix b) => a -> b -> b
7656 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7658 h :: Eq a => a -> a -> a
7659 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7661 The last of these examples will generate a
7662 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7663 well. If you use this kind of specialisation, let us know how well it works.
7666 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7667 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7668 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7669 The <literal>INLINE</literal> pragma affects the specialised version of the
7670 function (only), and applies even if the function is recursive. The motivating
7673 -- A GADT for arrays with type-indexed representation
7675 ArrInt :: !Int -> ByteArray# -> Arr Int
7676 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7678 (!:) :: Arr e -> Int -> e
7679 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7680 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7681 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7682 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7684 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7685 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7686 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7687 the specialised function will be inlined. It has two calls to
7688 <literal>(!:)</literal>,
7689 both at type <literal>Int</literal>. Both these calls fire the first
7690 specialisation, whose body is also inlined. The result is a type-based
7691 unrolling of the indexing function.</para>
7692 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7693 on an ordinarily-recursive function.</para>
7695 <para>Note: In earlier versions of GHC, it was possible to provide your own
7696 specialised function for a given type:
7699 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7702 This feature has been removed, as it is now subsumed by the
7703 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7707 <sect2 id="specialize-instance-pragma">
7708 <title>SPECIALIZE instance pragma
7712 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7713 <indexterm><primary>overloading, death to</primary></indexterm>
7714 Same idea, except for instance declarations. For example:
7717 instance (Eq a) => Eq (Foo a) where {
7718 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7722 The pragma must occur inside the <literal>where</literal> part
7723 of the instance declaration.
7726 Compatible with HBC, by the way, except perhaps in the placement
7732 <sect2 id="unpack-pragma">
7733 <title>UNPACK pragma</title>
7735 <indexterm><primary>UNPACK</primary></indexterm>
7737 <para>The <literal>UNPACK</literal> indicates to the compiler
7738 that it should unpack the contents of a constructor field into
7739 the constructor itself, removing a level of indirection. For
7743 data T = T {-# UNPACK #-} !Float
7744 {-# UNPACK #-} !Float
7747 <para>will create a constructor <literal>T</literal> containing
7748 two unboxed floats. This may not always be an optimisation: if
7749 the <function>T</function> constructor is scrutinised and the
7750 floats passed to a non-strict function for example, they will
7751 have to be reboxed (this is done automatically by the
7754 <para>Unpacking constructor fields should only be used in
7755 conjunction with <option>-O</option>, in order to expose
7756 unfoldings to the compiler so the reboxing can be removed as
7757 often as possible. For example:</para>
7761 f (T f1 f2) = f1 + f2
7764 <para>The compiler will avoid reboxing <function>f1</function>
7765 and <function>f2</function> by inlining <function>+</function>
7766 on floats, but only when <option>-O</option> is on.</para>
7768 <para>Any single-constructor data is eligible for unpacking; for
7772 data T = T {-# UNPACK #-} !(Int,Int)
7775 <para>will store the two <literal>Int</literal>s directly in the
7776 <function>T</function> constructor, by flattening the pair.
7777 Multi-level unpacking is also supported:
7780 data T = T {-# UNPACK #-} !S
7781 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7784 will store two unboxed <literal>Int#</literal>s
7785 directly in the <function>T</function> constructor. The
7786 unpacker can see through newtypes, too.</para>
7788 <para>If a field cannot be unpacked, you will not get a warning,
7789 so it might be an idea to check the generated code with
7790 <option>-ddump-simpl</option>.</para>
7792 <para>See also the <option>-funbox-strict-fields</option> flag,
7793 which essentially has the effect of adding
7794 <literal>{-# UNPACK #-}</literal> to every strict
7795 constructor field.</para>
7798 <sect2 id="source-pragma">
7799 <title>SOURCE pragma</title>
7801 <indexterm><primary>SOURCE</primary></indexterm>
7802 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7803 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7809 <!-- ======================= REWRITE RULES ======================== -->
7811 <sect1 id="rewrite-rules">
7812 <title>Rewrite rules
7814 <indexterm><primary>RULES pragma</primary></indexterm>
7815 <indexterm><primary>pragma, RULES</primary></indexterm>
7816 <indexterm><primary>rewrite rules</primary></indexterm></title>
7819 The programmer can specify rewrite rules as part of the source program
7825 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7830 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7831 If you need more information, then <option>-ddump-rule-firings</option> shows you
7832 each individual rule firing in detail.
7836 <title>Syntax</title>
7839 From a syntactic point of view:
7845 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7846 may be generated by the layout rule).
7852 The layout rule applies in a pragma.
7853 Currently no new indentation level
7854 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7855 you must lay out the starting in the same column as the enclosing definitions.
7858 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7859 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7862 Furthermore, the closing <literal>#-}</literal>
7863 should start in a column to the right of the opening <literal>{-#</literal>.
7869 Each rule has a name, enclosed in double quotes. The name itself has
7870 no significance at all. It is only used when reporting how many times the rule fired.
7876 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7877 immediately after the name of the rule. Thus:
7880 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7883 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7884 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7893 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7894 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7895 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7896 by spaces, just like in a type <literal>forall</literal>.
7902 A pattern variable may optionally have a type signature.
7903 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7904 For example, here is the <literal>foldr/build</literal> rule:
7907 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7908 foldr k z (build g) = g k z
7911 Since <function>g</function> has a polymorphic type, it must have a type signature.
7918 The left hand side of a rule must consist of a top-level variable applied
7919 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7922 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7923 "wrong2" forall f. f True = True
7926 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7933 A rule does not need to be in the same module as (any of) the
7934 variables it mentions, though of course they need to be in scope.
7940 All rules are implicitly exported from the module, and are therefore
7941 in force in any module that imports the module that defined the rule, directly
7942 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7943 in force when compiling A.) The situation is very similar to that for instance
7951 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7952 any other flag settings. Furthermore, inside a RULE, the language extension
7953 <option>-XScopedTypeVariables</option> is automatically enabled; see
7954 <xref linkend="scoped-type-variables"/>.
7960 Like other pragmas, RULE pragmas are always checked for scope errors, and
7961 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7962 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7963 if the <option>-fenable-rewrite-rules</option> flag is
7964 on (see <xref linkend="rule-semantics"/>).
7973 <sect2 id="rule-semantics">
7974 <title>Semantics</title>
7977 From a semantic point of view:
7982 Rules are enabled (that is, used during optimisation)
7983 by the <option>-fenable-rewrite-rules</option> flag.
7984 This flag is implied by <option>-O</option>, and may be switched
7985 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7986 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7987 may not do what you expect, though, because without <option>-O</option> GHC
7988 ignores all optimisation information in interface files;
7989 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7990 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7991 has no effect on parsing or typechecking.
7997 Rules are regarded as left-to-right rewrite rules.
7998 When GHC finds an expression that is a substitution instance of the LHS
7999 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8000 By "a substitution instance" we mean that the LHS can be made equal to the
8001 expression by substituting for the pattern variables.
8008 GHC makes absolutely no attempt to verify that the LHS and RHS
8009 of a rule have the same meaning. That is undecidable in general, and
8010 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8017 GHC makes no attempt to make sure that the rules are confluent or
8018 terminating. For example:
8021 "loop" forall x y. f x y = f y x
8024 This rule will cause the compiler to go into an infinite loop.
8031 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8037 GHC currently uses a very simple, syntactic, matching algorithm
8038 for matching a rule LHS with an expression. It seeks a substitution
8039 which makes the LHS and expression syntactically equal modulo alpha
8040 conversion. The pattern (rule), but not the expression, is eta-expanded if
8041 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8042 But not beta conversion (that's called higher-order matching).
8046 Matching is carried out on GHC's intermediate language, which includes
8047 type abstractions and applications. So a rule only matches if the
8048 types match too. See <xref linkend="rule-spec"/> below.
8054 GHC keeps trying to apply the rules as it optimises the program.
8055 For example, consider:
8064 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8065 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8066 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8067 not be substituted, and the rule would not fire.
8074 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8075 results. Consider this (artificial) example
8078 {-# RULES "f" f True = False #-}
8084 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8089 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8091 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8092 would have been a better chance that <literal>f</literal>'s RULE might fire.
8095 The way to get predictable behaviour is to use a NOINLINE
8096 pragma on <literal>f</literal>, to ensure
8097 that it is not inlined until its RULEs have had a chance to fire.
8107 <title>List fusion</title>
8110 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8111 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8112 intermediate list should be eliminated entirely.
8116 The following are good producers:
8128 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8134 Explicit lists (e.g. <literal>[True, False]</literal>)
8140 The cons constructor (e.g <literal>3:4:[]</literal>)
8146 <function>++</function>
8152 <function>map</function>
8158 <function>take</function>, <function>filter</function>
8164 <function>iterate</function>, <function>repeat</function>
8170 <function>zip</function>, <function>zipWith</function>
8179 The following are good consumers:
8191 <function>array</function> (on its second argument)
8197 <function>++</function> (on its first argument)
8203 <function>foldr</function>
8209 <function>map</function>
8215 <function>take</function>, <function>filter</function>
8221 <function>concat</function>
8227 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8233 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8234 will fuse with one but not the other)
8240 <function>partition</function>
8246 <function>head</function>
8252 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8258 <function>sequence_</function>
8264 <function>msum</function>
8270 <function>sortBy</function>
8279 So, for example, the following should generate no intermediate lists:
8282 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8288 This list could readily be extended; if there are Prelude functions that you use
8289 a lot which are not included, please tell us.
8293 If you want to write your own good consumers or producers, look at the
8294 Prelude definitions of the above functions to see how to do so.
8299 <sect2 id="rule-spec">
8300 <title>Specialisation
8304 Rewrite rules can be used to get the same effect as a feature
8305 present in earlier versions of GHC.
8306 For example, suppose that:
8309 genericLookup :: Ord a => Table a b -> a -> b
8310 intLookup :: Table Int b -> Int -> b
8313 where <function>intLookup</function> is an implementation of
8314 <function>genericLookup</function> that works very fast for
8315 keys of type <literal>Int</literal>. You might wish
8316 to tell GHC to use <function>intLookup</function> instead of
8317 <function>genericLookup</function> whenever the latter was called with
8318 type <literal>Table Int b -> Int -> b</literal>.
8319 It used to be possible to write
8322 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8325 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8328 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8331 This slightly odd-looking rule instructs GHC to replace
8332 <function>genericLookup</function> by <function>intLookup</function>
8333 <emphasis>whenever the types match</emphasis>.
8334 What is more, this rule does not need to be in the same
8335 file as <function>genericLookup</function>, unlike the
8336 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8337 have an original definition available to specialise).
8340 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8341 <function>intLookup</function> really behaves as a specialised version
8342 of <function>genericLookup</function>!!!</para>
8344 <para>An example in which using <literal>RULES</literal> for
8345 specialisation will Win Big:
8348 toDouble :: Real a => a -> Double
8349 toDouble = fromRational . toRational
8351 {-# RULES "toDouble/Int" toDouble = i2d #-}
8352 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8355 The <function>i2d</function> function is virtually one machine
8356 instruction; the default conversion—via an intermediate
8357 <literal>Rational</literal>—is obscenely expensive by
8364 <title>Controlling what's going on</title>
8372 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8378 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8379 If you add <option>-dppr-debug</option> you get a more detailed listing.
8385 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8388 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8389 {-# INLINE build #-}
8393 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8394 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8395 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8396 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8403 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8404 see how to write rules that will do fusion and yet give an efficient
8405 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8415 <sect2 id="core-pragma">
8416 <title>CORE pragma</title>
8418 <indexterm><primary>CORE pragma</primary></indexterm>
8419 <indexterm><primary>pragma, CORE</primary></indexterm>
8420 <indexterm><primary>core, annotation</primary></indexterm>
8423 The external core format supports <quote>Note</quote> annotations;
8424 the <literal>CORE</literal> pragma gives a way to specify what these
8425 should be in your Haskell source code. Syntactically, core
8426 annotations are attached to expressions and take a Haskell string
8427 literal as an argument. The following function definition shows an
8431 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8434 Semantically, this is equivalent to:
8442 However, when external core is generated (via
8443 <option>-fext-core</option>), there will be Notes attached to the
8444 expressions <function>show</function> and <varname>x</varname>.
8445 The core function declaration for <function>f</function> is:
8449 f :: %forall a . GHCziShow.ZCTShow a ->
8450 a -> GHCziBase.ZMZN GHCziBase.Char =
8451 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8453 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8455 (tpl1::GHCziBase.Int ->
8457 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8459 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8460 (tpl3::GHCziBase.ZMZN a ->
8461 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8469 Here, we can see that the function <function>show</function> (which
8470 has been expanded out to a case expression over the Show dictionary)
8471 has a <literal>%note</literal> attached to it, as does the
8472 expression <varname>eta</varname> (which used to be called
8473 <varname>x</varname>).
8480 <sect1 id="special-ids">
8481 <title>Special built-in functions</title>
8482 <para>GHC has a few built-in functions with special behaviour. These
8483 are now described in the module <ulink
8484 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8485 in the library documentation.</para>
8489 <sect1 id="generic-classes">
8490 <title>Generic classes</title>
8493 The ideas behind this extension are described in detail in "Derivable type classes",
8494 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8495 An example will give the idea:
8503 fromBin :: [Int] -> (a, [Int])
8505 toBin {| Unit |} Unit = []
8506 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8507 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8508 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8510 fromBin {| Unit |} bs = (Unit, bs)
8511 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8512 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8513 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8514 (y,bs'') = fromBin bs'
8517 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8518 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8519 which are defined thus in the library module <literal>Generics</literal>:
8523 data a :+: b = Inl a | Inr b
8524 data a :*: b = a :*: b
8527 Now you can make a data type into an instance of Bin like this:
8529 instance (Bin a, Bin b) => Bin (a,b)
8530 instance Bin a => Bin [a]
8532 That is, just leave off the "where" clause. Of course, you can put in the
8533 where clause and over-ride whichever methods you please.
8537 <title> Using generics </title>
8538 <para>To use generics you need to</para>
8541 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8542 <option>-XGenerics</option> (to generate extra per-data-type code),
8543 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8547 <para>Import the module <literal>Generics</literal> from the
8548 <literal>lang</literal> package. This import brings into
8549 scope the data types <literal>Unit</literal>,
8550 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8551 don't need this import if you don't mention these types
8552 explicitly; for example, if you are simply giving instance
8553 declarations.)</para>
8558 <sect2> <title> Changes wrt the paper </title>
8560 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8561 can be written infix (indeed, you can now use
8562 any operator starting in a colon as an infix type constructor). Also note that
8563 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8564 Finally, note that the syntax of the type patterns in the class declaration
8565 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8566 alone would ambiguous when they appear on right hand sides (an extension we
8567 anticipate wanting).
8571 <sect2> <title>Terminology and restrictions</title>
8573 Terminology. A "generic default method" in a class declaration
8574 is one that is defined using type patterns as above.
8575 A "polymorphic default method" is a default method defined as in Haskell 98.
8576 A "generic class declaration" is a class declaration with at least one
8577 generic default method.
8585 Alas, we do not yet implement the stuff about constructor names and
8592 A generic class can have only one parameter; you can't have a generic
8593 multi-parameter class.
8599 A default method must be defined entirely using type patterns, or entirely
8600 without. So this is illegal:
8603 op :: a -> (a, Bool)
8604 op {| Unit |} Unit = (Unit, True)
8607 However it is perfectly OK for some methods of a generic class to have
8608 generic default methods and others to have polymorphic default methods.
8614 The type variable(s) in the type pattern for a generic method declaration
8615 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:
8619 op {| p :*: q |} (x :*: y) = op (x :: p)
8627 The type patterns in a generic default method must take one of the forms:
8633 where "a" and "b" are type variables. Furthermore, all the type patterns for
8634 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8635 must use the same type variables. So this is illegal:
8639 op {| a :+: b |} (Inl x) = True
8640 op {| p :+: q |} (Inr y) = False
8642 The type patterns must be identical, even in equations for different methods of the class.
8643 So this too is illegal:
8647 op1 {| a :*: b |} (x :*: y) = True
8650 op2 {| p :*: q |} (x :*: y) = False
8652 (The reason for this restriction is that we gather all the equations for a particular type constructor
8653 into a single generic instance declaration.)
8659 A generic method declaration must give a case for each of the three type constructors.
8665 The type for a generic method can be built only from:
8667 <listitem> <para> Function arrows </para> </listitem>
8668 <listitem> <para> Type variables </para> </listitem>
8669 <listitem> <para> Tuples </para> </listitem>
8670 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8672 Here are some example type signatures for generic methods:
8675 op2 :: Bool -> (a,Bool)
8676 op3 :: [Int] -> a -> a
8679 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8683 This restriction is an implementation restriction: we just haven't got around to
8684 implementing the necessary bidirectional maps over arbitrary type constructors.
8685 It would be relatively easy to add specific type constructors, such as Maybe and list,
8686 to the ones that are allowed.</para>
8691 In an instance declaration for a generic class, the idea is that the compiler
8692 will fill in the methods for you, based on the generic templates. However it can only
8697 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8702 No constructor of the instance type has unboxed fields.
8706 (Of course, these things can only arise if you are already using GHC extensions.)
8707 However, you can still give an instance declarations for types which break these rules,
8708 provided you give explicit code to override any generic default methods.
8716 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8717 what the compiler does with generic declarations.
8722 <sect2> <title> Another example </title>
8724 Just to finish with, here's another example I rather like:
8728 nCons {| Unit |} _ = 1
8729 nCons {| a :*: b |} _ = 1
8730 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8733 tag {| Unit |} _ = 1
8734 tag {| a :*: b |} _ = 1
8735 tag {| a :+: b |} (Inl x) = tag x
8736 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8742 <sect1 id="monomorphism">
8743 <title>Control over monomorphism</title>
8745 <para>GHC supports two flags that control the way in which generalisation is
8746 carried out at let and where bindings.
8750 <title>Switching off the dreaded Monomorphism Restriction</title>
8751 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8753 <para>Haskell's monomorphism restriction (see
8754 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8756 of the Haskell Report)
8757 can be completely switched off by
8758 <option>-XNoMonomorphismRestriction</option>.
8763 <title>Monomorphic pattern bindings</title>
8764 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8765 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8767 <para> As an experimental change, we are exploring the possibility of
8768 making pattern bindings monomorphic; that is, not generalised at all.
8769 A pattern binding is a binding whose LHS has no function arguments,
8770 and is not a simple variable. For example:
8772 f x = x -- Not a pattern binding
8773 f = \x -> x -- Not a pattern binding
8774 f :: Int -> Int = \x -> x -- Not a pattern binding
8776 (g,h) = e -- A pattern binding
8777 (f) = e -- A pattern binding
8778 [x] = e -- A pattern binding
8780 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8781 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8790 ;;; Local Variables: ***
8792 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8793 ;;; ispell-local-dictionary: "british" ***
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