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, with flag <option>-XMultiParamTypeClasses</option>.
3165 class Collection c a where
3166 union :: c a -> c a -> c a
3173 <sect3 id="superclass-rules">
3174 <title>The superclasses of a class declaration</title>
3177 In Haskell 98 the context of a class declaration (which introduces superclasses)
3178 must be simple; that is, each predicate must consist of a class applied to
3179 type variables. The flag <option>-XFlexibleContexts</option>
3180 (<xref linkend="flexible-contexts"/>)
3181 lifts this restriction,
3182 so that the only restriction on the context in a class declaration is
3183 that the class hierarchy must be acyclic. So these class declarations are OK:
3187 class Functor (m k) => FiniteMap m k where
3190 class (Monad m, Monad (t m)) => Transform t m where
3191 lift :: m a -> (t m) a
3197 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3198 of "acyclic" involves only the superclass relationships. For example,
3204 op :: D b => a -> b -> b
3207 class C a => D a where { ... }
3211 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3212 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3213 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3220 <sect3 id="class-method-types">
3221 <title>Class method types</title>
3224 Haskell 98 prohibits class method types to mention constraints on the
3225 class type variable, thus:
3228 fromList :: [a] -> s a
3229 elem :: Eq a => a -> s a -> Bool
3231 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3232 contains the constraint <literal>Eq a</literal>, constrains only the
3233 class type variable (in this case <literal>a</literal>).
3234 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3241 <sect2 id="functional-dependencies">
3242 <title>Functional dependencies
3245 <para> Functional dependencies are implemented as described by Mark Jones
3246 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3247 In Proceedings of the 9th European Symposium on Programming,
3248 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3252 Functional dependencies are introduced by a vertical bar in the syntax of a
3253 class declaration; e.g.
3255 class (Monad m) => MonadState s m | m -> s where ...
3257 class Foo a b c | a b -> c where ...
3259 There should be more documentation, but there isn't (yet). Yell if you need it.
3262 <sect3><title>Rules for functional dependencies </title>
3264 In a class declaration, all of the class type variables must be reachable (in the sense
3265 mentioned in <xref linkend="type-restrictions"/>)
3266 from the free variables of each method type.
3270 class Coll s a where
3272 insert :: s -> a -> s
3275 is not OK, because the type of <literal>empty</literal> doesn't mention
3276 <literal>a</literal>. Functional dependencies can make the type variable
3279 class Coll s a | s -> a where
3281 insert :: s -> a -> s
3284 Alternatively <literal>Coll</literal> might be rewritten
3287 class Coll s a where
3289 insert :: s a -> a -> s a
3293 which makes the connection between the type of a collection of
3294 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3295 Occasionally this really doesn't work, in which case you can split the
3303 class CollE s => Coll s a where
3304 insert :: s -> a -> s
3311 <title>Background on functional dependencies</title>
3313 <para>The following description of the motivation and use of functional dependencies is taken
3314 from the Hugs user manual, reproduced here (with minor changes) by kind
3315 permission of Mark Jones.
3318 Consider the following class, intended as part of a
3319 library for collection types:
3321 class Collects e ce where
3323 insert :: e -> ce -> ce
3324 member :: e -> ce -> Bool
3326 The type variable e used here represents the element type, while ce is the type
3327 of the container itself. Within this framework, we might want to define
3328 instances of this class for lists or characteristic functions (both of which
3329 can be used to represent collections of any equality type), bit sets (which can
3330 be used to represent collections of characters), or hash tables (which can be
3331 used to represent any collection whose elements have a hash function). Omitting
3332 standard implementation details, this would lead to the following declarations:
3334 instance Eq e => Collects e [e] where ...
3335 instance Eq e => Collects e (e -> Bool) where ...
3336 instance Collects Char BitSet where ...
3337 instance (Hashable e, Collects a ce)
3338 => Collects e (Array Int ce) where ...
3340 All this looks quite promising; we have a class and a range of interesting
3341 implementations. Unfortunately, there are some serious problems with the class
3342 declaration. First, the empty function has an ambiguous type:
3344 empty :: Collects e ce => ce
3346 By "ambiguous" we mean that there is a type variable e that appears on the left
3347 of the <literal>=></literal> symbol, but not on the right. The problem with
3348 this is that, according to the theoretical foundations of Haskell overloading,
3349 we cannot guarantee a well-defined semantics for any term with an ambiguous
3353 We can sidestep this specific problem by removing the empty member from the
3354 class declaration. However, although the remaining members, insert and member,
3355 do not have ambiguous types, we still run into problems when we try to use
3356 them. For example, consider the following two functions:
3358 f x y = insert x . insert y
3361 for which GHC infers the following types:
3363 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3364 g :: (Collects Bool c, Collects Char c) => c -> c
3366 Notice that the type for f allows the two parameters x and y to be assigned
3367 different types, even though it attempts to insert each of the two values, one
3368 after the other, into the same collection. If we're trying to model collections
3369 that contain only one type of value, then this is clearly an inaccurate
3370 type. Worse still, the definition for g is accepted, without causing a type
3371 error. As a result, the error in this code will not be flagged at the point
3372 where it appears. Instead, it will show up only when we try to use g, which
3373 might even be in a different module.
3376 <sect4><title>An attempt to use constructor classes</title>
3379 Faced with the problems described above, some Haskell programmers might be
3380 tempted to use something like the following version of the class declaration:
3382 class Collects e c where
3384 insert :: e -> c e -> c e
3385 member :: e -> c e -> Bool
3387 The key difference here is that we abstract over the type constructor c that is
3388 used to form the collection type c e, and not over that collection type itself,
3389 represented by ce in the original class declaration. This avoids the immediate
3390 problems that we mentioned above: empty has type <literal>Collects e c => c
3391 e</literal>, which is not ambiguous.
3394 The function f from the previous section has a more accurate type:
3396 f :: (Collects e c) => e -> e -> c e -> c e
3398 The function g from the previous section is now rejected with a type error as
3399 we would hope because the type of f does not allow the two arguments to have
3401 This, then, is an example of a multiple parameter class that does actually work
3402 quite well in practice, without ambiguity problems.
3403 There is, however, a catch. This version of the Collects class is nowhere near
3404 as general as the original class seemed to be: only one of the four instances
3405 for <literal>Collects</literal>
3406 given above can be used with this version of Collects because only one of
3407 them---the instance for lists---has a collection type that can be written in
3408 the form c e, for some type constructor c, and element type e.
3412 <sect4><title>Adding functional dependencies</title>
3415 To get a more useful version of the Collects class, Hugs provides a mechanism
3416 that allows programmers to specify dependencies between the parameters of a
3417 multiple parameter class (For readers with an interest in theoretical
3418 foundations and previous work: The use of dependency information can be seen
3419 both as a generalization of the proposal for `parametric type classes' that was
3420 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3421 later framework for "improvement" of qualified types. The
3422 underlying ideas are also discussed in a more theoretical and abstract setting
3423 in a manuscript [implparam], where they are identified as one point in a
3424 general design space for systems of implicit parameterization.).
3426 To start with an abstract example, consider a declaration such as:
3428 class C a b where ...
3430 which tells us simply that C can be thought of as a binary relation on types
3431 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3432 included in the definition of classes to add information about dependencies
3433 between parameters, as in the following examples:
3435 class D a b | a -> b where ...
3436 class E a b | a -> b, b -> a where ...
3438 The notation <literal>a -> b</literal> used here between the | and where
3439 symbols --- not to be
3440 confused with a function type --- indicates that the a parameter uniquely
3441 determines the b parameter, and might be read as "a determines b." Thus D is
3442 not just a relation, but actually a (partial) function. Similarly, from the two
3443 dependencies that are included in the definition of E, we can see that E
3444 represents a (partial) one-one mapping between types.
3447 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3448 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3449 m>=0, meaning that the y parameters are uniquely determined by the x
3450 parameters. Spaces can be used as separators if more than one variable appears
3451 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3452 annotated with multiple dependencies using commas as separators, as in the
3453 definition of E above. Some dependencies that we can write in this notation are
3454 redundant, and will be rejected because they don't serve any useful
3455 purpose, and may instead indicate an error in the program. Examples of
3456 dependencies like this include <literal>a -> a </literal>,
3457 <literal>a -> a a </literal>,
3458 <literal>a -> </literal>, etc. There can also be
3459 some redundancy if multiple dependencies are given, as in
3460 <literal>a->b</literal>,
3461 <literal>b->c </literal>, <literal>a->c </literal>, and
3462 in which some subset implies the remaining dependencies. Examples like this are
3463 not treated as errors. Note that dependencies appear only in class
3464 declarations, and not in any other part of the language. In particular, the
3465 syntax for instance declarations, class constraints, and types is completely
3469 By including dependencies in a class declaration, we provide a mechanism for
3470 the programmer to specify each multiple parameter class more precisely. The
3471 compiler, on the other hand, is responsible for ensuring that the set of
3472 instances that are in scope at any given point in the program is consistent
3473 with any declared dependencies. For example, the following pair of instance
3474 declarations cannot appear together in the same scope because they violate the
3475 dependency for D, even though either one on its own would be acceptable:
3477 instance D Bool Int where ...
3478 instance D Bool Char where ...
3480 Note also that the following declaration is not allowed, even by itself:
3482 instance D [a] b where ...
3484 The problem here is that this instance would allow one particular choice of [a]
3485 to be associated with more than one choice for b, which contradicts the
3486 dependency specified in the definition of D. More generally, this means that,
3487 in any instance of the form:
3489 instance D t s where ...
3491 for some particular types t and s, the only variables that can appear in s are
3492 the ones that appear in t, and hence, if the type t is known, then s will be
3493 uniquely determined.
3496 The benefit of including dependency information is that it allows us to define
3497 more general multiple parameter classes, without ambiguity problems, and with
3498 the benefit of more accurate types. To illustrate this, we return to the
3499 collection class example, and annotate the original definition of <literal>Collects</literal>
3500 with a simple dependency:
3502 class Collects e ce | ce -> e where
3504 insert :: e -> ce -> ce
3505 member :: e -> ce -> Bool
3507 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3508 determined by the type of the collection ce. Note that both parameters of
3509 Collects are of kind *; there are no constructor classes here. Note too that
3510 all of the instances of Collects that we gave earlier can be used
3511 together with this new definition.
3514 What about the ambiguity problems that we encountered with the original
3515 definition? The empty function still has type Collects e ce => ce, but it is no
3516 longer necessary to regard that as an ambiguous type: Although the variable e
3517 does not appear on the right of the => symbol, the dependency for class
3518 Collects tells us that it is uniquely determined by ce, which does appear on
3519 the right of the => symbol. Hence the context in which empty is used can still
3520 give enough information to determine types for both ce and e, without
3521 ambiguity. More generally, we need only regard a type as ambiguous if it
3522 contains a variable on the left of the => that is not uniquely determined
3523 (either directly or indirectly) by the variables on the right.
3526 Dependencies also help to produce more accurate types for user defined
3527 functions, and hence to provide earlier detection of errors, and less cluttered
3528 types for programmers to work with. Recall the previous definition for a
3531 f x y = insert x y = insert x . insert y
3533 for which we originally obtained a type:
3535 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3537 Given the dependency information that we have for Collects, however, we can
3538 deduce that a and b must be equal because they both appear as the second
3539 parameter in a Collects constraint with the same first parameter c. Hence we
3540 can infer a shorter and more accurate type for f:
3542 f :: (Collects a c) => a -> a -> c -> c
3544 In a similar way, the earlier definition of g will now be flagged as a type error.
3547 Although we have given only a few examples here, it should be clear that the
3548 addition of dependency information can help to make multiple parameter classes
3549 more useful in practice, avoiding ambiguity problems, and allowing more general
3550 sets of instance declarations.
3556 <sect2 id="instance-decls">
3557 <title>Instance declarations</title>
3559 <para>An instance declaration has the form
3561 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 ...
3563 The part before the "<literal>=></literal>" is the
3564 <emphasis>context</emphasis>, while the part after the
3565 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3568 <sect3 id="flexible-instance-head">
3569 <title>Relaxed rules for the instance head</title>
3572 In Haskell 98 the head of an instance declaration
3573 must be of the form <literal>C (T a1 ... an)</literal>, where
3574 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3575 and the <literal>a1 ... an</literal> are distinct type variables.
3576 GHC relaxes these rules in two ways.
3580 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3581 declaration to mention arbitrary nested types.
3582 For example, this becomes a legal instance declaration
3584 instance C (Maybe Int) where ...
3586 See also the <link linkend="instance-overlap">rules on overlap</link>.
3589 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3590 synonyms. As always, using a type synonym is just shorthand for
3591 writing the RHS of the type synonym definition. For example:
3595 type Point = (Int,Int)
3596 instance C Point where ...
3597 instance C [Point] where ...
3601 is legal. However, if you added
3605 instance C (Int,Int) where ...
3609 as well, then the compiler will complain about the overlapping
3610 (actually, identical) instance declarations. As always, type synonyms
3611 must be fully applied. You cannot, for example, write:
3615 instance Monad P where ...
3623 <sect3 id="instance-rules">
3624 <title>Relaxed rules for instance contexts</title>
3626 <para>In Haskell 98, the assertions in the context of the instance declaration
3627 must be of the form <literal>C a</literal> where <literal>a</literal>
3628 is a type variable that occurs in the head.
3632 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3633 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3634 With this flag the context of the instance declaration can each consist of arbitrary
3635 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3639 The Paterson Conditions: for each assertion in the context
3641 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3642 <listitem><para>The assertion has fewer constructors and variables (taken together
3643 and counting repetitions) than the head</para></listitem>
3647 <listitem><para>The Coverage Condition. For each functional dependency,
3648 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3649 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3650 every type variable in
3651 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3652 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3653 substitution mapping each type variable in the class declaration to the
3654 corresponding type in the instance declaration.
3657 These restrictions ensure that context reduction terminates: each reduction
3658 step makes the problem smaller by at least one
3659 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3660 if you give the <option>-XUndecidableInstances</option>
3661 flag (<xref linkend="undecidable-instances"/>).
3662 You can find lots of background material about the reason for these
3663 restrictions in the paper <ulink
3664 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3665 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3668 For example, these are OK:
3670 instance C Int [a] -- Multiple parameters
3671 instance Eq (S [a]) -- Structured type in head
3673 -- Repeated type variable in head
3674 instance C4 a a => C4 [a] [a]
3675 instance Stateful (ST s) (MutVar s)
3677 -- Head can consist of type variables only
3679 instance (Eq a, Show b) => C2 a b
3681 -- Non-type variables in context
3682 instance Show (s a) => Show (Sized s a)
3683 instance C2 Int a => C3 Bool [a]
3684 instance C2 Int a => C3 [a] b
3688 -- Context assertion no smaller than head
3689 instance C a => C a where ...
3690 -- (C b b) has more more occurrences of b than the head
3691 instance C b b => Foo [b] where ...
3696 The same restrictions apply to instances generated by
3697 <literal>deriving</literal> clauses. Thus the following is accepted:
3699 data MinHeap h a = H a (h a)
3702 because the derived instance
3704 instance (Show a, Show (h a)) => Show (MinHeap h a)
3706 conforms to the above rules.
3710 A useful idiom permitted by the above rules is as follows.
3711 If one allows overlapping instance declarations then it's quite
3712 convenient to have a "default instance" declaration that applies if
3713 something more specific does not:
3721 <sect3 id="undecidable-instances">
3722 <title>Undecidable instances</title>
3725 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3726 For example, sometimes you might want to use the following to get the
3727 effect of a "class synonym":
3729 class (C1 a, C2 a, C3 a) => C a where { }
3731 instance (C1 a, C2 a, C3 a) => C a where { }
3733 This allows you to write shorter signatures:
3739 f :: (C1 a, C2 a, C3 a) => ...
3741 The restrictions on functional dependencies (<xref
3742 linkend="functional-dependencies"/>) are particularly troublesome.
3743 It is tempting to introduce type variables in the context that do not appear in
3744 the head, something that is excluded by the normal rules. For example:
3746 class HasConverter a b | a -> b where
3749 data Foo a = MkFoo a
3751 instance (HasConverter a b,Show b) => Show (Foo a) where
3752 show (MkFoo value) = show (convert value)
3754 This is dangerous territory, however. Here, for example, is a program that would make the
3759 instance F [a] [[a]]
3760 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3762 Similarly, it can be tempting to lift the coverage condition:
3764 class Mul a b c | a b -> c where
3765 (.*.) :: a -> b -> c
3767 instance Mul Int Int Int where (.*.) = (*)
3768 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3769 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3771 The third instance declaration does not obey the coverage condition;
3772 and indeed the (somewhat strange) definition:
3774 f = \ b x y -> if b then x .*. [y] else y
3776 makes instance inference go into a loop, because it requires the constraint
3777 <literal>(Mul a [b] b)</literal>.
3780 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3781 the experimental flag <option>-XUndecidableInstances</option>
3782 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3783 both the Paterson Conditions and the Coverage Condition
3784 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3785 fixed-depth recursion stack. If you exceed the stack depth you get a
3786 sort of backtrace, and the opportunity to increase the stack depth
3787 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3793 <sect3 id="instance-overlap">
3794 <title>Overlapping instances</title>
3796 In general, <emphasis>GHC requires that that it be unambiguous which instance
3798 should be used to resolve a type-class constraint</emphasis>. This behaviour
3799 can be modified by two flags: <option>-XOverlappingInstances</option>
3800 <indexterm><primary>-XOverlappingInstances
3801 </primary></indexterm>
3802 and <option>-XIncoherentInstances</option>
3803 <indexterm><primary>-XIncoherentInstances
3804 </primary></indexterm>, as this section discusses. Both these
3805 flags are dynamic flags, and can be set on a per-module basis, using
3806 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3808 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3809 it tries to match every instance declaration against the
3811 by instantiating the head of the instance declaration. For example, consider
3814 instance context1 => C Int a where ... -- (A)
3815 instance context2 => C a Bool where ... -- (B)
3816 instance context3 => C Int [a] where ... -- (C)
3817 instance context4 => C Int [Int] where ... -- (D)
3819 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3820 but (C) and (D) do not. When matching, GHC takes
3821 no account of the context of the instance declaration
3822 (<literal>context1</literal> etc).
3823 GHC's default behaviour is that <emphasis>exactly one instance must match the
3824 constraint it is trying to resolve</emphasis>.
3825 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3826 including both declarations (A) and (B), say); an error is only reported if a
3827 particular constraint matches more than one.
3831 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3832 more than one instance to match, provided there is a most specific one. For
3833 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3834 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3835 most-specific match, the program is rejected.
3838 However, GHC is conservative about committing to an overlapping instance. For example:
3843 Suppose that from the RHS of <literal>f</literal> we get the constraint
3844 <literal>C Int [b]</literal>. But
3845 GHC does not commit to instance (C), because in a particular
3846 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3847 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3848 So GHC rejects the program.
3849 (If you add the flag <option>-XIncoherentInstances</option>,
3850 GHC will instead pick (C), without complaining about
3851 the problem of subsequent instantiations.)
3854 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3855 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3856 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3857 it instead. In this case, GHC will refrain from
3858 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3859 as before) but, rather than rejecting the program, it will infer the type
3861 f :: C Int [b] => [b] -> [b]
3863 That postpones the question of which instance to pick to the
3864 call site for <literal>f</literal>
3865 by which time more is known about the type <literal>b</literal>.
3866 You can write this type signature yourself if you use the
3867 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3871 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3875 instance Foo [b] where
3878 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3879 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3880 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3881 declaration. The solution is to postpone the choice by adding the constraint to the context
3882 of the instance declaration, thus:
3884 instance C Int [b] => Foo [b] where
3887 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3890 The willingness to be overlapped or incoherent is a property of
3891 the <emphasis>instance declaration</emphasis> itself, controlled by the
3892 presence or otherwise of the <option>-XOverlappingInstances</option>
3893 and <option>-XIncoherentInstances</option> flags when that module is
3894 being defined. Neither flag is required in a module that imports and uses the
3895 instance declaration. Specifically, during the lookup process:
3898 An instance declaration is ignored during the lookup process if (a) a more specific
3899 match is found, and (b) the instance declaration was compiled with
3900 <option>-XOverlappingInstances</option>. The flag setting for the
3901 more-specific instance does not matter.
3904 Suppose an instance declaration does not match the constraint being looked up, but
3905 does unify with it, so that it might match when the constraint is further
3906 instantiated. Usually GHC will regard this as a reason for not committing to
3907 some other constraint. But if the instance declaration was compiled with
3908 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3909 check for that declaration.
3912 These rules make it possible for a library author to design a library that relies on
3913 overlapping instances without the library client having to know.
3916 If an instance declaration is compiled without
3917 <option>-XOverlappingInstances</option>,
3918 then that instance can never be overlapped. This could perhaps be
3919 inconvenient. Perhaps the rule should instead say that the
3920 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3921 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3922 at a usage site should be permitted regardless of how the instance declarations
3923 are compiled, if the <option>-XOverlappingInstances</option> flag is
3924 used at the usage site. (Mind you, the exact usage site can occasionally be
3925 hard to pin down.) We are interested to receive feedback on these points.
3927 <para>The <option>-XIncoherentInstances</option> flag implies the
3928 <option>-XOverlappingInstances</option> flag, but not vice versa.
3936 <sect2 id="overloaded-strings">
3937 <title>Overloaded string literals
3941 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3942 string literal has type <literal>String</literal>, but with overloaded string
3943 literals enabled (with <literal>-XOverloadedStrings</literal>)
3944 a string literal has type <literal>(IsString a) => a</literal>.
3947 This means that the usual string syntax can be used, e.g., for packed strings
3948 and other variations of string like types. String literals behave very much
3949 like integer literals, i.e., they can be used in both expressions and patterns.
3950 If used in a pattern the literal with be replaced by an equality test, in the same
3951 way as an integer literal is.
3954 The class <literal>IsString</literal> is defined as:
3956 class IsString a where
3957 fromString :: String -> a
3959 The only predefined instance is the obvious one to make strings work as usual:
3961 instance IsString [Char] where
3964 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3965 it explicitly (for example, to give an instance declaration for it), you can import it
3966 from module <literal>GHC.Exts</literal>.
3969 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3973 Each type in a default declaration must be an
3974 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3978 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3979 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3980 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3981 <emphasis>or</emphasis> <literal>IsString</literal>.
3990 import GHC.Exts( IsString(..) )
3992 newtype MyString = MyString String deriving (Eq, Show)
3993 instance IsString MyString where
3994 fromString = MyString
3996 greet :: MyString -> MyString
3997 greet "hello" = "world"
4001 print $ greet "hello"
4002 print $ greet "fool"
4006 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4007 to work since it gets translated into an equality comparison.
4013 <sect1 id="type-families">
4014 <title>Type families</title>
4017 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4018 facilitate type-level
4019 programming. Type families are a generalisation of <firstterm>associated
4020 data types</firstterm>
4021 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4022 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4023 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4024 Symposium on Principles of Programming Languages (POPL'05)”, pages
4025 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4026 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4027 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4029 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4030 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4031 themselves are described in the paper “<ulink
4032 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4033 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4035 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4036 13th ACM SIGPLAN International Conference on Functional
4037 Programming”, ACM Press, pages 51-62, 2008. Type families
4038 essentially provide type-indexed data types and named functions on types,
4039 which are useful for generic programming and highly parameterised library
4040 interfaces as well as interfaces with enhanced static information, much like
4041 dependent types. They might also be regarded as an alternative to functional
4042 dependencies, but provide a more functional style of type-level programming
4043 than the relational style of functional dependencies.
4046 Indexed type families, or type families for short, are type constructors that
4047 represent sets of types. Set members are denoted by supplying the type family
4048 constructor with type parameters, which are called <firstterm>type
4049 indices</firstterm>. The
4050 difference between vanilla parametrised type constructors and family
4051 constructors is much like between parametrically polymorphic functions and
4052 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4053 behave the same at all type instances, whereas class methods can change their
4054 behaviour in dependence on the class type parameters. Similarly, vanilla type
4055 constructors imply the same data representation for all type instances, but
4056 family constructors can have varying representation types for varying type
4060 Indexed type families come in two flavours: <firstterm>data
4061 families</firstterm> and <firstterm>type synonym
4062 families</firstterm>. They are the indexed family variants of algebraic
4063 data types and type synonyms, respectively. The instances of data families
4064 can be data types and newtypes.
4067 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4068 Additional information on the use of type families in GHC is available on
4069 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4070 Haskell wiki page on type families</ulink>.
4073 <sect2 id="data-families">
4074 <title>Data families</title>
4077 Data families appear in two flavours: (1) they can be defined on the
4079 or (2) they can appear inside type classes (in which case they are known as
4080 associated types). The former is the more general variant, as it lacks the
4081 requirement for the type-indexes to coincide with the class
4082 parameters. However, the latter can lead to more clearly structured code and
4083 compiler warnings if some type instances were - possibly accidentally -
4084 omitted. In the following, we always discuss the general toplevel form first
4085 and then cover the additional constraints placed on associated types.
4088 <sect3 id="data-family-declarations">
4089 <title>Data family declarations</title>
4092 Indexed data families are introduced by a signature, such as
4094 data family GMap k :: * -> *
4096 The special <literal>family</literal> distinguishes family from standard
4097 data declarations. The result kind annotation is optional and, as
4098 usual, defaults to <literal>*</literal> if omitted. An example is
4102 Named arguments can also be given explicit kind signatures if needed.
4104 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4105 declarations] named arguments are entirely optional, so that we can
4106 declare <literal>Array</literal> alternatively with
4108 data family Array :: * -> *
4112 <sect4 id="assoc-data-family-decl">
4113 <title>Associated data family declarations</title>
4115 When a data family is declared as part of a type class, we drop
4116 the <literal>family</literal> special. The <literal>GMap</literal>
4117 declaration takes the following form
4119 class GMapKey k where
4120 data GMap k :: * -> *
4123 In contrast to toplevel declarations, named arguments must be used for
4124 all type parameters that are to be used as type-indexes. Moreover,
4125 the argument names must be class parameters. Each class parameter may
4126 only be used at most once per associated type, but some may be omitted
4127 and they may be in an order other than in the class head. Hence, the
4128 following contrived example is admissible:
4137 <sect3 id="data-instance-declarations">
4138 <title>Data instance declarations</title>
4141 Instance declarations of data and newtype families are very similar to
4142 standard data and newtype declarations. The only two differences are
4143 that the keyword <literal>data</literal> or <literal>newtype</literal>
4144 is followed by <literal>instance</literal> and that some or all of the
4145 type arguments can be non-variable types, but may not contain forall
4146 types or type synonym families. However, data families are generally
4147 allowed in type parameters, and type synonyms are allowed as long as
4148 they are fully applied and expand to a type that is itself admissible -
4149 exactly as this is required for occurrences of type synonyms in class
4150 instance parameters. For example, the <literal>Either</literal>
4151 instance for <literal>GMap</literal> is
4153 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4155 In this example, the declaration has only one variant. In general, it
4159 Data and newtype instance declarations are only permitted when an
4160 appropriate family declaration is in scope - just as a class instance declaratoin
4161 requires the class declaration to be visible. Moreover, each instance
4162 declaration has to conform to the kind determined by its family
4163 declaration. This implies that the number of parameters of an instance
4164 declaration matches the arity determined by the kind of the family.
4167 A data family instance declaration can use the full exprssiveness of
4168 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4170 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4171 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4172 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4175 data instance T Int = T1 Int | T2 Bool
4176 newtype instance T Char = TC Bool
4179 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4180 and indeed can define a GADT. For example:
4183 data instance G [a] b where
4184 G1 :: c -> G [Int] b
4188 <listitem><para> You can use a <literal>deriving</literal> clause on a
4189 <literal>data instance</literal> or <literal>newtype instance</literal>
4196 Even if type families are defined as toplevel declarations, functions
4197 that perform different computations for different family instances may still
4198 need to be defined as methods of type classes. In particular, the
4199 following is not possible:
4202 data instance T Int = A
4203 data instance T Char = B
4205 foo A = 1 -- WRONG: These two equations together...
4206 foo B = 2 -- ...will produce a type error.
4208 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4212 instance Foo Int where
4214 instance Foo Char where
4217 (Given the functionality provided by GADTs (Generalised Algebraic Data
4218 Types), it might seem as if a definition, such as the above, should be
4219 feasible. However, type families are - in contrast to GADTs - are
4220 <emphasis>open;</emphasis> i.e., new instances can always be added,
4222 modules. Supporting pattern matching across different data instances
4223 would require a form of extensible case construct.)
4226 <sect4 id="assoc-data-inst">
4227 <title>Associated data instances</title>
4229 When an associated data family instance is declared within a type
4230 class instance, we drop the <literal>instance</literal> keyword in the
4231 family instance. So, the <literal>Either</literal> instance
4232 for <literal>GMap</literal> becomes:
4234 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4235 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4238 The most important point about associated family instances is that the
4239 type indexes corresponding to class parameters must be identical to
4240 the type given in the instance head; here this is the first argument
4241 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4242 which coincides with the only class parameter. Any parameters to the
4243 family constructor that do not correspond to class parameters, need to
4244 be variables in every instance; here this is the
4245 variable <literal>v</literal>.
4248 Instances for an associated family can only appear as part of
4249 instances declarations of the class in which the family was declared -
4250 just as with the equations of the methods of a class. Also in
4251 correspondence to how methods are handled, declarations of associated
4252 types can be omitted in class instances. If an associated family
4253 instance is omitted, the corresponding instance type is not inhabited;
4254 i.e., only diverging expressions, such
4255 as <literal>undefined</literal>, can assume the type.
4259 <sect4 id="scoping-class-params">
4260 <title>Scoping of class parameters</title>
4262 In the case of multi-parameter type classes, the visibility of class
4263 parameters in the right-hand side of associated family instances
4264 depends <emphasis>solely</emphasis> on the parameters of the data
4265 family. As an example, consider the simple class declaration
4270 Only one of the two class parameters is a parameter to the data
4271 family. Hence, the following instance declaration is invalid:
4273 instance C [c] d where
4274 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4276 Here, the right-hand side of the data instance mentions the type
4277 variable <literal>d</literal> that does not occur in its left-hand
4278 side. We cannot admit such data instances as they would compromise
4283 <sect4 id="family-class-inst">
4284 <title>Type class instances of family instances</title>
4286 Type class instances of instances of data families can be defined as
4287 usual, and in particular data instance declarations can
4288 have <literal>deriving</literal> clauses. For example, we can write
4290 data GMap () v = GMapUnit (Maybe v)
4293 which implicitly defines an instance of the form
4295 instance Show v => Show (GMap () v) where ...
4299 Note that class instances are always for
4300 particular <emphasis>instances</emphasis> of a data family and never
4301 for an entire family as a whole. This is for essentially the same
4302 reasons that we cannot define a toplevel function that performs
4303 pattern matching on the data constructors
4304 of <emphasis>different</emphasis> instances of a single type family.
4305 It would require a form of extensible case construct.
4309 <sect4 id="data-family-overlap">
4310 <title>Overlap of data instances</title>
4312 The instance declarations of a data family used in a single program
4313 may not overlap at all, independent of whether they are associated or
4314 not. In contrast to type class instances, this is not only a matter
4315 of consistency, but one of type safety.
4321 <sect3 id="data-family-import-export">
4322 <title>Import and export</title>
4325 The association of data constructors with type families is more dynamic
4326 than that is the case with standard data and newtype declarations. In
4327 the standard case, the notation <literal>T(..)</literal> in an import or
4328 export list denotes the type constructor and all the data constructors
4329 introduced in its declaration. However, a family declaration never
4330 introduces any data constructors; instead, data constructors are
4331 introduced by family instances. As a result, which data constructors
4332 are associated with a type family depends on the currently visible
4333 instance declarations for that family. Consequently, an import or
4334 export item of the form <literal>T(..)</literal> denotes the family
4335 constructor and all currently visible data constructors - in the case of
4336 an export item, these may be either imported or defined in the current
4337 module. The treatment of import and export items that explicitly list
4338 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4342 <sect4 id="data-family-impexp-assoc">
4343 <title>Associated families</title>
4345 As expected, an import or export item of the
4346 form <literal>C(..)</literal> denotes all of the class' methods and
4347 associated types. However, when associated types are explicitly
4348 listed as subitems of a class, we need some new syntax, as uppercase
4349 identifiers as subitems are usually data constructors, not type
4350 constructors. To clarify that we denote types here, each associated
4351 type name needs to be prefixed by the keyword <literal>type</literal>.
4352 So for example, when explicitly listing the components of
4353 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4354 GMap, empty, lookup, insert)</literal>.
4358 <sect4 id="data-family-impexp-examples">
4359 <title>Examples</title>
4361 Assuming our running <literal>GMapKey</literal> class example, let us
4362 look at some export lists and their meaning:
4365 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4366 just the class name.</para>
4369 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4370 Exports the class, the associated type <literal>GMap</literal>
4372 functions <literal>empty</literal>, <literal>lookup</literal>,
4373 and <literal>insert</literal>. None of the data constructors is
4377 <para><literal>module GMap (GMapKey(..), GMap(..))
4378 where...</literal>: As before, but also exports all the data
4379 constructors <literal>GMapInt</literal>,
4380 <literal>GMapChar</literal>,
4381 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4382 and <literal>GMapUnit</literal>.</para>
4385 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4386 GMap(..)) where...</literal>: As before.</para>
4389 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4390 where...</literal>: As before.</para>
4395 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4396 both the class <literal>GMapKey</literal> as well as its associated
4397 type <literal>GMap</literal>. However, you cannot
4398 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4399 sub-component specifications cannot be nested. To
4400 specify <literal>GMap</literal>'s data constructors, you have to list
4405 <sect4 id="data-family-impexp-instances">
4406 <title>Instances</title>
4408 Family instances are implicitly exported, just like class instances.
4409 However, this applies only to the heads of instances, not to the data
4410 constructors an instance defines.
4418 <sect2 id="synonym-families">
4419 <title>Synonym families</title>
4422 Type families appear in two flavours: (1) they can be defined on the
4423 toplevel or (2) they can appear inside type classes (in which case they
4424 are known as associated type synonyms). The former is the more general
4425 variant, as it lacks the requirement for the type-indexes to coincide with
4426 the class parameters. However, the latter can lead to more clearly
4427 structured code and compiler warnings if some type instances were -
4428 possibly accidentally - omitted. In the following, we always discuss the
4429 general toplevel form first and then cover the additional constraints
4430 placed on associated types.
4433 <sect3 id="type-family-declarations">
4434 <title>Type family declarations</title>
4437 Indexed type families are introduced by a signature, such as
4439 type family Elem c :: *
4441 The special <literal>family</literal> distinguishes family from standard
4442 type declarations. The result kind annotation is optional and, as
4443 usual, defaults to <literal>*</literal> if omitted. An example is
4447 Parameters can also be given explicit kind signatures if needed. We
4448 call the number of parameters in a type family declaration, the family's
4449 arity, and all applications of a type family must be fully saturated
4450 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4451 and it implies that the kind of a type family is not sufficient to
4452 determine a family's arity, and hence in general, also insufficient to
4453 determine whether a type family application is well formed. As an
4454 example, consider the following declaration:
4456 type family F a b :: * -> * -- F's arity is 2,
4457 -- although its overall kind is * -> * -> * -> *
4459 Given this declaration the following are examples of well-formed and
4462 F Char [Int] -- OK! Kind: * -> *
4463 F Char [Int] Bool -- OK! Kind: *
4464 F IO Bool -- WRONG: kind mismatch in the first argument
4465 F Bool -- WRONG: unsaturated application
4469 <sect4 id="assoc-type-family-decl">
4470 <title>Associated type family declarations</title>
4472 When a type family is declared as part of a type class, we drop
4473 the <literal>family</literal> special. The <literal>Elem</literal>
4474 declaration takes the following form
4476 class Collects ce where
4480 The argument names of the type family must be class parameters. Each
4481 class parameter may only be used at most once per associated type, but
4482 some may be omitted and they may be in an order other than in the
4483 class head. Hence, the following contrived example is admissible:
4488 These rules are exactly as for associated data families.
4493 <sect3 id="type-instance-declarations">
4494 <title>Type instance declarations</title>
4496 Instance declarations of type families are very similar to standard type
4497 synonym declarations. The only two differences are that the
4498 keyword <literal>type</literal> is followed
4499 by <literal>instance</literal> and that some or all of the type
4500 arguments can be non-variable types, but may not contain forall types or
4501 type synonym families. However, data families are generally allowed, and
4502 type synonyms are allowed as long as they are fully applied and expand
4503 to a type that is admissible - these are the exact same requirements as
4504 for data instances. For example, the <literal>[e]</literal> instance
4505 for <literal>Elem</literal> is
4507 type instance Elem [e] = e
4511 Type family instance declarations are only legitimate when an
4512 appropriate family declaration is in scope - just like class instances
4513 require the class declaration to be visible. Moreover, each instance
4514 declaration has to conform to the kind determined by its family
4515 declaration, and the number of type parameters in an instance
4516 declaration must match the number of type parameters in the family
4517 declaration. Finally, the right-hand side of a type instance must be a
4518 monotype (i.e., it may not include foralls) and after the expansion of
4519 all saturated vanilla type synonyms, no synonyms, except family synonyms
4520 may remain. Here are some examples of admissible and illegal type
4523 type family F a :: *
4524 type instance F [Int] = Int -- OK!
4525 type instance F String = Char -- OK!
4526 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4527 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4528 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4530 type family G a b :: * -> *
4531 type instance G Int = (,) -- WRONG: must be two type parameters
4532 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4536 <sect4 id="assoc-type-instance">
4537 <title>Associated type instance declarations</title>
4539 When an associated family instance is declared within a type class
4540 instance, we drop the <literal>instance</literal> keyword in the family
4541 instance. So, the <literal>[e]</literal> instance
4542 for <literal>Elem</literal> becomes:
4544 instance (Eq (Elem [e])) => Collects ([e]) where
4548 The most important point about associated family instances is that the
4549 type indexes corresponding to class parameters must be identical to the
4550 type given in the instance head; here this is <literal>[e]</literal>,
4551 which coincides with the only class parameter.
4554 Instances for an associated family can only appear as part of instances
4555 declarations of the class in which the family was declared - just as
4556 with the equations of the methods of a class. Also in correspondence to
4557 how methods are handled, declarations of associated types can be omitted
4558 in class instances. If an associated family instance is omitted, the
4559 corresponding instance type is not inhabited; i.e., only diverging
4560 expressions, such as <literal>undefined</literal>, can assume the type.
4564 <sect4 id="type-family-overlap">
4565 <title>Overlap of type synonym instances</title>
4567 The instance declarations of a type family used in a single program
4568 may only overlap if the right-hand sides of the overlapping instances
4569 coincide for the overlapping types. More formally, two instance
4570 declarations overlap if there is a substitution that makes the
4571 left-hand sides of the instances syntactically the same. Whenever
4572 that is the case, the right-hand sides of the instances must also be
4573 syntactically equal under the same substitution. This condition is
4574 independent of whether the type family is associated or not, and it is
4575 not only a matter of consistency, but one of type safety.
4578 Here are two example to illustrate the condition under which overlap
4581 type instance F (a, Int) = [a]
4582 type instance F (Int, b) = [b] -- overlap permitted
4584 type instance G (a, Int) = [a]
4585 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4590 <sect4 id="type-family-decidability">
4591 <title>Decidability of type synonym instances</title>
4593 In order to guarantee that type inference in the presence of type
4594 families decidable, we need to place a number of additional
4595 restrictions on the formation of type instance declarations (c.f.,
4596 Definition 5 (Relaxed Conditions) of “<ulink
4597 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4598 Checking with Open Type Functions</ulink>”). Instance
4599 declarations have the general form
4601 type instance F t1 .. tn = t
4603 where we require that for every type family application <literal>(G s1
4604 .. sm)</literal> in <literal>t</literal>,
4607 <para><literal>s1 .. sm</literal> do not contain any type family
4608 constructors,</para>
4611 <para>the total number of symbols (data type constructors and type
4612 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4613 in <literal>t1 .. tn</literal>, and</para>
4616 <para>for every type
4617 variable <literal>a</literal>, <literal>a</literal> occurs
4618 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4619 .. tn</literal>.</para>
4622 These restrictions are easily verified and ensure termination of type
4623 inference. However, they are not sufficient to guarantee completeness
4624 of type inference in the presence of, so called, ''loopy equalities'',
4625 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4626 a type variable is underneath a family application and data
4627 constructor application - see the above mentioned paper for details.
4630 If the option <option>-XUndecidableInstances</option> is passed to the
4631 compiler, the above restrictions are not enforced and it is on the
4632 programmer to ensure termination of the normalisation of type families
4633 during type inference.
4638 <sect3 id-="equality-constraints">
4639 <title>Equality constraints</title>
4641 Type context can include equality constraints of the form <literal>t1 ~
4642 t2</literal>, which denote that the types <literal>t1</literal>
4643 and <literal>t2</literal> need to be the same. In the presence of type
4644 families, whether two types are equal cannot generally be decided
4645 locally. Hence, the contexts of function signatures may include
4646 equality constraints, as in the following example:
4648 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4650 where we require that the element type of <literal>c1</literal>
4651 and <literal>c2</literal> are the same. In general, the
4652 types <literal>t1</literal> and <literal>t2</literal> of an equality
4653 constraint may be arbitrary monotypes; i.e., they may not contain any
4654 quantifiers, independent of whether higher-rank types are otherwise
4658 Equality constraints can also appear in class and instance contexts.
4659 The former enable a simple translation of programs using functional
4660 dependencies into programs using family synonyms instead. The general
4661 idea is to rewrite a class declaration of the form
4663 class C a b | a -> b
4667 class (F a ~ b) => C a b where
4670 That is, we represent every functional dependency (FD) <literal>a1 .. an
4671 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4672 superclass context equality <literal>F a1 .. an ~ b</literal>,
4673 essentially giving a name to the functional dependency. In class
4674 instances, we define the type instances of FD families in accordance
4675 with the class head. Method signatures are not affected by that
4679 NB: Equalities in superclass contexts are not fully implemented in
4684 <sect3 id-="ty-fams-in-instances">
4685 <title>Type families and instance declarations</title>
4686 <para>Type families require us to extend the rules for
4687 the form of instance heads, which are given
4688 in <xref linkend="flexible-instance-head"/>.
4691 <listitem><para>Data type families may appear in an instance head</para></listitem>
4692 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4694 The reason for the latter restriction is that there is no way to check for. Consider
4697 type instance F Bool = Int
4704 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4705 The situation is especially bad because the type instance for <literal>F Bool</literal>
4706 might be in another module, or even in a module that is not yet written.
4713 <sect1 id="other-type-extensions">
4714 <title>Other type system extensions</title>
4716 <sect2 id="type-restrictions">
4717 <title>Type signatures</title>
4719 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4721 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4722 that the type-class constraints in a type signature must have the
4723 form <emphasis>(class type-variable)</emphasis> or
4724 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4725 With <option>-XFlexibleContexts</option>
4726 these type signatures are perfectly OK
4729 g :: Ord (T a ()) => ...
4731 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4732 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4733 (<xref linkend="instance-rules"/>).
4737 GHC imposes the following restrictions on the constraints in a type signature.
4741 forall tv1..tvn (c1, ...,cn) => type
4744 (Here, we write the "foralls" explicitly, although the Haskell source
4745 language omits them; in Haskell 98, all the free type variables of an
4746 explicit source-language type signature are universally quantified,
4747 except for the class type variables in a class declaration. However,
4748 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4757 <emphasis>Each universally quantified type variable
4758 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4760 A type variable <literal>a</literal> is "reachable" if it appears
4761 in the same constraint as either a type variable free in
4762 <literal>type</literal>, or another reachable type variable.
4763 A value with a type that does not obey
4764 this reachability restriction cannot be used without introducing
4765 ambiguity; that is why the type is rejected.
4766 Here, for example, is an illegal type:
4770 forall a. Eq a => Int
4774 When a value with this type was used, the constraint <literal>Eq tv</literal>
4775 would be introduced where <literal>tv</literal> is a fresh type variable, and
4776 (in the dictionary-translation implementation) the value would be
4777 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4778 can never know which instance of <literal>Eq</literal> to use because we never
4779 get any more information about <literal>tv</literal>.
4783 that the reachability condition is weaker than saying that <literal>a</literal> is
4784 functionally dependent on a type variable free in
4785 <literal>type</literal> (see <xref
4786 linkend="functional-dependencies"/>). The reason for this is there
4787 might be a "hidden" dependency, in a superclass perhaps. So
4788 "reachable" is a conservative approximation to "functionally dependent".
4789 For example, consider:
4791 class C a b | a -> b where ...
4792 class C a b => D a b where ...
4793 f :: forall a b. D a b => a -> a
4795 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4796 but that is not immediately apparent from <literal>f</literal>'s type.
4802 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4803 universally quantified type variables <literal>tvi</literal></emphasis>.
4805 For example, this type is OK because <literal>C a b</literal> mentions the
4806 universally quantified type variable <literal>b</literal>:
4810 forall a. C a b => burble
4814 The next type is illegal because the constraint <literal>Eq b</literal> does not
4815 mention <literal>a</literal>:
4819 forall a. Eq b => burble
4823 The reason for this restriction is milder than the other one. The
4824 excluded types are never useful or necessary (because the offending
4825 context doesn't need to be witnessed at this point; it can be floated
4826 out). Furthermore, floating them out increases sharing. Lastly,
4827 excluding them is a conservative choice; it leaves a patch of
4828 territory free in case we need it later.
4842 <sect2 id="implicit-parameters">
4843 <title>Implicit parameters</title>
4845 <para> Implicit parameters are implemented as described in
4846 "Implicit parameters: dynamic scoping with static types",
4847 J Lewis, MB Shields, E Meijer, J Launchbury,
4848 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4852 <para>(Most of the following, still rather incomplete, documentation is
4853 due to Jeff Lewis.)</para>
4855 <para>Implicit parameter support is enabled with the option
4856 <option>-XImplicitParams</option>.</para>
4859 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4860 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4861 context. In Haskell, all variables are statically bound. Dynamic
4862 binding of variables is a notion that goes back to Lisp, but was later
4863 discarded in more modern incarnations, such as Scheme. Dynamic binding
4864 can be very confusing in an untyped language, and unfortunately, typed
4865 languages, in particular Hindley-Milner typed languages like Haskell,
4866 only support static scoping of variables.
4869 However, by a simple extension to the type class system of Haskell, we
4870 can support dynamic binding. Basically, we express the use of a
4871 dynamically bound variable as a constraint on the type. These
4872 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4873 function uses a dynamically-bound variable <literal>?x</literal>
4874 of type <literal>t'</literal>". For
4875 example, the following expresses the type of a sort function,
4876 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4878 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4880 The dynamic binding constraints are just a new form of predicate in the type class system.
4883 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4884 where <literal>x</literal> is
4885 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4886 Use of this construct also introduces a new
4887 dynamic-binding constraint in the type of the expression.
4888 For example, the following definition
4889 shows how we can define an implicitly parameterized sort function in
4890 terms of an explicitly parameterized <literal>sortBy</literal> function:
4892 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4894 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4900 <title>Implicit-parameter type constraints</title>
4902 Dynamic binding constraints behave just like other type class
4903 constraints in that they are automatically propagated. Thus, when a
4904 function is used, its implicit parameters are inherited by the
4905 function that called it. For example, our <literal>sort</literal> function might be used
4906 to pick out the least value in a list:
4908 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4909 least xs = head (sort xs)
4911 Without lifting a finger, the <literal>?cmp</literal> parameter is
4912 propagated to become a parameter of <literal>least</literal> as well. With explicit
4913 parameters, the default is that parameters must always be explicit
4914 propagated. With implicit parameters, the default is to always
4918 An implicit-parameter type constraint differs from other type class constraints in the
4919 following way: All uses of a particular implicit parameter must have
4920 the same type. This means that the type of <literal>(?x, ?x)</literal>
4921 is <literal>(?x::a) => (a,a)</literal>, and not
4922 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4926 <para> You can't have an implicit parameter in the context of a class or instance
4927 declaration. For example, both these declarations are illegal:
4929 class (?x::Int) => C a where ...
4930 instance (?x::a) => Foo [a] where ...
4932 Reason: exactly which implicit parameter you pick up depends on exactly where
4933 you invoke a function. But the ``invocation'' of instance declarations is done
4934 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4935 Easiest thing is to outlaw the offending types.</para>
4937 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4939 f :: (?x :: [a]) => Int -> Int
4942 g :: (Read a, Show a) => String -> String
4945 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4946 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4947 quite unambiguous, and fixes the type <literal>a</literal>.
4952 <title>Implicit-parameter bindings</title>
4955 An implicit parameter is <emphasis>bound</emphasis> using the standard
4956 <literal>let</literal> or <literal>where</literal> binding forms.
4957 For example, we define the <literal>min</literal> function by binding
4958 <literal>cmp</literal>.
4961 min = let ?cmp = (<=) in least
4965 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4966 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4967 (including in a list comprehension, or do-notation, or pattern guards),
4968 or a <literal>where</literal> clause.
4969 Note the following points:
4972 An implicit-parameter binding group must be a
4973 collection of simple bindings to implicit-style variables (no
4974 function-style bindings, and no type signatures); these bindings are
4975 neither polymorphic or recursive.
4978 You may not mix implicit-parameter bindings with ordinary bindings in a
4979 single <literal>let</literal>
4980 expression; use two nested <literal>let</literal>s instead.
4981 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4985 You may put multiple implicit-parameter bindings in a
4986 single binding group; but they are <emphasis>not</emphasis> treated
4987 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4988 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4989 parameter. The bindings are not nested, and may be re-ordered without changing
4990 the meaning of the program.
4991 For example, consider:
4993 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4995 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4996 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4998 f :: (?x::Int) => Int -> Int
5006 <sect3><title>Implicit parameters and polymorphic recursion</title>
5009 Consider these two definitions:
5012 len1 xs = let ?acc = 0 in len_acc1 xs
5015 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5020 len2 xs = let ?acc = 0 in len_acc2 xs
5022 len_acc2 :: (?acc :: Int) => [a] -> Int
5024 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5026 The only difference between the two groups is that in the second group
5027 <literal>len_acc</literal> is given a type signature.
5028 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5029 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5030 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5031 has a type signature, the recursive call is made to the
5032 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5033 as an implicit parameter. So we get the following results in GHCi:
5040 Adding a type signature dramatically changes the result! This is a rather
5041 counter-intuitive phenomenon, worth watching out for.
5045 <sect3><title>Implicit parameters and monomorphism</title>
5047 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5048 Haskell Report) to implicit parameters. For example, consider:
5056 Since the binding for <literal>y</literal> falls under the Monomorphism
5057 Restriction it is not generalised, so the type of <literal>y</literal> is
5058 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5059 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5060 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5061 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5062 <literal>y</literal> in the body of the <literal>let</literal> will see the
5063 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5064 <literal>14</literal>.
5069 <!-- ======================= COMMENTED OUT ========================
5071 We intend to remove linear implicit parameters, so I'm at least removing
5072 them from the 6.6 user manual
5074 <sect2 id="linear-implicit-parameters">
5075 <title>Linear implicit parameters</title>
5077 Linear implicit parameters are an idea developed by Koen Claessen,
5078 Mark Shields, and Simon PJ. They address the long-standing
5079 problem that monads seem over-kill for certain sorts of problem, notably:
5082 <listitem> <para> distributing a supply of unique names </para> </listitem>
5083 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5084 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5088 Linear implicit parameters are just like ordinary implicit parameters,
5089 except that they are "linear"; that is, they cannot be copied, and
5090 must be explicitly "split" instead. Linear implicit parameters are
5091 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5092 (The '/' in the '%' suggests the split!)
5097 import GHC.Exts( Splittable )
5099 data NameSupply = ...
5101 splitNS :: NameSupply -> (NameSupply, NameSupply)
5102 newName :: NameSupply -> Name
5104 instance Splittable NameSupply where
5108 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5109 f env (Lam x e) = Lam x' (f env e)
5112 env' = extend env x x'
5113 ...more equations for f...
5115 Notice that the implicit parameter %ns is consumed
5117 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5118 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5122 So the translation done by the type checker makes
5123 the parameter explicit:
5125 f :: NameSupply -> Env -> Expr -> Expr
5126 f ns env (Lam x e) = Lam x' (f ns1 env e)
5128 (ns1,ns2) = splitNS ns
5130 env = extend env x x'
5132 Notice the call to 'split' introduced by the type checker.
5133 How did it know to use 'splitNS'? Because what it really did
5134 was to introduce a call to the overloaded function 'split',
5135 defined by the class <literal>Splittable</literal>:
5137 class Splittable a where
5140 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5141 split for name supplies. But we can simply write
5147 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5149 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5150 <literal>GHC.Exts</literal>.
5155 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5156 are entirely distinct implicit parameters: you
5157 can use them together and they won't interfere with each other. </para>
5160 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5162 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5163 in the context of a class or instance declaration. </para></listitem>
5167 <sect3><title>Warnings</title>
5170 The monomorphism restriction is even more important than usual.
5171 Consider the example above:
5173 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5174 f env (Lam x e) = Lam x' (f env e)
5177 env' = extend env x x'
5179 If we replaced the two occurrences of x' by (newName %ns), which is
5180 usually a harmless thing to do, we get:
5182 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5183 f env (Lam x e) = Lam (newName %ns) (f env e)
5185 env' = extend env x (newName %ns)
5187 But now the name supply is consumed in <emphasis>three</emphasis> places
5188 (the two calls to newName,and the recursive call to f), so
5189 the result is utterly different. Urk! We don't even have
5193 Well, this is an experimental change. With implicit
5194 parameters we have already lost beta reduction anyway, and
5195 (as John Launchbury puts it) we can't sensibly reason about
5196 Haskell programs without knowing their typing.
5201 <sect3><title>Recursive functions</title>
5202 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5205 foo :: %x::T => Int -> [Int]
5207 foo n = %x : foo (n-1)
5209 where T is some type in class Splittable.</para>
5211 Do you get a list of all the same T's or all different T's
5212 (assuming that split gives two distinct T's back)?
5214 If you supply the type signature, taking advantage of polymorphic
5215 recursion, you get what you'd probably expect. Here's the
5216 translated term, where the implicit param is made explicit:
5219 foo x n = let (x1,x2) = split x
5220 in x1 : foo x2 (n-1)
5222 But if you don't supply a type signature, GHC uses the Hindley
5223 Milner trick of using a single monomorphic instance of the function
5224 for the recursive calls. That is what makes Hindley Milner type inference
5225 work. So the translation becomes
5229 foom n = x : foom (n-1)
5233 Result: 'x' is not split, and you get a list of identical T's. So the
5234 semantics of the program depends on whether or not foo has a type signature.
5237 You may say that this is a good reason to dislike linear implicit parameters
5238 and you'd be right. That is why they are an experimental feature.
5244 ================ END OF Linear Implicit Parameters commented out -->
5246 <sect2 id="kinding">
5247 <title>Explicitly-kinded quantification</title>
5250 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5251 to give the kind explicitly as (machine-checked) documentation,
5252 just as it is nice to give a type signature for a function. On some occasions,
5253 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5254 John Hughes had to define the data type:
5256 data Set cxt a = Set [a]
5257 | Unused (cxt a -> ())
5259 The only use for the <literal>Unused</literal> constructor was to force the correct
5260 kind for the type variable <literal>cxt</literal>.
5263 GHC now instead allows you to specify the kind of a type variable directly, wherever
5264 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5267 This flag enables kind signatures in the following places:
5269 <listitem><para><literal>data</literal> declarations:
5271 data Set (cxt :: * -> *) a = Set [a]
5272 </screen></para></listitem>
5273 <listitem><para><literal>type</literal> declarations:
5275 type T (f :: * -> *) = f Int
5276 </screen></para></listitem>
5277 <listitem><para><literal>class</literal> declarations:
5279 class (Eq a) => C (f :: * -> *) a where ...
5280 </screen></para></listitem>
5281 <listitem><para><literal>forall</literal>'s in type signatures:
5283 f :: forall (cxt :: * -> *). Set cxt Int
5284 </screen></para></listitem>
5289 The parentheses are required. Some of the spaces are required too, to
5290 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5291 will get a parse error, because "<literal>::*->*</literal>" is a
5292 single lexeme in Haskell.
5296 As part of the same extension, you can put kind annotations in types
5299 f :: (Int :: *) -> Int
5300 g :: forall a. a -> (a :: *)
5304 atype ::= '(' ctype '::' kind ')
5306 The parentheses are required.
5311 <sect2 id="universal-quantification">
5312 <title>Arbitrary-rank polymorphism
5316 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5317 allows us to say exactly what this means. For example:
5325 g :: forall b. (b -> b)
5327 The two are treated identically.
5331 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5332 explicit universal quantification in
5334 For example, all the following types are legal:
5336 f1 :: forall a b. a -> b -> a
5337 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5339 f2 :: (forall a. a->a) -> Int -> Int
5340 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5342 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5344 f4 :: Int -> (forall a. a -> a)
5346 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5347 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5348 The <literal>forall</literal> makes explicit the universal quantification that
5349 is implicitly added by Haskell.
5352 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5353 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5354 shows, the polymorphic type on the left of the function arrow can be overloaded.
5357 The function <literal>f3</literal> has a rank-3 type;
5358 it has rank-2 types on the left of a function arrow.
5361 GHC has three flags to control higher-rank types:
5364 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5367 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5370 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5371 That is, you can nest <literal>forall</literal>s
5372 arbitrarily deep in function arrows.
5373 In particular, a forall-type (also called a "type scheme"),
5374 including an operational type class context, is legal:
5376 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5377 of a function arrow </para> </listitem>
5378 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5379 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5380 field type signatures.</para> </listitem>
5381 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5382 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5386 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5387 a type variable any more!
5396 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5397 the types of the constructor arguments. Here are several examples:
5403 data T a = T1 (forall b. b -> b -> b) a
5405 data MonadT m = MkMonad { return :: forall a. a -> m a,
5406 bind :: forall a b. m a -> (a -> m b) -> m b
5409 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5415 The constructors have rank-2 types:
5421 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5422 MkMonad :: forall m. (forall a. a -> m a)
5423 -> (forall a b. m a -> (a -> m b) -> m b)
5425 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5431 Notice that you don't need to use a <literal>forall</literal> if there's an
5432 explicit context. For example in the first argument of the
5433 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5434 prefixed to the argument type. The implicit <literal>forall</literal>
5435 quantifies all type variables that are not already in scope, and are
5436 mentioned in the type quantified over.
5440 As for type signatures, implicit quantification happens for non-overloaded
5441 types too. So if you write this:
5444 data T a = MkT (Either a b) (b -> b)
5447 it's just as if you had written this:
5450 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5453 That is, since the type variable <literal>b</literal> isn't in scope, it's
5454 implicitly universally quantified. (Arguably, it would be better
5455 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5456 where that is what is wanted. Feedback welcomed.)
5460 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5461 the constructor to suitable values, just as usual. For example,
5472 a3 = MkSwizzle reverse
5475 a4 = let r x = Just x
5482 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5483 mkTs f x y = [T1 f x, T1 f y]
5489 The type of the argument can, as usual, be more general than the type
5490 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5491 does not need the <literal>Ord</literal> constraint.)
5495 When you use pattern matching, the bound variables may now have
5496 polymorphic types. For example:
5502 f :: T a -> a -> (a, Char)
5503 f (T1 w k) x = (w k x, w 'c' 'd')
5505 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5506 g (MkSwizzle s) xs f = s (map f (s xs))
5508 h :: MonadT m -> [m a] -> m [a]
5509 h m [] = return m []
5510 h m (x:xs) = bind m x $ \y ->
5511 bind m (h m xs) $ \ys ->
5518 In the function <function>h</function> we use the record selectors <literal>return</literal>
5519 and <literal>bind</literal> to extract the polymorphic bind and return functions
5520 from the <literal>MonadT</literal> data structure, rather than using pattern
5526 <title>Type inference</title>
5529 In general, type inference for arbitrary-rank types is undecidable.
5530 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5531 to get a decidable algorithm by requiring some help from the programmer.
5532 We do not yet have a formal specification of "some help" but the rule is this:
5535 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5536 provides an explicit polymorphic type for x, or GHC's type inference will assume
5537 that x's type has no foralls in it</emphasis>.
5540 What does it mean to "provide" an explicit type for x? You can do that by
5541 giving a type signature for x directly, using a pattern type signature
5542 (<xref linkend="scoped-type-variables"/>), thus:
5544 \ f :: (forall a. a->a) -> (f True, f 'c')
5546 Alternatively, you can give a type signature to the enclosing
5547 context, which GHC can "push down" to find the type for the variable:
5549 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5551 Here the type signature on the expression can be pushed inwards
5552 to give a type signature for f. Similarly, and more commonly,
5553 one can give a type signature for the function itself:
5555 h :: (forall a. a->a) -> (Bool,Char)
5556 h f = (f True, f 'c')
5558 You don't need to give a type signature if the lambda bound variable
5559 is a constructor argument. Here is an example we saw earlier:
5561 f :: T a -> a -> (a, Char)
5562 f (T1 w k) x = (w k x, w 'c' 'd')
5564 Here we do not need to give a type signature to <literal>w</literal>, because
5565 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5572 <sect3 id="implicit-quant">
5573 <title>Implicit quantification</title>
5576 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5577 user-written types, if and only if there is no explicit <literal>forall</literal>,
5578 GHC finds all the type variables mentioned in the type that are not already
5579 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5583 f :: forall a. a -> a
5590 h :: forall b. a -> b -> b
5596 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5599 f :: (a -> a) -> Int
5601 f :: forall a. (a -> a) -> Int
5603 f :: (forall a. a -> a) -> Int
5606 g :: (Ord a => a -> a) -> Int
5607 -- MEANS the illegal type
5608 g :: forall a. (Ord a => a -> a) -> Int
5610 g :: (forall a. Ord a => a -> a) -> Int
5612 The latter produces an illegal type, which you might think is silly,
5613 but at least the rule is simple. If you want the latter type, you
5614 can write your for-alls explicitly. Indeed, doing so is strongly advised
5621 <sect2 id="impredicative-polymorphism">
5622 <title>Impredicative polymorphism
5624 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5625 enabled with <option>-XImpredicativeTypes</option>.
5627 that you can call a polymorphic function at a polymorphic type, and
5628 parameterise data structures over polymorphic types. For example:
5630 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5631 f (Just g) = Just (g [3], g "hello")
5634 Notice here that the <literal>Maybe</literal> type is parameterised by the
5635 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5638 <para>The technical details of this extension are described in the paper
5639 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5640 type inference for higher-rank types and impredicativity</ulink>,
5641 which appeared at ICFP 2006.
5645 <sect2 id="scoped-type-variables">
5646 <title>Lexically scoped type variables
5650 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5651 which some type signatures are simply impossible to write. For example:
5653 f :: forall a. [a] -> [a]
5659 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5660 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5661 The type variables bound by a <literal>forall</literal> scope over
5662 the entire definition of the accompanying value declaration.
5663 In this example, the type variable <literal>a</literal> scopes over the whole
5664 definition of <literal>f</literal>, including over
5665 the type signature for <varname>ys</varname>.
5666 In Haskell 98 it is not possible to declare
5667 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5668 it becomes possible to do so.
5670 <para>Lexically-scoped type variables are enabled by
5671 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5673 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5674 variables work, compared to earlier releases. Read this section
5678 <title>Overview</title>
5680 <para>The design follows the following principles
5682 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5683 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5684 design.)</para></listitem>
5685 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5686 type variables. This means that every programmer-written type signature
5687 (including one that contains free scoped type variables) denotes a
5688 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5689 checker, and no inference is involved.</para></listitem>
5690 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5691 changing the program.</para></listitem>
5695 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5697 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5698 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5699 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5700 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5704 In Haskell, a programmer-written type signature is implicitly quantified over
5705 its free type variables (<ulink
5706 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5708 of the Haskell Report).
5709 Lexically scoped type variables affect this implicit quantification rules
5710 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5711 quantified. For example, if type variable <literal>a</literal> is in scope,
5714 (e :: a -> a) means (e :: a -> a)
5715 (e :: b -> b) means (e :: forall b. b->b)
5716 (e :: a -> b) means (e :: forall b. a->b)
5724 <sect3 id="decl-type-sigs">
5725 <title>Declaration type signatures</title>
5726 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5727 quantification (using <literal>forall</literal>) brings into scope the
5728 explicitly-quantified
5729 type variables, in the definition of the named function. For example:
5731 f :: forall a. [a] -> [a]
5732 f (x:xs) = xs ++ [ x :: a ]
5734 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5735 the definition of "<literal>f</literal>".
5737 <para>This only happens if:
5739 <listitem><para> The quantification in <literal>f</literal>'s type
5740 signature is explicit. For example:
5743 g (x:xs) = xs ++ [ x :: a ]
5745 This program will be rejected, because "<literal>a</literal>" does not scope
5746 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5747 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5748 quantification rules.
5750 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5751 not a pattern binding.
5754 f1 :: forall a. [a] -> [a]
5755 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5757 f2 :: forall a. [a] -> [a]
5758 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5760 f3 :: forall a. [a] -> [a]
5761 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5763 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5764 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5765 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5766 the type signature brings <literal>a</literal> into scope.
5772 <sect3 id="exp-type-sigs">
5773 <title>Expression type signatures</title>
5775 <para>An expression type signature that has <emphasis>explicit</emphasis>
5776 quantification (using <literal>forall</literal>) brings into scope the
5777 explicitly-quantified
5778 type variables, in the annotated expression. For example:
5780 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5782 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5783 type variable <literal>s</literal> into scope, in the annotated expression
5784 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5789 <sect3 id="pattern-type-sigs">
5790 <title>Pattern type signatures</title>
5792 A type signature may occur in any pattern; this is a <emphasis>pattern type
5793 signature</emphasis>.
5796 -- f and g assume that 'a' is already in scope
5797 f = \(x::Int, y::a) -> x
5799 h ((x,y) :: (Int,Bool)) = (y,x)
5801 In the case where all the type variables in the pattern type signature are
5802 already in scope (i.e. bound by the enclosing context), matters are simple: the
5803 signature simply constrains the type of the pattern in the obvious way.
5806 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5807 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5808 that are already in scope. For example:
5810 f :: forall a. [a] -> (Int, [a])
5813 (ys::[a], n) = (reverse xs, length xs) -- OK
5814 zs::[a] = xs ++ ys -- OK
5816 Just (v::b) = ... -- Not OK; b is not in scope
5818 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5819 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5823 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5824 type signature may mention a type variable that is not in scope; in this case,
5825 <emphasis>the signature brings that type variable into scope</emphasis>.
5826 This is particularly important for existential data constructors. For example:
5828 data T = forall a. MkT [a]
5831 k (MkT [t::a]) = MkT t3
5835 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5836 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5837 because it is bound by the pattern match. GHC's rule is that in this situation
5838 (and only then), a pattern type signature can mention a type variable that is
5839 not already in scope; the effect is to bring it into scope, standing for the
5840 existentially-bound type variable.
5843 When a pattern type signature binds a type variable in this way, GHC insists that the
5844 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5845 This means that any user-written type signature always stands for a completely known type.
5848 If all this seems a little odd, we think so too. But we must have
5849 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5850 could not name existentially-bound type variables in subsequent type signatures.
5853 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5854 signature is allowed to mention a lexical variable that is not already in
5856 For example, both <literal>f</literal> and <literal>g</literal> would be
5857 illegal if <literal>a</literal> was not already in scope.
5863 <!-- ==================== Commented out part about result type signatures
5865 <sect3 id="result-type-sigs">
5866 <title>Result type signatures</title>
5869 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5872 {- f assumes that 'a' is already in scope -}
5873 f x y :: [a] = [x,y,x]
5875 g = \ x :: [Int] -> [3,4]
5877 h :: forall a. [a] -> a
5881 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5882 the result of the function. Similarly, the body of the lambda in the RHS of
5883 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5884 alternative in <literal>h</literal> is <literal>a</literal>.
5886 <para> A result type signature never brings new type variables into scope.</para>
5888 There are a couple of syntactic wrinkles. First, notice that all three
5889 examples would parse quite differently with parentheses:
5891 {- f assumes that 'a' is already in scope -}
5892 f x (y :: [a]) = [x,y,x]
5894 g = \ (x :: [Int]) -> [3,4]
5896 h :: forall a. [a] -> a
5900 Now the signature is on the <emphasis>pattern</emphasis>; and
5901 <literal>h</literal> would certainly be ill-typed (since the pattern
5902 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5904 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5905 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5906 token or a parenthesised type of some sort). To see why,
5907 consider how one would parse this:
5916 <sect3 id="cls-inst-scoped-tyvars">
5917 <title>Class and instance declarations</title>
5920 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5921 scope over the methods defined in the <literal>where</literal> part. For example:
5939 <sect2 id="typing-binds">
5940 <title>Generalised typing of mutually recursive bindings</title>
5943 The Haskell Report specifies that a group of bindings (at top level, or in a
5944 <literal>let</literal> or <literal>where</literal>) should be sorted into
5945 strongly-connected components, and then type-checked in dependency order
5946 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5947 Report, Section 4.5.1</ulink>).
5948 As each group is type-checked, any binders of the group that
5950 an explicit type signature are put in the type environment with the specified
5952 and all others are monomorphic until the group is generalised
5953 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5956 <para>Following a suggestion of Mark Jones, in his paper
5957 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5959 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5961 <emphasis>the dependency analysis ignores references to variables that have an explicit
5962 type signature</emphasis>.
5963 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5964 typecheck. For example, consider:
5966 f :: Eq a => a -> Bool
5967 f x = (x == x) || g True || g "Yes"
5969 g y = (y <= y) || f True
5971 This is rejected by Haskell 98, but under Jones's scheme the definition for
5972 <literal>g</literal> is typechecked first, separately from that for
5973 <literal>f</literal>,
5974 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5975 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5976 type is generalised, to get
5978 g :: Ord a => a -> Bool
5980 Now, the definition for <literal>f</literal> is typechecked, with this type for
5981 <literal>g</literal> in the type environment.
5985 The same refined dependency analysis also allows the type signatures of
5986 mutually-recursive functions to have different contexts, something that is illegal in
5987 Haskell 98 (Section 4.5.2, last sentence). With
5988 <option>-XRelaxedPolyRec</option>
5989 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5990 type signatures; in practice this means that only variables bound by the same
5991 pattern binding must have the same context. For example, this is fine:
5993 f :: Eq a => a -> Bool
5994 f x = (x == x) || g True
5996 g :: Ord a => a -> Bool
5997 g y = (y <= y) || f True
6003 <!-- ==================== End of type system extensions ================= -->
6005 <!-- ====================== TEMPLATE HASKELL ======================= -->
6007 <sect1 id="template-haskell">
6008 <title>Template Haskell</title>
6010 <para>Template Haskell allows you to do compile-time meta-programming in
6013 the main technical innovations is discussed in "<ulink
6014 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6015 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6018 There is a Wiki page about
6019 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6020 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6024 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6025 Haskell library reference material</ulink>
6026 (look for module <literal>Language.Haskell.TH</literal>).
6027 Many changes to the original design are described in
6028 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6029 Notes on Template Haskell version 2</ulink>.
6030 Not all of these changes are in GHC, however.
6033 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6034 as a worked example to help get you started.
6038 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6039 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6044 <title>Syntax</title>
6046 <para> Template Haskell has the following new syntactic
6047 constructions. You need to use the flag
6048 <option>-XTemplateHaskell</option>
6049 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6050 </indexterm>to switch these syntactic extensions on
6051 (<option>-XTemplateHaskell</option> is no longer implied by
6052 <option>-fglasgow-exts</option>).</para>
6056 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6057 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6058 There must be no space between the "$" and the identifier or parenthesis. This use
6059 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6060 of "." as an infix operator. If you want the infix operator, put spaces around it.
6062 <para> A splice can occur in place of
6064 <listitem><para> an expression; the spliced expression must
6065 have type <literal>Q Exp</literal></para></listitem>
6066 <listitem><para> an type; the spliced expression must
6067 have type <literal>Q Typ</literal></para></listitem>
6068 <listitem><para> a list of top-level declarations; the spliced expression
6069 must have type <literal>Q [Dec]</literal></para></listitem>
6071 Inside a splice you can can only call functions defined in imported modules,
6072 not functions defined elsewhere in the same module.</para></listitem>
6075 A expression quotation is written in Oxford brackets, thus:
6077 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
6078 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6079 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6080 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6081 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6082 the quotation has type <literal>Q Typ</literal>.</para></listitem>
6083 </itemizedlist></para></listitem>
6086 A quasi-quotation can appear in either a pattern context or an
6087 expression context and is also written in Oxford brackets:
6089 <listitem><para> <literal>[$<replaceable>varid</replaceable>| ... |]</literal>,
6090 where the "..." is an arbitrary string; a full description of the
6091 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6092 </itemizedlist></para></listitem>
6095 A name can be quoted with either one or two prefix single quotes:
6097 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6098 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6099 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6101 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6102 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6105 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6106 may also be given as an argument to the <literal>reify</literal> function.
6110 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6111 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6118 $(deriveStuff 'f) -- Uses the $(...) notation
6122 deriveStuff 'g -- Omits the $(...)
6126 This abbreviation makes top-level declaration slices quieter and less intimidating.
6131 (Compared to the original paper, there are many differences of detail.
6132 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6133 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6134 Pattern splices and quotations are not implemented.)
6138 <sect2> <title> Using Template Haskell </title>
6142 The data types and monadic constructor functions for Template Haskell are in the library
6143 <literal>Language.Haskell.THSyntax</literal>.
6147 You can only run a function at compile time if it is imported from another module. That is,
6148 you can't define a function in a module, and call it from within a splice in the same module.
6149 (It would make sense to do so, but it's hard to implement.)
6153 You can only run a function at compile time if it is imported
6154 from another module <emphasis>that is not part of a mutually-recursive group of modules
6155 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6156 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6157 splice is to be run.</para>
6159 For example, when compiling module A,
6160 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6161 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6165 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6168 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6169 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6170 compiles and runs a program, and then looks at the result. So it's important that
6171 the program it compiles produces results whose representations are identical to
6172 those of the compiler itself.
6176 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6177 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6182 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6183 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6184 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6191 -- Import our template "pr"
6192 import Printf ( pr )
6194 -- The splice operator $ takes the Haskell source code
6195 -- generated at compile time by "pr" and splices it into
6196 -- the argument of "putStrLn".
6197 main = putStrLn ( $(pr "Hello") )
6203 -- Skeletal printf from the paper.
6204 -- It needs to be in a separate module to the one where
6205 -- you intend to use it.
6207 -- Import some Template Haskell syntax
6208 import Language.Haskell.TH
6210 -- Describe a format string
6211 data Format = D | S | L String
6213 -- Parse a format string. This is left largely to you
6214 -- as we are here interested in building our first ever
6215 -- Template Haskell program and not in building printf.
6216 parse :: String -> [Format]
6219 -- Generate Haskell source code from a parsed representation
6220 -- of the format string. This code will be spliced into
6221 -- the module which calls "pr", at compile time.
6222 gen :: [Format] -> Q Exp
6223 gen [D] = [| \n -> show n |]
6224 gen [S] = [| \s -> s |]
6225 gen [L s] = stringE s
6227 -- Here we generate the Haskell code for the splice
6228 -- from an input format string.
6229 pr :: String -> Q Exp
6230 pr s = gen (parse s)
6233 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6236 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6239 <para>Run "main.exe" and here is your output:</para>
6249 <title>Using Template Haskell with Profiling</title>
6250 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6252 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6253 interpreter to run the splice expressions. The bytecode interpreter
6254 runs the compiled expression on top of the same runtime on which GHC
6255 itself is running; this means that the compiled code referred to by
6256 the interpreted expression must be compatible with this runtime, and
6257 in particular this means that object code that is compiled for
6258 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6259 expression, because profiled object code is only compatible with the
6260 profiling version of the runtime.</para>
6262 <para>This causes difficulties if you have a multi-module program
6263 containing Template Haskell code and you need to compile it for
6264 profiling, because GHC cannot load the profiled object code and use it
6265 when executing the splices. Fortunately GHC provides a workaround.
6266 The basic idea is to compile the program twice:</para>
6270 <para>Compile the program or library first the normal way, without
6271 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6274 <para>Then compile it again with <option>-prof</option>, and
6275 additionally use <option>-osuf
6276 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6277 to name the object files differently (you can choose any suffix
6278 that isn't the normal object suffix here). GHC will automatically
6279 load the object files built in the first step when executing splice
6280 expressions. If you omit the <option>-osuf</option> flag when
6281 building with <option>-prof</option> and Template Haskell is used,
6282 GHC will emit an error message. </para>
6287 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6288 <para>Quasi-quotation allows patterns and expressions to be written using
6289 programmer-defined concrete syntax; the motivation behind the extension and
6290 several examples are documented in
6291 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6292 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6293 2007). The example below shows how to write a quasiquoter for a simple
6294 expression language.</para>
6297 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6298 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6299 functions for quoting expressions and patterns, respectively. The first argument
6300 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6301 context of the quasi-quotation statement determines which of the two parsers is
6302 called: if the quasi-quotation occurs in an expression context, the expression
6303 parser is called, and if it occurs in a pattern context, the pattern parser is
6307 Note that in the example we make use of an antiquoted
6308 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6309 (this syntax for anti-quotation was defined by the parser's
6310 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6311 integer value argument of the constructor <literal>IntExpr</literal> when
6312 pattern matching. Please see the referenced paper for further details regarding
6313 anti-quotation as well as the description of a technique that uses SYB to
6314 leverage a single parser of type <literal>String -> a</literal> to generate both
6315 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6316 pattern parser that returns a value of type <literal>Q Pat</literal>.
6319 <para>In general, a quasi-quote has the form
6320 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6321 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6322 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6323 can be arbitrary, and may contain newlines.
6326 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6327 the example, <literal>expr</literal> cannot be defined
6328 in <literal>Main.hs</literal> where it is used, but must be imported.
6339 main = do { print $ eval [$expr|1 + 2|]
6341 { [$expr|'int:n|] -> print n
6350 import qualified Language.Haskell.TH as TH
6351 import Language.Haskell.TH.Quote
6353 data Expr = IntExpr Integer
6354 | AntiIntExpr String
6355 | BinopExpr BinOp Expr Expr
6357 deriving(Show, Typeable, Data)
6363 deriving(Show, Typeable, Data)
6365 eval :: Expr -> Integer
6366 eval (IntExpr n) = n
6367 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6374 expr = QuasiQuoter parseExprExp parseExprPat
6376 -- Parse an Expr, returning its representation as
6377 -- either a Q Exp or a Q Pat. See the referenced paper
6378 -- for how to use SYB to do this by writing a single
6379 -- parser of type String -> Expr instead of two
6380 -- separate parsers.
6382 parseExprExp :: String -> Q Exp
6385 parseExprPat :: String -> Q Pat
6389 <para>Now run the compiler:
6392 $ ghc --make -XQuasiQuotes Main.hs -o main
6395 <para>Run "main" and here is your output:</para>
6407 <!-- ===================== Arrow notation =================== -->
6409 <sect1 id="arrow-notation">
6410 <title>Arrow notation
6413 <para>Arrows are a generalization of monads introduced by John Hughes.
6414 For more details, see
6419 “Generalising Monads to Arrows”,
6420 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6421 pp67–111, May 2000.
6422 The paper that introduced arrows: a friendly introduction, motivated with
6423 programming examples.
6429 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6430 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6431 Introduced the notation described here.
6437 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6438 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6445 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6446 John Hughes, in <citetitle>5th International Summer School on
6447 Advanced Functional Programming</citetitle>,
6448 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6450 This paper includes another introduction to the notation,
6451 with practical examples.
6457 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6458 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6459 A terse enumeration of the formal rules used
6460 (extracted from comments in the source code).
6466 The arrows web page at
6467 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6472 With the <option>-XArrows</option> flag, GHC supports the arrow
6473 notation described in the second of these papers,
6474 translating it using combinators from the
6475 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6477 What follows is a brief introduction to the notation;
6478 it won't make much sense unless you've read Hughes's paper.
6481 <para>The extension adds a new kind of expression for defining arrows:
6483 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6484 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6486 where <literal>proc</literal> is a new keyword.
6487 The variables of the pattern are bound in the body of the
6488 <literal>proc</literal>-expression,
6489 which is a new sort of thing called a <firstterm>command</firstterm>.
6490 The syntax of commands is as follows:
6492 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6493 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6494 | <replaceable>cmd</replaceable><superscript>0</superscript>
6496 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6497 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6498 infix operators as for expressions, and
6500 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6501 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6502 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6503 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6504 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6505 | <replaceable>fcmd</replaceable>
6507 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6508 | ( <replaceable>cmd</replaceable> )
6509 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6511 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6512 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6513 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6514 | <replaceable>cmd</replaceable>
6516 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6517 except that the bodies are commands instead of expressions.
6521 Commands produce values, but (like monadic computations)
6522 may yield more than one value,
6523 or none, and may do other things as well.
6524 For the most part, familiarity with monadic notation is a good guide to
6526 However the values of expressions, even monadic ones,
6527 are determined by the values of the variables they contain;
6528 this is not necessarily the case for commands.
6532 A simple example of the new notation is the expression
6534 proc x -> f -< x+1
6536 We call this a <firstterm>procedure</firstterm> or
6537 <firstterm>arrow abstraction</firstterm>.
6538 As with a lambda expression, the variable <literal>x</literal>
6539 is a new variable bound within the <literal>proc</literal>-expression.
6540 It refers to the input to the arrow.
6541 In the above example, <literal>-<</literal> is not an identifier but an
6542 new reserved symbol used for building commands from an expression of arrow
6543 type and an expression to be fed as input to that arrow.
6544 (The weird look will make more sense later.)
6545 It may be read as analogue of application for arrows.
6546 The above example is equivalent to the Haskell expression
6548 arr (\ x -> x+1) >>> f
6550 That would make no sense if the expression to the left of
6551 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6552 More generally, the expression to the left of <literal>-<</literal>
6553 may not involve any <firstterm>local variable</firstterm>,
6554 i.e. a variable bound in the current arrow abstraction.
6555 For such a situation there is a variant <literal>-<<</literal>, as in
6557 proc x -> f x -<< x+1
6559 which is equivalent to
6561 arr (\ x -> (f x, x+1)) >>> app
6563 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6565 Such an arrow is equivalent to a monad, so if you're using this form
6566 you may find a monadic formulation more convenient.
6570 <title>do-notation for commands</title>
6573 Another form of command is a form of <literal>do</literal>-notation.
6574 For example, you can write
6583 You can read this much like ordinary <literal>do</literal>-notation,
6584 but with commands in place of monadic expressions.
6585 The first line sends the value of <literal>x+1</literal> as an input to
6586 the arrow <literal>f</literal>, and matches its output against
6587 <literal>y</literal>.
6588 In the next line, the output is discarded.
6589 The arrow <function>returnA</function> is defined in the
6590 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6591 module as <literal>arr id</literal>.
6592 The above example is treated as an abbreviation for
6594 arr (\ x -> (x, x)) >>>
6595 first (arr (\ x -> x+1) >>> f) >>>
6596 arr (\ (y, x) -> (y, (x, y))) >>>
6597 first (arr (\ y -> 2*y) >>> g) >>>
6599 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6600 first (arr (\ (x, z) -> x*z) >>> h) >>>
6601 arr (\ (t, z) -> t+z) >>>
6604 Note that variables not used later in the composition are projected out.
6605 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6607 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6608 module, this reduces to
6610 arr (\ x -> (x+1, x)) >>>
6612 arr (\ (y, x) -> (2*y, (x, y))) >>>
6614 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6616 arr (\ (t, z) -> t+z)
6618 which is what you might have written by hand.
6619 With arrow notation, GHC keeps track of all those tuples of variables for you.
6623 Note that although the above translation suggests that
6624 <literal>let</literal>-bound variables like <literal>z</literal> must be
6625 monomorphic, the actual translation produces Core,
6626 so polymorphic variables are allowed.
6630 It's also possible to have mutually recursive bindings,
6631 using the new <literal>rec</literal> keyword, as in the following example:
6633 counter :: ArrowCircuit a => a Bool Int
6634 counter = proc reset -> do
6635 rec output <- returnA -< if reset then 0 else next
6636 next <- delay 0 -< output+1
6637 returnA -< output
6639 The translation of such forms uses the <function>loop</function> combinator,
6640 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6646 <title>Conditional commands</title>
6649 In the previous example, we used a conditional expression to construct the
6651 Sometimes we want to conditionally execute different commands, as in
6658 which is translated to
6660 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6661 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6663 Since the translation uses <function>|||</function>,
6664 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6668 There are also <literal>case</literal> commands, like
6674 y <- h -< (x1, x2)
6678 The syntax is the same as for <literal>case</literal> expressions,
6679 except that the bodies of the alternatives are commands rather than expressions.
6680 The translation is similar to that of <literal>if</literal> commands.
6686 <title>Defining your own control structures</title>
6689 As we're seen, arrow notation provides constructs,
6690 modelled on those for expressions,
6691 for sequencing, value recursion and conditionals.
6692 But suitable combinators,
6693 which you can define in ordinary Haskell,
6694 may also be used to build new commands out of existing ones.
6695 The basic idea is that a command defines an arrow from environments to values.
6696 These environments assign values to the free local variables of the command.
6697 Thus combinators that produce arrows from arrows
6698 may also be used to build commands from commands.
6699 For example, the <literal>ArrowChoice</literal> class includes a combinator
6701 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6703 so we can use it to build commands:
6705 expr' = proc x -> do
6708 symbol Plus -< ()
6709 y <- term -< ()
6712 symbol Minus -< ()
6713 y <- term -< ()
6716 (The <literal>do</literal> on the first line is needed to prevent the first
6717 <literal><+> ...</literal> from being interpreted as part of the
6718 expression on the previous line.)
6719 This is equivalent to
6721 expr' = (proc x -> returnA -< x)
6722 <+> (proc x -> do
6723 symbol Plus -< ()
6724 y <- term -< ()
6726 <+> (proc x -> do
6727 symbol Minus -< ()
6728 y <- term -< ()
6731 It is essential that this operator be polymorphic in <literal>e</literal>
6732 (representing the environment input to the command
6733 and thence to its subcommands)
6734 and satisfy the corresponding naturality property
6736 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6738 at least for strict <literal>k</literal>.
6739 (This should be automatic if you're not using <function>seq</function>.)
6740 This ensures that environments seen by the subcommands are environments
6741 of the whole command,
6742 and also allows the translation to safely trim these environments.
6743 The operator must also not use any variable defined within the current
6748 We could define our own operator
6750 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6751 untilA body cond = proc x ->
6752 b <- cond -< x
6753 if b then returnA -< ()
6756 untilA body cond -< x
6758 and use it in the same way.
6759 Of course this infix syntax only makes sense for binary operators;
6760 there is also a more general syntax involving special brackets:
6764 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6771 <title>Primitive constructs</title>
6774 Some operators will need to pass additional inputs to their subcommands.
6775 For example, in an arrow type supporting exceptions,
6776 the operator that attaches an exception handler will wish to pass the
6777 exception that occurred to the handler.
6778 Such an operator might have a type
6780 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6782 where <literal>Ex</literal> is the type of exceptions handled.
6783 You could then use this with arrow notation by writing a command
6785 body `handleA` \ ex -> handler
6787 so that if an exception is raised in the command <literal>body</literal>,
6788 the variable <literal>ex</literal> is bound to the value of the exception
6789 and the command <literal>handler</literal>,
6790 which typically refers to <literal>ex</literal>, is entered.
6791 Though the syntax here looks like a functional lambda,
6792 we are talking about commands, and something different is going on.
6793 The input to the arrow represented by a command consists of values for
6794 the free local variables in the command, plus a stack of anonymous values.
6795 In all the prior examples, this stack was empty.
6796 In the second argument to <function>handleA</function>,
6797 this stack consists of one value, the value of the exception.
6798 The command form of lambda merely gives this value a name.
6803 the values on the stack are paired to the right of the environment.
6804 So operators like <function>handleA</function> that pass
6805 extra inputs to their subcommands can be designed for use with the notation
6806 by pairing the values with the environment in this way.
6807 More precisely, the type of each argument of the operator (and its result)
6808 should have the form
6810 a (...(e,t1), ... tn) t
6812 where <replaceable>e</replaceable> is a polymorphic variable
6813 (representing the environment)
6814 and <replaceable>ti</replaceable> are the types of the values on the stack,
6815 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6816 The polymorphic variable <replaceable>e</replaceable> must not occur in
6817 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6818 <replaceable>t</replaceable>.
6819 However the arrows involved need not be the same.
6820 Here are some more examples of suitable operators:
6822 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6823 runReader :: ... => a e c -> a' (e,State) c
6824 runState :: ... => a e c -> a' (e,State) (c,State)
6826 We can supply the extra input required by commands built with the last two
6827 by applying them to ordinary expressions, as in
6831 (|runReader (do { ... })|) s
6833 which adds <literal>s</literal> to the stack of inputs to the command
6834 built using <function>runReader</function>.
6838 The command versions of lambda abstraction and application are analogous to
6839 the expression versions.
6840 In particular, the beta and eta rules describe equivalences of commands.
6841 These three features (operators, lambda abstraction and application)
6842 are the core of the notation; everything else can be built using them,
6843 though the results would be somewhat clumsy.
6844 For example, we could simulate <literal>do</literal>-notation by defining
6846 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6847 u `bind` f = returnA &&& u >>> f
6849 bind_ :: Arrow a => a e b -> a e c -> a e c
6850 u `bind_` f = u `bind` (arr fst >>> f)
6852 We could simulate <literal>if</literal> by defining
6854 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6855 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6862 <title>Differences with the paper</title>
6867 <para>Instead of a single form of arrow application (arrow tail) with two
6868 translations, the implementation provides two forms
6869 <quote><literal>-<</literal></quote> (first-order)
6870 and <quote><literal>-<<</literal></quote> (higher-order).
6875 <para>User-defined operators are flagged with banana brackets instead of
6876 a new <literal>form</literal> keyword.
6885 <title>Portability</title>
6888 Although only GHC implements arrow notation directly,
6889 there is also a preprocessor
6891 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6892 that translates arrow notation into Haskell 98
6893 for use with other Haskell systems.
6894 You would still want to check arrow programs with GHC;
6895 tracing type errors in the preprocessor output is not easy.
6896 Modules intended for both GHC and the preprocessor must observe some
6897 additional restrictions:
6902 The module must import
6903 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6909 The preprocessor cannot cope with other Haskell extensions.
6910 These would have to go in separate modules.
6916 Because the preprocessor targets Haskell (rather than Core),
6917 <literal>let</literal>-bound variables are monomorphic.
6928 <!-- ==================== BANG PATTERNS ================= -->
6930 <sect1 id="bang-patterns">
6931 <title>Bang patterns
6932 <indexterm><primary>Bang patterns</primary></indexterm>
6934 <para>GHC supports an extension of pattern matching called <emphasis>bang
6935 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6936 Bang patterns are under consideration for Haskell Prime.
6938 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6939 prime feature description</ulink> contains more discussion and examples
6940 than the material below.
6943 The key change is the addition of a new rule to the
6944 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6945 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6946 against a value <replaceable>v</replaceable> behaves as follows:
6948 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6949 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6953 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6956 <sect2 id="bang-patterns-informal">
6957 <title>Informal description of bang patterns
6960 The main idea is to add a single new production to the syntax of patterns:
6964 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6965 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6970 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6971 whereas without the bang it would be lazy.
6972 Bang patterns can be nested of course:
6976 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6977 <literal>y</literal>.
6978 A bang only really has an effect if it precedes a variable or wild-card pattern:
6983 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6984 putting a bang before a pattern that
6985 forces evaluation anyway does nothing.
6988 There is one (apparent) exception to this general rule that a bang only
6989 makes a difference when it precedes a variable or wild-card: a bang at the
6990 top level of a <literal>let</literal> or <literal>where</literal>
6991 binding makes the binding strict, regardless of the pattern. For example:
6995 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6996 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6997 (We say "apparent" exception because the Right Way to think of it is that the bang
6998 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6999 is part of the syntax of the <emphasis>binding</emphasis>.)
7000 Nested bangs in a pattern binding behave uniformly with all other forms of
7001 pattern matching. For example
7003 let (!x,[y]) = e in b
7005 is equivalent to this:
7007 let { t = case e of (x,[y]) -> x `seq` (x,y)
7012 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7013 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7014 evaluation of <literal>x</literal>.
7017 Bang patterns work in <literal>case</literal> expressions too, of course:
7019 g5 x = let y = f x in body
7020 g6 x = case f x of { y -> body }
7021 g7 x = case f x of { !y -> body }
7023 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7024 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7025 result, and then evaluates <literal>body</literal>.
7030 <sect2 id="bang-patterns-sem">
7031 <title>Syntax and semantics
7035 We add a single new production to the syntax of patterns:
7039 There is one problem with syntactic ambiguity. Consider:
7043 Is this a definition of the infix function "<literal>(!)</literal>",
7044 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7045 ambiguity in favour of the latter. If you want to define
7046 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7051 The semantics of Haskell pattern matching is described in <ulink
7052 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7053 Section 3.17.2</ulink> of the Haskell Report. To this description add
7054 one extra item 10, saying:
7055 <itemizedlist><listitem><para>Matching
7056 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7057 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7058 <listitem><para>otherwise, <literal>pat</literal> is matched against
7059 <literal>v</literal></para></listitem>
7061 </para></listitem></itemizedlist>
7062 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7063 Section 3.17.3</ulink>, add a new case (t):
7065 case v of { !pat -> e; _ -> e' }
7066 = v `seq` case v of { pat -> e; _ -> e' }
7069 That leaves let expressions, whose translation is given in
7070 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7072 of the Haskell Report.
7073 In the translation box, first apply
7074 the following transformation: for each pattern <literal>pi</literal> that is of
7075 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7076 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7077 have a bang at the top, apply the rules in the existing box.
7079 <para>The effect of the let rule is to force complete matching of the pattern
7080 <literal>qi</literal> before evaluation of the body is begun. The bang is
7081 retained in the translated form in case <literal>qi</literal> is a variable,
7089 The let-binding can be recursive. However, it is much more common for
7090 the let-binding to be non-recursive, in which case the following law holds:
7091 <literal>(let !p = rhs in body)</literal>
7093 <literal>(case rhs of !p -> body)</literal>
7096 A pattern with a bang at the outermost level is not allowed at the top level of
7102 <!-- ==================== ASSERTIONS ================= -->
7104 <sect1 id="assertions">
7106 <indexterm><primary>Assertions</primary></indexterm>
7110 If you want to make use of assertions in your standard Haskell code, you
7111 could define a function like the following:
7117 assert :: Bool -> a -> a
7118 assert False x = error "assertion failed!"
7125 which works, but gives you back a less than useful error message --
7126 an assertion failed, but which and where?
7130 One way out is to define an extended <function>assert</function> function which also
7131 takes a descriptive string to include in the error message and
7132 perhaps combine this with the use of a pre-processor which inserts
7133 the source location where <function>assert</function> was used.
7137 Ghc offers a helping hand here, doing all of this for you. For every
7138 use of <function>assert</function> in the user's source:
7144 kelvinToC :: Double -> Double
7145 kelvinToC k = assert (k >= 0.0) (k+273.15)
7151 Ghc will rewrite this to also include the source location where the
7158 assert pred val ==> assertError "Main.hs|15" pred val
7164 The rewrite is only performed by the compiler when it spots
7165 applications of <function>Control.Exception.assert</function>, so you
7166 can still define and use your own versions of
7167 <function>assert</function>, should you so wish. If not, import
7168 <literal>Control.Exception</literal> to make use
7169 <function>assert</function> in your code.
7173 GHC ignores assertions when optimisation is turned on with the
7174 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7175 <literal>assert pred e</literal> will be rewritten to
7176 <literal>e</literal>. You can also disable assertions using the
7177 <option>-fignore-asserts</option>
7178 option<indexterm><primary><option>-fignore-asserts</option></primary>
7179 </indexterm>.</para>
7182 Assertion failures can be caught, see the documentation for the
7183 <literal>Control.Exception</literal> library for the details.
7189 <!-- =============================== PRAGMAS =========================== -->
7191 <sect1 id="pragmas">
7192 <title>Pragmas</title>
7194 <indexterm><primary>pragma</primary></indexterm>
7196 <para>GHC supports several pragmas, or instructions to the
7197 compiler placed in the source code. Pragmas don't normally affect
7198 the meaning of the program, but they might affect the efficiency
7199 of the generated code.</para>
7201 <para>Pragmas all take the form
7203 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7205 where <replaceable>word</replaceable> indicates the type of
7206 pragma, and is followed optionally by information specific to that
7207 type of pragma. Case is ignored in
7208 <replaceable>word</replaceable>. The various values for
7209 <replaceable>word</replaceable> that GHC understands are described
7210 in the following sections; any pragma encountered with an
7211 unrecognised <replaceable>word</replaceable> is
7212 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7213 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7215 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7219 pragma must precede the <literal>module</literal> keyword in the file.
7222 There can be as many file-header pragmas as you please, and they can be
7223 preceded or followed by comments.
7226 File-header pragmas are read once only, before
7227 pre-processing the file (e.g. with cpp).
7230 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7231 <literal>{-# OPTIONS_GHC #-}</literal>, and
7232 <literal>{-# INCLUDE #-}</literal>.
7237 <sect2 id="language-pragma">
7238 <title>LANGUAGE pragma</title>
7240 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7241 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7243 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7245 It is the intention that all Haskell compilers support the
7246 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7247 all extensions are supported by all compilers, of
7248 course. The <literal>LANGUAGE</literal> pragma should be used instead
7249 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7251 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7253 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7255 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7257 <para>Every language extension can also be turned into a command-line flag
7258 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7259 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7262 <para>A list of all supported language extensions can be obtained by invoking
7263 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7265 <para>Any extension from the <literal>Extension</literal> type defined in
7267 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7268 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7272 <sect2 id="options-pragma">
7273 <title>OPTIONS_GHC pragma</title>
7274 <indexterm><primary>OPTIONS_GHC</primary>
7276 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7279 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7280 additional options that are given to the compiler when compiling
7281 this source file. See <xref linkend="source-file-options"/> for
7284 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7285 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7288 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7290 <sect2 id="include-pragma">
7291 <title>INCLUDE pragma</title>
7293 <para>The <literal>INCLUDE</literal> used to be necessary for
7294 specifying header files to be included when using the FFI and
7295 compiling via C. It is no longer required for GHC, but is
7296 accepted (and ignored) for compatibility with other
7300 <sect2 id="warning-deprecated-pragma">
7301 <title>WARNING and DEPRECATED pragmas</title>
7302 <indexterm><primary>WARNING</primary></indexterm>
7303 <indexterm><primary>DEPRECATED</primary></indexterm>
7305 <para>The WARNING pragma allows you to attach an arbitrary warning
7306 to a particular function, class, or type.
7307 A DEPRECATED pragma lets you specify that
7308 a particular function, class, or type is deprecated.
7309 There are two ways of using these pragmas.
7313 <para>You can work on an entire module thus:</para>
7315 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7320 module Wibble {-# WARNING "This is an unstable interface." #-} where
7323 <para>When you compile any module that import
7324 <literal>Wibble</literal>, GHC will print the specified
7329 <para>You can attach a warning to a function, class, type, or data constructor, with the
7330 following top-level declarations:</para>
7332 {-# DEPRECATED f, C, T "Don't use these" #-}
7333 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7335 <para>When you compile any module that imports and uses any
7336 of the specified entities, GHC will print the specified
7338 <para> You can only attach to entities declared at top level in the module
7339 being compiled, and you can only use unqualified names in the list of
7340 entities. A capitalised name, such as <literal>T</literal>
7341 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7342 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7343 both are in scope. If both are in scope, there is currently no way to
7344 specify one without the other (c.f. fixities
7345 <xref linkend="infix-tycons"/>).</para>
7348 Warnings and deprecations are not reported for
7349 (a) uses within the defining module, and
7350 (b) uses in an export list.
7351 The latter reduces spurious complaints within a library
7352 in which one module gathers together and re-exports
7353 the exports of several others.
7355 <para>You can suppress the warnings with the flag
7356 <option>-fno-warn-warnings-deprecations</option>.</para>
7359 <sect2 id="inline-noinline-pragma">
7360 <title>INLINE and NOINLINE pragmas</title>
7362 <para>These pragmas control the inlining of function
7365 <sect3 id="inline-pragma">
7366 <title>INLINE pragma</title>
7367 <indexterm><primary>INLINE</primary></indexterm>
7369 <para>GHC (with <option>-O</option>, as always) tries to
7370 inline (or “unfold”) functions/values that are
7371 “small enough,” thus avoiding the call overhead
7372 and possibly exposing other more-wonderful optimisations.
7373 Normally, if GHC decides a function is “too
7374 expensive” to inline, it will not do so, nor will it
7375 export that unfolding for other modules to use.</para>
7377 <para>The sledgehammer you can bring to bear is the
7378 <literal>INLINE</literal><indexterm><primary>INLINE
7379 pragma</primary></indexterm> pragma, used thusly:</para>
7382 key_function :: Int -> String -> (Bool, Double)
7383 {-# INLINE key_function #-}
7386 <para>The major effect of an <literal>INLINE</literal> pragma
7387 is to declare a function's “cost” to be very low.
7388 The normal unfolding machinery will then be very keen to
7389 inline it. However, an <literal>INLINE</literal> pragma for a
7390 function "<literal>f</literal>" has a number of other effects:
7393 No functions are inlined into <literal>f</literal>. Otherwise
7394 GHC might inline a big function into <literal>f</literal>'s right hand side,
7395 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7398 The float-in, float-out, and common-sub-expression transformations are not
7399 applied to the body of <literal>f</literal>.
7402 An INLINE function is not worker/wrappered by strictness analysis.
7403 It's going to be inlined wholesale instead.
7406 All of these effects are aimed at ensuring that what gets inlined is
7407 exactly what you asked for, no more and no less.
7409 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7410 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7411 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7412 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7413 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7414 when there is no choice even an INLINE function can be selected, in which case
7415 the INLINE pragma is ignored.
7416 For example, for a self-recursive function, the loop breaker can only be the function
7417 itself, so an INLINE pragma is always ignored.</para>
7419 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7420 function can be put anywhere its type signature could be
7423 <para><literal>INLINE</literal> pragmas are a particularly
7425 <literal>then</literal>/<literal>return</literal> (or
7426 <literal>bind</literal>/<literal>unit</literal>) functions in
7427 a monad. For example, in GHC's own
7428 <literal>UniqueSupply</literal> monad code, we have:</para>
7431 {-# INLINE thenUs #-}
7432 {-# INLINE returnUs #-}
7435 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7436 linkend="noinline-pragma"/>).</para>
7438 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7439 so if you want your code to be HBC-compatible you'll have to surround
7440 the pragma with C pre-processor directives
7441 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7445 <sect3 id="noinline-pragma">
7446 <title>NOINLINE pragma</title>
7448 <indexterm><primary>NOINLINE</primary></indexterm>
7449 <indexterm><primary>NOTINLINE</primary></indexterm>
7451 <para>The <literal>NOINLINE</literal> pragma does exactly what
7452 you'd expect: it stops the named function from being inlined
7453 by the compiler. You shouldn't ever need to do this, unless
7454 you're very cautious about code size.</para>
7456 <para><literal>NOTINLINE</literal> is a synonym for
7457 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7458 specified by Haskell 98 as the standard way to disable
7459 inlining, so it should be used if you want your code to be
7463 <sect3 id="phase-control">
7464 <title>Phase control</title>
7466 <para> Sometimes you want to control exactly when in GHC's
7467 pipeline the INLINE pragma is switched on. Inlining happens
7468 only during runs of the <emphasis>simplifier</emphasis>. Each
7469 run of the simplifier has a different <emphasis>phase
7470 number</emphasis>; the phase number decreases towards zero.
7471 If you use <option>-dverbose-core2core</option> you'll see the
7472 sequence of phase numbers for successive runs of the
7473 simplifier. In an INLINE pragma you can optionally specify a
7477 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7478 <literal>f</literal>
7479 until phase <literal>k</literal>, but from phase
7480 <literal>k</literal> onwards be very keen to inline it.
7483 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7484 <literal>f</literal>
7485 until phase <literal>k</literal>, but from phase
7486 <literal>k</literal> onwards do not inline it.
7489 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7490 <literal>f</literal>
7491 until phase <literal>k</literal>, but from phase
7492 <literal>k</literal> onwards be willing to inline it (as if
7493 there was no pragma).
7496 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7497 <literal>f</literal>
7498 until phase <literal>k</literal>, but from phase
7499 <literal>k</literal> onwards do not inline it.
7502 The same information is summarised here:
7504 -- Before phase 2 Phase 2 and later
7505 {-# INLINE [2] f #-} -- No Yes
7506 {-# INLINE [~2] f #-} -- Yes No
7507 {-# NOINLINE [2] f #-} -- No Maybe
7508 {-# NOINLINE [~2] f #-} -- Maybe No
7510 {-# INLINE f #-} -- Yes Yes
7511 {-# NOINLINE f #-} -- No No
7513 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7514 function body is small, or it is applied to interesting-looking arguments etc).
7515 Another way to understand the semantics is this:
7517 <listitem><para>For both INLINE and NOINLINE, the phase number says
7518 when inlining is allowed at all.</para></listitem>
7519 <listitem><para>The INLINE pragma has the additional effect of making the
7520 function body look small, so that when inlining is allowed it is very likely to
7525 <para>The same phase-numbering control is available for RULES
7526 (<xref linkend="rewrite-rules"/>).</para>
7530 <sect2 id="annotation-pragmas">
7531 <title>ANN pragmas</title>
7533 <para>GHC offers the ability to annotate various code constructs with additional
7534 data by using three pragmas. This data can then be inspected at a later date by
7535 using GHC-as-a-library.</para>
7537 <sect3 id="ann-pragma">
7538 <title>Annotating values</title>
7540 <indexterm><primary>ANN</primary></indexterm>
7542 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7543 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7544 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7545 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7546 you would do this:</para>
7549 {-# ANN foo (Just "Hello") #-}
7554 A number of restrictions apply to use of annotations:
7556 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7557 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7558 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7559 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7560 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7562 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7563 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7566 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7567 please give the GHC team a shout</ulink>.
7570 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7571 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7574 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7579 <sect3 id="typeann-pragma">
7580 <title>Annotating types</title>
7582 <indexterm><primary>ANN type</primary></indexterm>
7583 <indexterm><primary>ANN</primary></indexterm>
7585 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7588 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7593 <sect3 id="modann-pragma">
7594 <title>Annotating modules</title>
7596 <indexterm><primary>ANN module</primary></indexterm>
7597 <indexterm><primary>ANN</primary></indexterm>
7599 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7602 {-# ANN module (Just "A `Maybe String' annotation") #-}
7607 <sect2 id="line-pragma">
7608 <title>LINE pragma</title>
7610 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7611 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7612 <para>This pragma is similar to C's <literal>#line</literal>
7613 pragma, and is mainly for use in automatically generated Haskell
7614 code. It lets you specify the line number and filename of the
7615 original code; for example</para>
7617 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7619 <para>if you'd generated the current file from something called
7620 <filename>Foo.vhs</filename> and this line corresponds to line
7621 42 in the original. GHC will adjust its error messages to refer
7622 to the line/file named in the <literal>LINE</literal>
7627 <title>RULES pragma</title>
7629 <para>The RULES pragma lets you specify rewrite rules. It is
7630 described in <xref linkend="rewrite-rules"/>.</para>
7633 <sect2 id="specialize-pragma">
7634 <title>SPECIALIZE pragma</title>
7636 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7637 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7638 <indexterm><primary>overloading, death to</primary></indexterm>
7640 <para>(UK spelling also accepted.) For key overloaded
7641 functions, you can create extra versions (NB: more code space)
7642 specialised to particular types. Thus, if you have an
7643 overloaded function:</para>
7646 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7649 <para>If it is heavily used on lists with
7650 <literal>Widget</literal> keys, you could specialise it as
7654 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7657 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7658 be put anywhere its type signature could be put.</para>
7660 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7661 (a) a specialised version of the function and (b) a rewrite rule
7662 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7663 un-specialised function into a call to the specialised one.</para>
7665 <para>The type in a SPECIALIZE pragma can be any type that is less
7666 polymorphic than the type of the original function. In concrete terms,
7667 if the original function is <literal>f</literal> then the pragma
7669 {-# SPECIALIZE f :: <type> #-}
7671 is valid if and only if the definition
7673 f_spec :: <type>
7676 is valid. Here are some examples (where we only give the type signature
7677 for the original function, not its code):
7679 f :: Eq a => a -> b -> b
7680 {-# SPECIALISE f :: Int -> b -> b #-}
7682 g :: (Eq a, Ix b) => a -> b -> b
7683 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7685 h :: Eq a => a -> a -> a
7686 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7688 The last of these examples will generate a
7689 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7690 well. If you use this kind of specialisation, let us know how well it works.
7693 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7694 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7695 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7696 The <literal>INLINE</literal> pragma affects the specialised version of the
7697 function (only), and applies even if the function is recursive. The motivating
7700 -- A GADT for arrays with type-indexed representation
7702 ArrInt :: !Int -> ByteArray# -> Arr Int
7703 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7705 (!:) :: Arr e -> Int -> e
7706 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7707 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7708 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7709 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7711 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7712 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7713 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7714 the specialised function will be inlined. It has two calls to
7715 <literal>(!:)</literal>,
7716 both at type <literal>Int</literal>. Both these calls fire the first
7717 specialisation, whose body is also inlined. The result is a type-based
7718 unrolling of the indexing function.</para>
7719 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7720 on an ordinarily-recursive function.</para>
7722 <para>Note: In earlier versions of GHC, it was possible to provide your own
7723 specialised function for a given type:
7726 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7729 This feature has been removed, as it is now subsumed by the
7730 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7734 <sect2 id="specialize-instance-pragma">
7735 <title>SPECIALIZE instance pragma
7739 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7740 <indexterm><primary>overloading, death to</primary></indexterm>
7741 Same idea, except for instance declarations. For example:
7744 instance (Eq a) => Eq (Foo a) where {
7745 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7749 The pragma must occur inside the <literal>where</literal> part
7750 of the instance declaration.
7753 Compatible with HBC, by the way, except perhaps in the placement
7759 <sect2 id="unpack-pragma">
7760 <title>UNPACK pragma</title>
7762 <indexterm><primary>UNPACK</primary></indexterm>
7764 <para>The <literal>UNPACK</literal> indicates to the compiler
7765 that it should unpack the contents of a constructor field into
7766 the constructor itself, removing a level of indirection. For
7770 data T = T {-# UNPACK #-} !Float
7771 {-# UNPACK #-} !Float
7774 <para>will create a constructor <literal>T</literal> containing
7775 two unboxed floats. This may not always be an optimisation: if
7776 the <function>T</function> constructor is scrutinised and the
7777 floats passed to a non-strict function for example, they will
7778 have to be reboxed (this is done automatically by the
7781 <para>Unpacking constructor fields should only be used in
7782 conjunction with <option>-O</option>, in order to expose
7783 unfoldings to the compiler so the reboxing can be removed as
7784 often as possible. For example:</para>
7788 f (T f1 f2) = f1 + f2
7791 <para>The compiler will avoid reboxing <function>f1</function>
7792 and <function>f2</function> by inlining <function>+</function>
7793 on floats, but only when <option>-O</option> is on.</para>
7795 <para>Any single-constructor data is eligible for unpacking; for
7799 data T = T {-# UNPACK #-} !(Int,Int)
7802 <para>will store the two <literal>Int</literal>s directly in the
7803 <function>T</function> constructor, by flattening the pair.
7804 Multi-level unpacking is also supported:
7807 data T = T {-# UNPACK #-} !S
7808 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7811 will store two unboxed <literal>Int#</literal>s
7812 directly in the <function>T</function> constructor. The
7813 unpacker can see through newtypes, too.</para>
7815 <para>If a field cannot be unpacked, you will not get a warning,
7816 so it might be an idea to check the generated code with
7817 <option>-ddump-simpl</option>.</para>
7819 <para>See also the <option>-funbox-strict-fields</option> flag,
7820 which essentially has the effect of adding
7821 <literal>{-# UNPACK #-}</literal> to every strict
7822 constructor field.</para>
7825 <sect2 id="source-pragma">
7826 <title>SOURCE pragma</title>
7828 <indexterm><primary>SOURCE</primary></indexterm>
7829 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7830 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7836 <!-- ======================= REWRITE RULES ======================== -->
7838 <sect1 id="rewrite-rules">
7839 <title>Rewrite rules
7841 <indexterm><primary>RULES pragma</primary></indexterm>
7842 <indexterm><primary>pragma, RULES</primary></indexterm>
7843 <indexterm><primary>rewrite rules</primary></indexterm></title>
7846 The programmer can specify rewrite rules as part of the source program
7852 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7857 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7858 If you need more information, then <option>-ddump-rule-firings</option> shows you
7859 each individual rule firing in detail.
7863 <title>Syntax</title>
7866 From a syntactic point of view:
7872 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7873 may be generated by the layout rule).
7879 The layout rule applies in a pragma.
7880 Currently no new indentation level
7881 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7882 you must lay out the starting in the same column as the enclosing definitions.
7885 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7886 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7889 Furthermore, the closing <literal>#-}</literal>
7890 should start in a column to the right of the opening <literal>{-#</literal>.
7896 Each rule has a name, enclosed in double quotes. The name itself has
7897 no significance at all. It is only used when reporting how many times the rule fired.
7903 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7904 immediately after the name of the rule. Thus:
7907 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7910 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7911 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7920 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7921 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7922 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7923 by spaces, just like in a type <literal>forall</literal>.
7929 A pattern variable may optionally have a type signature.
7930 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7931 For example, here is the <literal>foldr/build</literal> rule:
7934 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7935 foldr k z (build g) = g k z
7938 Since <function>g</function> has a polymorphic type, it must have a type signature.
7945 The left hand side of a rule must consist of a top-level variable applied
7946 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7949 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7950 "wrong2" forall f. f True = True
7953 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7960 A rule does not need to be in the same module as (any of) the
7961 variables it mentions, though of course they need to be in scope.
7967 All rules are implicitly exported from the module, and are therefore
7968 in force in any module that imports the module that defined the rule, directly
7969 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7970 in force when compiling A.) The situation is very similar to that for instance
7978 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7979 any other flag settings. Furthermore, inside a RULE, the language extension
7980 <option>-XScopedTypeVariables</option> is automatically enabled; see
7981 <xref linkend="scoped-type-variables"/>.
7987 Like other pragmas, RULE pragmas are always checked for scope errors, and
7988 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7989 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7990 if the <option>-fenable-rewrite-rules</option> flag is
7991 on (see <xref linkend="rule-semantics"/>).
8000 <sect2 id="rule-semantics">
8001 <title>Semantics</title>
8004 From a semantic point of view:
8009 Rules are enabled (that is, used during optimisation)
8010 by the <option>-fenable-rewrite-rules</option> flag.
8011 This flag is implied by <option>-O</option>, and may be switched
8012 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8013 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8014 may not do what you expect, though, because without <option>-O</option> GHC
8015 ignores all optimisation information in interface files;
8016 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8017 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8018 has no effect on parsing or typechecking.
8024 Rules are regarded as left-to-right rewrite rules.
8025 When GHC finds an expression that is a substitution instance of the LHS
8026 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8027 By "a substitution instance" we mean that the LHS can be made equal to the
8028 expression by substituting for the pattern variables.
8035 GHC makes absolutely no attempt to verify that the LHS and RHS
8036 of a rule have the same meaning. That is undecidable in general, and
8037 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8044 GHC makes no attempt to make sure that the rules are confluent or
8045 terminating. For example:
8048 "loop" forall x y. f x y = f y x
8051 This rule will cause the compiler to go into an infinite loop.
8058 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8064 GHC currently uses a very simple, syntactic, matching algorithm
8065 for matching a rule LHS with an expression. It seeks a substitution
8066 which makes the LHS and expression syntactically equal modulo alpha
8067 conversion. The pattern (rule), but not the expression, is eta-expanded if
8068 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8069 But not beta conversion (that's called higher-order matching).
8073 Matching is carried out on GHC's intermediate language, which includes
8074 type abstractions and applications. So a rule only matches if the
8075 types match too. See <xref linkend="rule-spec"/> below.
8081 GHC keeps trying to apply the rules as it optimises the program.
8082 For example, consider:
8091 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8092 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8093 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8094 not be substituted, and the rule would not fire.
8101 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8102 results. Consider this (artificial) example
8105 {-# RULES "f" f True = False #-}
8111 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8116 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8118 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8119 would have been a better chance that <literal>f</literal>'s RULE might fire.
8122 The way to get predictable behaviour is to use a NOINLINE
8123 pragma on <literal>f</literal>, to ensure
8124 that it is not inlined until its RULEs have had a chance to fire.
8134 <title>List fusion</title>
8137 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8138 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8139 intermediate list should be eliminated entirely.
8143 The following are good producers:
8155 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8161 Explicit lists (e.g. <literal>[True, False]</literal>)
8167 The cons constructor (e.g <literal>3:4:[]</literal>)
8173 <function>++</function>
8179 <function>map</function>
8185 <function>take</function>, <function>filter</function>
8191 <function>iterate</function>, <function>repeat</function>
8197 <function>zip</function>, <function>zipWith</function>
8206 The following are good consumers:
8218 <function>array</function> (on its second argument)
8224 <function>++</function> (on its first argument)
8230 <function>foldr</function>
8236 <function>map</function>
8242 <function>take</function>, <function>filter</function>
8248 <function>concat</function>
8254 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8260 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8261 will fuse with one but not the other)
8267 <function>partition</function>
8273 <function>head</function>
8279 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8285 <function>sequence_</function>
8291 <function>msum</function>
8297 <function>sortBy</function>
8306 So, for example, the following should generate no intermediate lists:
8309 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8315 This list could readily be extended; if there are Prelude functions that you use
8316 a lot which are not included, please tell us.
8320 If you want to write your own good consumers or producers, look at the
8321 Prelude definitions of the above functions to see how to do so.
8326 <sect2 id="rule-spec">
8327 <title>Specialisation
8331 Rewrite rules can be used to get the same effect as a feature
8332 present in earlier versions of GHC.
8333 For example, suppose that:
8336 genericLookup :: Ord a => Table a b -> a -> b
8337 intLookup :: Table Int b -> Int -> b
8340 where <function>intLookup</function> is an implementation of
8341 <function>genericLookup</function> that works very fast for
8342 keys of type <literal>Int</literal>. You might wish
8343 to tell GHC to use <function>intLookup</function> instead of
8344 <function>genericLookup</function> whenever the latter was called with
8345 type <literal>Table Int b -> Int -> b</literal>.
8346 It used to be possible to write
8349 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8352 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8355 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8358 This slightly odd-looking rule instructs GHC to replace
8359 <function>genericLookup</function> by <function>intLookup</function>
8360 <emphasis>whenever the types match</emphasis>.
8361 What is more, this rule does not need to be in the same
8362 file as <function>genericLookup</function>, unlike the
8363 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8364 have an original definition available to specialise).
8367 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8368 <function>intLookup</function> really behaves as a specialised version
8369 of <function>genericLookup</function>!!!</para>
8371 <para>An example in which using <literal>RULES</literal> for
8372 specialisation will Win Big:
8375 toDouble :: Real a => a -> Double
8376 toDouble = fromRational . toRational
8378 {-# RULES "toDouble/Int" toDouble = i2d #-}
8379 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8382 The <function>i2d</function> function is virtually one machine
8383 instruction; the default conversion—via an intermediate
8384 <literal>Rational</literal>—is obscenely expensive by
8391 <title>Controlling what's going on</title>
8399 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8405 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8406 If you add <option>-dppr-debug</option> you get a more detailed listing.
8412 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8415 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8416 {-# INLINE build #-}
8420 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8421 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8422 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8423 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8430 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8431 see how to write rules that will do fusion and yet give an efficient
8432 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8442 <sect2 id="core-pragma">
8443 <title>CORE pragma</title>
8445 <indexterm><primary>CORE pragma</primary></indexterm>
8446 <indexterm><primary>pragma, CORE</primary></indexterm>
8447 <indexterm><primary>core, annotation</primary></indexterm>
8450 The external core format supports <quote>Note</quote> annotations;
8451 the <literal>CORE</literal> pragma gives a way to specify what these
8452 should be in your Haskell source code. Syntactically, core
8453 annotations are attached to expressions and take a Haskell string
8454 literal as an argument. The following function definition shows an
8458 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8461 Semantically, this is equivalent to:
8469 However, when external core is generated (via
8470 <option>-fext-core</option>), there will be Notes attached to the
8471 expressions <function>show</function> and <varname>x</varname>.
8472 The core function declaration for <function>f</function> is:
8476 f :: %forall a . GHCziShow.ZCTShow a ->
8477 a -> GHCziBase.ZMZN GHCziBase.Char =
8478 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8480 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8482 (tpl1::GHCziBase.Int ->
8484 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8486 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8487 (tpl3::GHCziBase.ZMZN a ->
8488 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8496 Here, we can see that the function <function>show</function> (which
8497 has been expanded out to a case expression over the Show dictionary)
8498 has a <literal>%note</literal> attached to it, as does the
8499 expression <varname>eta</varname> (which used to be called
8500 <varname>x</varname>).
8507 <sect1 id="special-ids">
8508 <title>Special built-in functions</title>
8509 <para>GHC has a few built-in functions with special behaviour. These
8510 are now described in the module <ulink
8511 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8512 in the library documentation.</para>
8516 <sect1 id="generic-classes">
8517 <title>Generic classes</title>
8520 The ideas behind this extension are described in detail in "Derivable type classes",
8521 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8522 An example will give the idea:
8530 fromBin :: [Int] -> (a, [Int])
8532 toBin {| Unit |} Unit = []
8533 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8534 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8535 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8537 fromBin {| Unit |} bs = (Unit, bs)
8538 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8539 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8540 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8541 (y,bs'') = fromBin bs'
8544 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8545 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8546 which are defined thus in the library module <literal>Generics</literal>:
8550 data a :+: b = Inl a | Inr b
8551 data a :*: b = a :*: b
8554 Now you can make a data type into an instance of Bin like this:
8556 instance (Bin a, Bin b) => Bin (a,b)
8557 instance Bin a => Bin [a]
8559 That is, just leave off the "where" clause. Of course, you can put in the
8560 where clause and over-ride whichever methods you please.
8564 <title> Using generics </title>
8565 <para>To use generics you need to</para>
8568 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8569 <option>-XGenerics</option> (to generate extra per-data-type code),
8570 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8574 <para>Import the module <literal>Generics</literal> from the
8575 <literal>lang</literal> package. This import brings into
8576 scope the data types <literal>Unit</literal>,
8577 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8578 don't need this import if you don't mention these types
8579 explicitly; for example, if you are simply giving instance
8580 declarations.)</para>
8585 <sect2> <title> Changes wrt the paper </title>
8587 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8588 can be written infix (indeed, you can now use
8589 any operator starting in a colon as an infix type constructor). Also note that
8590 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8591 Finally, note that the syntax of the type patterns in the class declaration
8592 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8593 alone would ambiguous when they appear on right hand sides (an extension we
8594 anticipate wanting).
8598 <sect2> <title>Terminology and restrictions</title>
8600 Terminology. A "generic default method" in a class declaration
8601 is one that is defined using type patterns as above.
8602 A "polymorphic default method" is a default method defined as in Haskell 98.
8603 A "generic class declaration" is a class declaration with at least one
8604 generic default method.
8612 Alas, we do not yet implement the stuff about constructor names and
8619 A generic class can have only one parameter; you can't have a generic
8620 multi-parameter class.
8626 A default method must be defined entirely using type patterns, or entirely
8627 without. So this is illegal:
8630 op :: a -> (a, Bool)
8631 op {| Unit |} Unit = (Unit, True)
8634 However it is perfectly OK for some methods of a generic class to have
8635 generic default methods and others to have polymorphic default methods.
8641 The type variable(s) in the type pattern for a generic method declaration
8642 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:
8646 op {| p :*: q |} (x :*: y) = op (x :: p)
8654 The type patterns in a generic default method must take one of the forms:
8660 where "a" and "b" are type variables. Furthermore, all the type patterns for
8661 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8662 must use the same type variables. So this is illegal:
8666 op {| a :+: b |} (Inl x) = True
8667 op {| p :+: q |} (Inr y) = False
8669 The type patterns must be identical, even in equations for different methods of the class.
8670 So this too is illegal:
8674 op1 {| a :*: b |} (x :*: y) = True
8677 op2 {| p :*: q |} (x :*: y) = False
8679 (The reason for this restriction is that we gather all the equations for a particular type constructor
8680 into a single generic instance declaration.)
8686 A generic method declaration must give a case for each of the three type constructors.
8692 The type for a generic method can be built only from:
8694 <listitem> <para> Function arrows </para> </listitem>
8695 <listitem> <para> Type variables </para> </listitem>
8696 <listitem> <para> Tuples </para> </listitem>
8697 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8699 Here are some example type signatures for generic methods:
8702 op2 :: Bool -> (a,Bool)
8703 op3 :: [Int] -> a -> a
8706 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8710 This restriction is an implementation restriction: we just haven't got around to
8711 implementing the necessary bidirectional maps over arbitrary type constructors.
8712 It would be relatively easy to add specific type constructors, such as Maybe and list,
8713 to the ones that are allowed.</para>
8718 In an instance declaration for a generic class, the idea is that the compiler
8719 will fill in the methods for you, based on the generic templates. However it can only
8724 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8729 No constructor of the instance type has unboxed fields.
8733 (Of course, these things can only arise if you are already using GHC extensions.)
8734 However, you can still give an instance declarations for types which break these rules,
8735 provided you give explicit code to override any generic default methods.
8743 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8744 what the compiler does with generic declarations.
8749 <sect2> <title> Another example </title>
8751 Just to finish with, here's another example I rather like:
8755 nCons {| Unit |} _ = 1
8756 nCons {| a :*: b |} _ = 1
8757 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8760 tag {| Unit |} _ = 1
8761 tag {| a :*: b |} _ = 1
8762 tag {| a :+: b |} (Inl x) = tag x
8763 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8769 <sect1 id="monomorphism">
8770 <title>Control over monomorphism</title>
8772 <para>GHC supports two flags that control the way in which generalisation is
8773 carried out at let and where bindings.
8777 <title>Switching off the dreaded Monomorphism Restriction</title>
8778 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8780 <para>Haskell's monomorphism restriction (see
8781 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8783 of the Haskell Report)
8784 can be completely switched off by
8785 <option>-XNoMonomorphismRestriction</option>.
8790 <title>Monomorphic pattern bindings</title>
8791 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8792 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8794 <para> As an experimental change, we are exploring the possibility of
8795 making pattern bindings monomorphic; that is, not generalised at all.
8796 A pattern binding is a binding whose LHS has no function arguments,
8797 and is not a simple variable. For example:
8799 f x = x -- Not a pattern binding
8800 f = \x -> x -- Not a pattern binding
8801 f :: Int -> Int = \x -> x -- Not a pattern binding
8803 (g,h) = e -- A pattern binding
8804 (f) = e -- A pattern binding
8805 [x] = e -- A pattern binding
8807 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8808 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8817 ;;; Local Variables: ***
8819 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8820 ;;; ispell-local-dictionary: "british" ***
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