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>-XExplicitForAll</option>,
82 <option>-XRankNTypes</option>,
83 <option>-XImpredicativeTypes</option>,
84 <option>-XTypeOperators</option>,
85 <option>-XRecursiveDo</option>,
86 <option>-XParallelListComp</option>,
87 <option>-XEmptyDataDecls</option>,
88 <option>-XKindSignatures</option>,
89 <option>-XGeneralizedNewtypeDeriving</option>,
90 <option>-XTypeFamilies</option>.
91 Enabling these options is the <emphasis>only</emphasis>
92 effect of <option>-fglasgow-exts</option>.
93 We are trying to move away from this portmanteau flag,
94 and towards enabling features individually.</para>
98 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
99 <sect1 id="primitives">
100 <title>Unboxed types and primitive operations</title>
102 <para>GHC is built on a raft of primitive data types and operations;
103 "primitive" in the sense that they cannot be defined in Haskell itself.
104 While you really can use this stuff to write fast code,
105 we generally find it a lot less painful, and more satisfying in the
106 long run, to use higher-level language features and libraries. With
107 any luck, the code you write will be optimised to the efficient
108 unboxed version in any case. And if it isn't, we'd like to know
111 <para>All these primitive data types and operations are exported by the
112 library <literal>GHC.Prim</literal>, for which there is
113 <ulink url="../libraries/ghc-prim/GHC-Prim.html">detailed online documentation</ulink>.
114 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
117 If you want to mention any of the primitive data types or operations in your
118 program, you must first import <literal>GHC.Prim</literal> to bring them
119 into scope. Many of them have names ending in "#", and to mention such
120 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
123 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
124 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
125 we briefly summarise here. </para>
127 <sect2 id="glasgow-unboxed">
132 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
135 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
136 that values of that type are represented by a pointer to a heap
137 object. The representation of a Haskell <literal>Int</literal>, for
138 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
139 type, however, is represented by the value itself, no pointers or heap
140 allocation are involved.
144 Unboxed types correspond to the “raw machine” types you
145 would use in C: <literal>Int#</literal> (long int),
146 <literal>Double#</literal> (double), <literal>Addr#</literal>
147 (void *), etc. The <emphasis>primitive operations</emphasis>
148 (PrimOps) on these types are what you might expect; e.g.,
149 <literal>(+#)</literal> is addition on
150 <literal>Int#</literal>s, and is the machine-addition that we all
151 know and love—usually one instruction.
155 Primitive (unboxed) types cannot be defined in Haskell, and are
156 therefore built into the language and compiler. Primitive types are
157 always unlifted; that is, a value of a primitive type cannot be
158 bottom. We use the convention (but it is only a convention)
159 that primitive types, values, and
160 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
161 For some primitive types we have special syntax for literals, also
162 described in the <link linkend="magic-hash">same section</link>.
166 Primitive values are often represented by a simple bit-pattern, such
167 as <literal>Int#</literal>, <literal>Float#</literal>,
168 <literal>Double#</literal>. But this is not necessarily the case:
169 a primitive value might be represented by a pointer to a
170 heap-allocated object. Examples include
171 <literal>Array#</literal>, the type of primitive arrays. A
172 primitive array is heap-allocated because it is too big a value to fit
173 in a register, and would be too expensive to copy around; in a sense,
174 it is accidental that it is represented by a pointer. If a pointer
175 represents a primitive value, then it really does point to that value:
176 no unevaluated thunks, no indirections…nothing can be at the
177 other end of the pointer than the primitive value.
178 A numerically-intensive program using unboxed types can
179 go a <emphasis>lot</emphasis> faster than its “standard”
180 counterpart—we saw a threefold speedup on one example.
184 There are some restrictions on the use of primitive types:
186 <listitem><para>The main restriction
187 is that you can't pass a primitive value to a polymorphic
188 function or store one in a polymorphic data type. This rules out
189 things like <literal>[Int#]</literal> (i.e. lists of primitive
190 integers). The reason for this restriction is that polymorphic
191 arguments and constructor fields are assumed to be pointers: if an
192 unboxed integer is stored in one of these, the garbage collector would
193 attempt to follow it, leading to unpredictable space leaks. Or a
194 <function>seq</function> operation on the polymorphic component may
195 attempt to dereference the pointer, with disastrous results. Even
196 worse, the unboxed value might be larger than a pointer
197 (<literal>Double#</literal> for instance).
200 <listitem><para> You cannot define a newtype whose representation type
201 (the argument type of the data constructor) is an unboxed type. Thus,
207 <listitem><para> You cannot bind a variable with an unboxed type
208 in a <emphasis>top-level</emphasis> binding.
210 <listitem><para> You cannot bind a variable with an unboxed type
211 in a <emphasis>recursive</emphasis> binding.
213 <listitem><para> You may bind unboxed variables in a (non-recursive,
214 non-top-level) pattern binding, but you must make any such pattern-match
215 strict. For example, rather than:
217 data Foo = Foo Int Int#
219 f x = let (Foo a b, w) = ..rhs.. in ..body..
223 data Foo = Foo Int Int#
225 f x = let !(Foo a b, w) = ..rhs.. in ..body..
227 since <literal>b</literal> has type <literal>Int#</literal>.
235 <sect2 id="unboxed-tuples">
236 <title>Unboxed Tuples
240 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
241 they're available by default with <option>-fglasgow-exts</option>. An
242 unboxed tuple looks like this:
254 where <literal>e_1..e_n</literal> are expressions of any
255 type (primitive or non-primitive). The type of an unboxed tuple looks
260 Unboxed tuples are used for functions that need to return multiple
261 values, but they avoid the heap allocation normally associated with
262 using fully-fledged tuples. When an unboxed tuple is returned, the
263 components are put directly into registers or on the stack; the
264 unboxed tuple itself does not have a composite representation. Many
265 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
267 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
268 tuples to avoid unnecessary allocation during sequences of operations.
272 There are some pretty stringent restrictions on the use of unboxed tuples:
277 Values of unboxed tuple types are subject to the same restrictions as
278 other unboxed types; i.e. they may not be stored in polymorphic data
279 structures or passed to polymorphic functions.
286 No variable can have an unboxed tuple type, nor may a constructor or function
287 argument have an unboxed tuple type. The following are all illegal:
291 data Foo = Foo (# Int, Int #)
293 f :: (# Int, Int #) -> (# Int, Int #)
296 g :: (# Int, Int #) -> Int
299 h x = let y = (# x,x #) in ...
306 The typical use of unboxed tuples is simply to return multiple values,
307 binding those multiple results with a <literal>case</literal> expression, thus:
309 f x y = (# x+1, y-1 #)
310 g x = case f x x of { (# a, b #) -> a + b }
312 You can have an unboxed tuple in a pattern binding, thus
314 f x = let (# p,q #) = h x in ..body..
316 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
317 the resulting binding is lazy like any other Haskell pattern binding. The
318 above example desugars like this:
320 f x = let t = case h x o f{ (# p,q #) -> (p,q)
325 Indeed, the bindings can even be recursive.
332 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
334 <sect1 id="syntax-extns">
335 <title>Syntactic extensions</title>
337 <sect2 id="unicode-syntax">
338 <title>Unicode syntax</title>
340 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
341 enables Unicode characters to be used to stand for certain ASCII
342 character sequences. The following alternatives are provided:</para>
345 <tgroup cols="2" align="left" colsep="1" rowsep="1">
349 <entry>Unicode alternative</entry>
350 <entry>Code point</entry>
356 <entry><literal>::</literal></entry>
357 <entry>::</entry> <!-- no special char, apparently -->
358 <entry>0x2237</entry>
359 <entry>PROPORTION</entry>
364 <entry><literal>=></literal></entry>
365 <entry>⇒</entry>
366 <entry>0x21D2</entry>
367 <entry>RIGHTWARDS DOUBLE ARROW</entry>
372 <entry><literal>forall</literal></entry>
373 <entry>∀</entry>
374 <entry>0x2200</entry>
375 <entry>FOR ALL</entry>
380 <entry><literal>-></literal></entry>
381 <entry>→</entry>
382 <entry>0x2192</entry>
383 <entry>RIGHTWARDS ARROW</entry>
388 <entry><literal><-</literal></entry>
389 <entry>←</entry>
390 <entry>0x2190</entry>
391 <entry>LEFTWARDS ARROW</entry>
397 <entry>…</entry>
398 <entry>0x22EF</entry>
399 <entry>MIDLINE HORIZONTAL ELLIPSIS</entry>
406 <sect2 id="magic-hash">
407 <title>The magic hash</title>
408 <para>The language extension <option>-XMagicHash</option> allows "#" as a
409 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
410 a valid type constructor or data constructor.</para>
412 <para>The hash sign does not change sematics at all. We tend to use variable
413 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
414 but there is no requirement to do so; they are just plain ordinary variables.
415 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
416 For example, to bring <literal>Int#</literal> into scope you must
417 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
418 the <option>-XMagicHash</option> extension
419 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
420 that is now in scope.</para>
421 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
423 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
424 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
425 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
426 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
427 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
428 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
429 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
430 is a <literal>Word#</literal>. </para> </listitem>
431 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
432 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
437 <sect2 id="new-qualified-operators">
438 <title>New qualified operator syntax</title>
440 <para>A new syntax for referencing qualified operators is
441 planned to be introduced by Haskell', and is enabled in GHC
443 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
444 option. In the new syntax, the prefix form of a qualified
446 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
447 (in Haskell 98 this would
448 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
449 and the infix form is
450 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
451 (in Haskell 98 this would
452 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
455 add x y = Prelude.(+) x y
456 subtract y = (`Prelude.(-)` y)
458 The new form of qualified operators is intended to regularise
459 the syntax by eliminating odd cases
460 like <literal>Prelude..</literal>. For example,
461 when <literal>NewQualifiedOperators</literal> is on, it is possible to
462 write the enumerated sequence <literal>[Monday..]</literal>
463 without spaces, whereas in Haskell 98 this would be a
464 reference to the operator ‘<literal>.</literal>‘
465 from module <literal>Monday</literal>.</para>
467 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
468 98 syntax for qualified operators is not accepted, so this
469 option may cause existing Haskell 98 code to break.</para>
474 <!-- ====================== HIERARCHICAL MODULES ======================= -->
477 <sect2 id="hierarchical-modules">
478 <title>Hierarchical Modules</title>
480 <para>GHC supports a small extension to the syntax of module
481 names: a module name is allowed to contain a dot
482 <literal>‘.’</literal>. This is also known as the
483 “hierarchical module namespace” extension, because
484 it extends the normally flat Haskell module namespace into a
485 more flexible hierarchy of modules.</para>
487 <para>This extension has very little impact on the language
488 itself; modules names are <emphasis>always</emphasis> fully
489 qualified, so you can just think of the fully qualified module
490 name as <quote>the module name</quote>. In particular, this
491 means that the full module name must be given after the
492 <literal>module</literal> keyword at the beginning of the
493 module; for example, the module <literal>A.B.C</literal> must
496 <programlisting>module A.B.C</programlisting>
499 <para>It is a common strategy to use the <literal>as</literal>
500 keyword to save some typing when using qualified names with
501 hierarchical modules. For example:</para>
504 import qualified Control.Monad.ST.Strict as ST
507 <para>For details on how GHC searches for source and interface
508 files in the presence of hierarchical modules, see <xref
509 linkend="search-path"/>.</para>
511 <para>GHC comes with a large collection of libraries arranged
512 hierarchically; see the accompanying <ulink
513 url="../libraries/index.html">library
514 documentation</ulink>. More libraries to install are available
516 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
519 <!-- ====================== PATTERN GUARDS ======================= -->
521 <sect2 id="pattern-guards">
522 <title>Pattern guards</title>
525 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
526 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.)
530 Suppose we have an abstract data type of finite maps, with a
534 lookup :: FiniteMap -> Int -> Maybe Int
537 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
538 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
542 clunky env var1 var2 | ok1 && ok2 = val1 + val2
543 | otherwise = var1 + var2
554 The auxiliary functions are
558 maybeToBool :: Maybe a -> Bool
559 maybeToBool (Just x) = True
560 maybeToBool Nothing = False
562 expectJust :: Maybe a -> a
563 expectJust (Just x) = x
564 expectJust Nothing = error "Unexpected Nothing"
568 What is <function>clunky</function> doing? The guard <literal>ok1 &&
569 ok2</literal> checks that both lookups succeed, using
570 <function>maybeToBool</function> to convert the <function>Maybe</function>
571 types to booleans. The (lazily evaluated) <function>expectJust</function>
572 calls extract the values from the results of the lookups, and binds the
573 returned values to <varname>val1</varname> and <varname>val2</varname>
574 respectively. If either lookup fails, then clunky takes the
575 <literal>otherwise</literal> case and returns the sum of its arguments.
579 This is certainly legal Haskell, but it is a tremendously verbose and
580 un-obvious way to achieve the desired effect. Arguably, a more direct way
581 to write clunky would be to use case expressions:
585 clunky env var1 var2 = case lookup env var1 of
587 Just val1 -> case lookup env var2 of
589 Just val2 -> val1 + val2
595 This is a bit shorter, but hardly better. Of course, we can rewrite any set
596 of pattern-matching, guarded equations as case expressions; that is
597 precisely what the compiler does when compiling equations! The reason that
598 Haskell provides guarded equations is because they allow us to write down
599 the cases we want to consider, one at a time, independently of each other.
600 This structure is hidden in the case version. Two of the right-hand sides
601 are really the same (<function>fail</function>), and the whole expression
602 tends to become more and more indented.
606 Here is how I would write clunky:
611 | Just val1 <- lookup env var1
612 , Just val2 <- lookup env var2
614 ...other equations for clunky...
618 The semantics should be clear enough. The qualifiers are matched in order.
619 For a <literal><-</literal> qualifier, which I call a pattern guard, the
620 right hand side is evaluated and matched against the pattern on the left.
621 If the match fails then the whole guard fails and the next equation is
622 tried. If it succeeds, then the appropriate binding takes place, and the
623 next qualifier is matched, in the augmented environment. Unlike list
624 comprehensions, however, the type of the expression to the right of the
625 <literal><-</literal> is the same as the type of the pattern to its
626 left. The bindings introduced by pattern guards scope over all the
627 remaining guard qualifiers, and over the right hand side of the equation.
631 Just as with list comprehensions, boolean expressions can be freely mixed
632 with among the pattern guards. For example:
643 Haskell's current guards therefore emerge as a special case, in which the
644 qualifier list has just one element, a boolean expression.
648 <!-- ===================== View patterns =================== -->
650 <sect2 id="view-patterns">
655 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
656 More information and examples of view patterns can be found on the
657 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
662 View patterns are somewhat like pattern guards that can be nested inside
663 of other patterns. They are a convenient way of pattern-matching
664 against values of abstract types. For example, in a programming language
665 implementation, we might represent the syntax of the types of the
674 view :: Type -> TypeView
676 -- additional operations for constructing Typ's ...
679 The representation of Typ is held abstract, permitting implementations
680 to use a fancy representation (e.g., hash-consing to manage sharing).
682 Without view patterns, using this signature a little inconvenient:
684 size :: Typ -> Integer
685 size t = case view t of
687 Arrow t1 t2 -> size t1 + size t2
690 It is necessary to iterate the case, rather than using an equational
691 function definition. And the situation is even worse when the matching
692 against <literal>t</literal> is buried deep inside another pattern.
696 View patterns permit calling the view function inside the pattern and
697 matching against the result:
699 size (view -> Unit) = 1
700 size (view -> Arrow t1 t2) = size t1 + size t2
703 That is, we add a new form of pattern, written
704 <replaceable>expression</replaceable> <literal>-></literal>
705 <replaceable>pattern</replaceable> that means "apply the expression to
706 whatever we're trying to match against, and then match the result of
707 that application against the pattern". The expression can be any Haskell
708 expression of function type, and view patterns can be used wherever
713 The semantics of a pattern <literal>(</literal>
714 <replaceable>exp</replaceable> <literal>-></literal>
715 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
721 <para>The variables bound by the view pattern are the variables bound by
722 <replaceable>pat</replaceable>.
726 Any variables in <replaceable>exp</replaceable> are bound occurrences,
727 but variables bound "to the left" in a pattern are in scope. This
728 feature permits, for example, one argument to a function to be used in
729 the view of another argument. For example, the function
730 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
731 written using view patterns as follows:
734 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
735 ...other equations for clunky...
740 More precisely, the scoping rules are:
744 In a single pattern, variables bound by patterns to the left of a view
745 pattern expression are in scope. For example:
747 example :: Maybe ((String -> Integer,Integer), String) -> Bool
748 example Just ((f,_), f -> 4) = True
751 Additionally, in function definitions, variables bound by matching earlier curried
752 arguments may be used in view pattern expressions in later arguments:
754 example :: (String -> Integer) -> String -> Bool
755 example f (f -> 4) = True
757 That is, the scoping is the same as it would be if the curried arguments
758 were collected into a tuple.
764 In mutually recursive bindings, such as <literal>let</literal>,
765 <literal>where</literal>, or the top level, view patterns in one
766 declaration may not mention variables bound by other declarations. That
767 is, each declaration must be self-contained. For example, the following
768 program is not allowed:
775 restriction in the future; the only cost is that type checking patterns
776 would get a little more complicated.)
786 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
787 <replaceable>T1</replaceable> <literal>-></literal>
788 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
789 a <replaceable>T2</replaceable>, then the whole view pattern matches a
790 <replaceable>T1</replaceable>.
793 <listitem><para> Matching: To the equations in Section 3.17.3 of the
794 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
795 Report</ulink>, add the following:
797 case v of { (e -> p) -> e1 ; _ -> e2 }
799 case (e v) of { p -> e1 ; _ -> e2 }
801 That is, to match a variable <replaceable>v</replaceable> against a pattern
802 <literal>(</literal> <replaceable>exp</replaceable>
803 <literal>-></literal> <replaceable>pat</replaceable>
804 <literal>)</literal>, evaluate <literal>(</literal>
805 <replaceable>exp</replaceable> <replaceable> v</replaceable>
806 <literal>)</literal> and match the result against
807 <replaceable>pat</replaceable>.
810 <listitem><para> Efficiency: When the same view function is applied in
811 multiple branches of a function definition or a case expression (e.g.,
812 in <literal>size</literal> above), GHC makes an attempt to collect these
813 applications into a single nested case expression, so that the view
814 function is only applied once. Pattern compilation in GHC follows the
815 matrix algorithm described in Chapter 4 of <ulink
816 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
817 Implementation of Functional Programming Languages</ulink>. When the
818 top rows of the first column of a matrix are all view patterns with the
819 "same" expression, these patterns are transformed into a single nested
820 case. This includes, for example, adjacent view patterns that line up
823 f ((view -> A, p1), p2) = e1
824 f ((view -> B, p3), p4) = e2
828 <para> The current notion of when two view pattern expressions are "the
829 same" is very restricted: it is not even full syntactic equality.
830 However, it does include variables, literals, applications, and tuples;
831 e.g., two instances of <literal>view ("hi", "there")</literal> will be
832 collected. However, the current implementation does not compare up to
833 alpha-equivalence, so two instances of <literal>(x, view x ->
834 y)</literal> will not be coalesced.
844 <!-- ===================== n+k patterns =================== -->
846 <sect2 id="n-k-patterns">
847 <title>n+k patterns</title>
848 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
851 <literal>n+k</literal> pattern support is enabled by default. To disable
852 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
857 <!-- ===================== Recursive do-notation =================== -->
859 <sect2 id="mdo-notation">
860 <title>The recursive do-notation
863 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
864 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
865 by Levent Erkok, John Launchbury,
866 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
867 This paper is essential reading for anyone making non-trivial use of mdo-notation,
868 and we do not repeat it here.
871 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
872 that is, the variables bound in a do-expression are visible only in the textually following
873 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
874 group. It turns out that several applications can benefit from recursive bindings in
875 the do-notation, and this extension provides the necessary syntactic support.
878 Here is a simple (yet contrived) example:
881 import Control.Monad.Fix
883 justOnes = mdo xs <- Just (1:xs)
887 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
891 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. Its definition is:
894 class Monad m => MonadFix m where
895 mfix :: (a -> m a) -> m a
898 The function <literal>mfix</literal>
899 dictates how the required recursion operation should be performed. For example,
900 <literal>justOnes</literal> desugars as follows:
902 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
904 For full details of the way in which mdo is typechecked and desugared, see
905 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
906 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
909 If recursive bindings are required for a monad,
910 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
911 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
912 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
913 for Haskell's internal state monad (strict and lazy, respectively).
916 Here are some important points in using the recursive-do notation:
919 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
920 than <literal>do</literal>).
924 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
925 <literal>-fglasgow-exts</literal>.
929 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
930 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
931 be distinct (Section 3.3 of the paper).
935 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
936 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
937 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
938 and improve termination (Section 3.2 of the paper).
944 Historical note: The old implementation of the mdo-notation (and most
945 of the existing documents) used the name
946 <literal>MonadRec</literal> for the class and the corresponding library.
947 This name is not supported by GHC.
953 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
955 <sect2 id="parallel-list-comprehensions">
956 <title>Parallel List Comprehensions</title>
957 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
959 <indexterm><primary>parallel list comprehensions</primary>
962 <para>Parallel list comprehensions are a natural extension to list
963 comprehensions. List comprehensions can be thought of as a nice
964 syntax for writing maps and filters. Parallel comprehensions
965 extend this to include the zipWith family.</para>
967 <para>A parallel list comprehension has multiple independent
968 branches of qualifier lists, each separated by a `|' symbol. For
969 example, the following zips together two lists:</para>
972 [ (x, y) | x <- xs | y <- ys ]
975 <para>The behavior of parallel list comprehensions follows that of
976 zip, in that the resulting list will have the same length as the
977 shortest branch.</para>
979 <para>We can define parallel list comprehensions by translation to
980 regular comprehensions. Here's the basic idea:</para>
982 <para>Given a parallel comprehension of the form: </para>
985 [ e | p1 <- e11, p2 <- e12, ...
986 | q1 <- e21, q2 <- e22, ...
991 <para>This will be translated to: </para>
994 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
995 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1000 <para>where `zipN' is the appropriate zip for the given number of
1005 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1007 <sect2 id="generalised-list-comprehensions">
1008 <title>Generalised (SQL-Like) List Comprehensions</title>
1009 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1011 <indexterm><primary>extended list comprehensions</primary>
1013 <indexterm><primary>group</primary></indexterm>
1014 <indexterm><primary>sql</primary></indexterm>
1017 <para>Generalised list comprehensions are a further enhancement to the
1018 list comprehension syntactic sugar to allow operations such as sorting
1019 and grouping which are familiar from SQL. They are fully described in the
1020 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1021 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1022 except that the syntax we use differs slightly from the paper.</para>
1023 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1024 <para>Here is an example:
1026 employees = [ ("Simon", "MS", 80)
1027 , ("Erik", "MS", 100)
1028 , ("Phil", "Ed", 40)
1029 , ("Gordon", "Ed", 45)
1030 , ("Paul", "Yale", 60)]
1032 output = [ (the dept, sum salary)
1033 | (name, dept, salary) <- employees
1034 , then group by dept
1035 , then sortWith by (sum salary)
1038 In this example, the list <literal>output</literal> would take on
1042 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1045 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1046 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1047 function that is exported by <literal>GHC.Exts</literal>.)</para>
1049 <para>There are five new forms of comprehension qualifier,
1050 all introduced by the (existing) keyword <literal>then</literal>:
1058 This statement requires that <literal>f</literal> have the type <literal>
1059 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1060 motivating example, as this form is used to apply <literal>take 5</literal>.
1071 This form is similar to the previous one, but allows you to create a function
1072 which will be passed as the first argument to f. As a consequence f must have
1073 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1074 from the type, this function lets f "project out" some information
1075 from the elements of the list it is transforming.</para>
1077 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1078 is supplied with a function that lets it find out the <literal>sum salary</literal>
1079 for any item in the list comprehension it transforms.</para>
1087 then group by e using f
1090 <para>This is the most general of the grouping-type statements. In this form,
1091 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1092 As with the <literal>then f by e</literal> case above, the first argument
1093 is a function supplied to f by the compiler which lets it compute e on every
1094 element of the list being transformed. However, unlike the non-grouping case,
1095 f additionally partitions the list into a number of sublists: this means that
1096 at every point after this statement, binders occurring before it in the comprehension
1097 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1098 this, let's look at an example:</para>
1101 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1102 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1103 groupRuns f = groupBy (\x y -> f x == f y)
1105 output = [ (the x, y)
1106 | x <- ([1..3] ++ [1..2])
1108 , then group by x using groupRuns ]
1111 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1114 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1117 <para>Note that we have used the <literal>the</literal> function to change the type
1118 of x from a list to its original numeric type. The variable y, in contrast, is left
1119 unchanged from the list form introduced by the grouping.</para>
1129 <para>This form of grouping is essentially the same as the one described above. However,
1130 since no function to use for the grouping has been supplied it will fall back on the
1131 <literal>groupWith</literal> function defined in
1132 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1133 is the form of the group statement that we made use of in the opening example.</para>
1144 <para>With this form of the group statement, f is required to simply have the type
1145 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1146 comprehension so far directly. An example of this form is as follows:</para>
1152 , then group using inits]
1155 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1158 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1166 <!-- ===================== REBINDABLE SYNTAX =================== -->
1168 <sect2 id="rebindable-syntax">
1169 <title>Rebindable syntax and the implicit Prelude import</title>
1171 <para><indexterm><primary>-XNoImplicitPrelude
1172 option</primary></indexterm> GHC normally imports
1173 <filename>Prelude.hi</filename> files for you. If you'd
1174 rather it didn't, then give it a
1175 <option>-XNoImplicitPrelude</option> option. The idea is
1176 that you can then import a Prelude of your own. (But don't
1177 call it <literal>Prelude</literal>; the Haskell module
1178 namespace is flat, and you must not conflict with any
1179 Prelude module.)</para>
1181 <para>Suppose you are importing a Prelude of your own
1182 in order to define your own numeric class
1183 hierarchy. It completely defeats that purpose if the
1184 literal "1" means "<literal>Prelude.fromInteger
1185 1</literal>", which is what the Haskell Report specifies.
1186 So the <option>-XNoImplicitPrelude</option>
1187 flag <emphasis>also</emphasis> causes
1188 the following pieces of built-in syntax to refer to
1189 <emphasis>whatever is in scope</emphasis>, not the Prelude
1193 <para>An integer literal <literal>368</literal> means
1194 "<literal>fromInteger (368::Integer)</literal>", rather than
1195 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1198 <listitem><para>Fractional literals are handed in just the same way,
1199 except that the translation is
1200 <literal>fromRational (3.68::Rational)</literal>.
1203 <listitem><para>The equality test in an overloaded numeric pattern
1204 uses whatever <literal>(==)</literal> is in scope.
1207 <listitem><para>The subtraction operation, and the
1208 greater-than-or-equal test, in <literal>n+k</literal> patterns
1209 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1213 <para>Negation (e.g. "<literal>- (f x)</literal>")
1214 means "<literal>negate (f x)</literal>", both in numeric
1215 patterns, and expressions.
1219 <para>"Do" notation is translated using whatever
1220 functions <literal>(>>=)</literal>,
1221 <literal>(>>)</literal>, and <literal>fail</literal>,
1222 are in scope (not the Prelude
1223 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1224 comprehensions, are unaffected. </para></listitem>
1228 notation (see <xref linkend="arrow-notation"/>)
1229 uses whatever <literal>arr</literal>,
1230 <literal>(>>>)</literal>, <literal>first</literal>,
1231 <literal>app</literal>, <literal>(|||)</literal> and
1232 <literal>loop</literal> functions are in scope. But unlike the
1233 other constructs, the types of these functions must match the
1234 Prelude types very closely. Details are in flux; if you want
1238 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1239 even if that is a little unexpected. For example, the
1240 static semantics of the literal <literal>368</literal>
1241 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1242 <literal>fromInteger</literal> to have any of the types:
1244 fromInteger :: Integer -> Integer
1245 fromInteger :: forall a. Foo a => Integer -> a
1246 fromInteger :: Num a => a -> Integer
1247 fromInteger :: Integer -> Bool -> Bool
1251 <para>Be warned: this is an experimental facility, with
1252 fewer checks than usual. Use <literal>-dcore-lint</literal>
1253 to typecheck the desugared program. If Core Lint is happy
1254 you should be all right.</para>
1258 <sect2 id="postfix-operators">
1259 <title>Postfix operators</title>
1262 The <option>-XPostfixOperators</option> flag enables a small
1263 extension to the syntax of left operator sections, which allows you to
1264 define postfix operators. The extension is this: the left section
1268 is equivalent (from the point of view of both type checking and execution) to the expression
1272 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1273 The strict Haskell 98 interpretation is that the section is equivalent to
1277 That is, the operator must be a function of two arguments. GHC allows it to
1278 take only one argument, and that in turn allows you to write the function
1281 <para>The extension does not extend to the left-hand side of function
1282 definitions; you must define such a function in prefix form.</para>
1286 <sect2 id="tuple-sections">
1287 <title>Tuple sections</title>
1290 The <option>-XTupleSections</option> flag enables Python-style partially applied
1291 tuple constructors. For example, the following program
1295 is considered to be an alternative notation for the more unwieldy alternative
1299 You can omit any combination of arguments to the tuple, as in the following
1301 (, "I", , , "Love", , 1337)
1305 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1310 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1311 will also be available for them, like so
1315 Because there is no unboxed unit tuple, the following expression
1319 continues to stand for the unboxed singleton tuple data constructor.
1324 <sect2 id="disambiguate-fields">
1325 <title>Record field disambiguation</title>
1327 In record construction and record pattern matching
1328 it is entirely unambiguous which field is referred to, even if there are two different
1329 data types in scope with a common field name. For example:
1332 data S = MkS { x :: Int, y :: Bool }
1337 data T = MkT { x :: Int }
1339 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1340 ok2 n = MkT { x = n+1 } -- Unambiguous
1342 bad1 k = k { x = 3 } -- Ambiguous
1343 bad2 k = x k -- Ambiguous
1345 Even though there are two <literal>x</literal>'s in scope,
1346 it is clear that the <literal>x</literal> in the pattern in the
1347 definition of <literal>ok1</literal> can only mean the field
1348 <literal>x</literal> from type <literal>S</literal>. Similarly for
1349 the function <literal>ok2</literal>. However, in the record update
1350 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1351 it is not clear which of the two types is intended.
1354 Haskell 98 regards all four as ambiguous, but with the
1355 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1356 the former two. The rules are precisely the same as those for instance
1357 declarations in Haskell 98, where the method names on the left-hand side
1358 of the method bindings in an instance declaration refer unambiguously
1359 to the method of that class (provided they are in scope at all), even
1360 if there are other variables in scope with the same name.
1361 This reduces the clutter of qualified names when you import two
1362 records from different modules that use the same field name.
1368 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1373 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1378 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1379 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1380 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1383 import qualified M -- Note qualified
1385 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1387 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1388 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1389 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1390 is not. (In effect, it is qualified by the constructor.)
1397 <!-- ===================== Record puns =================== -->
1399 <sect2 id="record-puns">
1404 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1408 When using records, it is common to write a pattern that binds a
1409 variable with the same name as a record field, such as:
1412 data C = C {a :: Int}
1418 Record punning permits the variable name to be elided, so one can simply
1425 to mean the same pattern as above. That is, in a record pattern, the
1426 pattern <literal>a</literal> expands into the pattern <literal>a =
1427 a</literal> for the same name <literal>a</literal>.
1434 Record punning can also be used in an expression, writing, for example,
1440 let a = 1 in C {a = a}
1442 The expansion is purely syntactic, so the expanded right-hand side
1443 expression refers to the nearest enclosing variable that is spelled the
1444 same as the field name.
1448 Puns and other patterns can be mixed in the same record:
1450 data C = C {a :: Int, b :: Int}
1451 f (C {a, b = 4}) = a
1456 Puns can be used wherever record patterns occur (e.g. in
1457 <literal>let</literal> bindings or at the top-level).
1461 A pun on a qualified field name is expanded by stripping off the module qualifier.
1468 f (M.C {M.a = a}) = a
1470 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1471 is only in scope in qualified form.)
1479 <!-- ===================== Record wildcards =================== -->
1481 <sect2 id="record-wildcards">
1482 <title>Record wildcards
1486 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1487 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1491 For records with many fields, it can be tiresome to write out each field
1492 individually in a record pattern, as in
1494 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1495 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1500 Record wildcard syntax permits a "<literal>..</literal>" in a record
1501 pattern, where each elided field <literal>f</literal> is replaced by the
1502 pattern <literal>f = f</literal>. For example, the above pattern can be
1505 f (C {a = 1, ..}) = b + c + d
1513 Wildcards can be mixed with other patterns, including puns
1514 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1515 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1516 wherever record patterns occur, including in <literal>let</literal>
1517 bindings and at the top-level. For example, the top-level binding
1521 defines <literal>b</literal>, <literal>c</literal>, and
1522 <literal>d</literal>.
1526 Record wildcards can also be used in expressions, writing, for example,
1528 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1532 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1534 The expansion is purely syntactic, so the record wildcard
1535 expression refers to the nearest enclosing variables that are spelled
1536 the same as the omitted field names.
1540 The "<literal>..</literal>" expands to the missing
1541 <emphasis>in-scope</emphasis> record fields, where "in scope"
1542 includes both unqualified and qualified-only.
1543 Any fields that are not in scope are not filled in. For example
1546 data R = R { a,b,c :: Int }
1548 import qualified M( R(a,b) )
1551 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1552 omitting <literal>c</literal> since it is not in scope at all.
1559 <!-- ===================== Local fixity declarations =================== -->
1561 <sect2 id="local-fixity-declarations">
1562 <title>Local Fixity Declarations
1565 <para>A careful reading of the Haskell 98 Report reveals that fixity
1566 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1567 <literal>infixr</literal>) are permitted to appear inside local bindings
1568 such those introduced by <literal>let</literal> and
1569 <literal>where</literal>. However, the Haskell Report does not specify
1570 the semantics of such bindings very precisely.
1573 <para>In GHC, a fixity declaration may accompany a local binding:
1580 and the fixity declaration applies wherever the binding is in scope.
1581 For example, in a <literal>let</literal>, it applies in the right-hand
1582 sides of other <literal>let</literal>-bindings and the body of the
1583 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1584 expressions (<xref linkend="mdo-notation"/>), the local fixity
1585 declarations of a <literal>let</literal> statement scope over other
1586 statements in the group, just as the bound name does.
1590 Moreover, a local fixity declaration *must* accompany a local binding of
1591 that name: it is not possible to revise the fixity of name bound
1594 let infixr 9 $ in ...
1597 Because local fixity declarations are technically Haskell 98, no flag is
1598 necessary to enable them.
1602 <sect2 id="package-imports">
1603 <title>Package-qualified imports</title>
1605 <para>With the <option>-XPackageImports</option> flag, GHC allows
1606 import declarations to be qualified by the package name that the
1607 module is intended to be imported from. For example:</para>
1610 import "network" Network.Socket
1613 <para>would import the module <literal>Network.Socket</literal> from
1614 the package <literal>network</literal> (any version). This may
1615 be used to disambiguate an import when the same module is
1616 available from multiple packages, or is present in both the
1617 current package being built and an external package.</para>
1619 <para>Note: you probably don't need to use this feature, it was
1620 added mainly so that we can build backwards-compatible versions of
1621 packages when APIs change. It can lead to fragile dependencies in
1622 the common case: modules occasionally move from one package to
1623 another, rendering any package-qualified imports broken.</para>
1626 <sect2 id="syntax-stolen">
1627 <title>Summary of stolen syntax</title>
1629 <para>Turning on an option that enables special syntax
1630 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1631 to compile, perhaps because it uses a variable name which has
1632 become a reserved word. This section lists the syntax that is
1633 "stolen" by language extensions.
1635 notation and nonterminal names from the Haskell 98 lexical syntax
1636 (see the Haskell 98 Report).
1637 We only list syntax changes here that might affect
1638 existing working programs (i.e. "stolen" syntax). Many of these
1639 extensions will also enable new context-free syntax, but in all
1640 cases programs written to use the new syntax would not be
1641 compilable without the option enabled.</para>
1643 <para>There are two classes of special
1648 <para>New reserved words and symbols: character sequences
1649 which are no longer available for use as identifiers in the
1653 <para>Other special syntax: sequences of characters that have
1654 a different meaning when this particular option is turned
1659 The following syntax is stolen:
1664 <literal>forall</literal>
1665 <indexterm><primary><literal>forall</literal></primary></indexterm>
1668 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1669 <option>-XScopedTypeVariables</option>,
1670 <option>-XLiberalTypeSynonyms</option>,
1671 <option>-XRank2Types</option>,
1672 <option>-XRankNTypes</option>,
1673 <option>-XPolymorphicComponents</option>,
1674 <option>-XExistentialQuantification</option>
1680 <literal>mdo</literal>
1681 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1684 Stolen by: <option>-XRecursiveDo</option>,
1690 <literal>foreign</literal>
1691 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1694 Stolen by: <option>-XForeignFunctionInterface</option>,
1700 <literal>rec</literal>,
1701 <literal>proc</literal>, <literal>-<</literal>,
1702 <literal>>-</literal>, <literal>-<<</literal>,
1703 <literal>>>-</literal>, and <literal>(|</literal>,
1704 <literal>|)</literal> brackets
1705 <indexterm><primary><literal>proc</literal></primary></indexterm>
1708 Stolen by: <option>-XArrows</option>,
1714 <literal>?<replaceable>varid</replaceable></literal>,
1715 <literal>%<replaceable>varid</replaceable></literal>
1716 <indexterm><primary>implicit parameters</primary></indexterm>
1719 Stolen by: <option>-XImplicitParams</option>,
1725 <literal>[|</literal>,
1726 <literal>[e|</literal>, <literal>[p|</literal>,
1727 <literal>[d|</literal>, <literal>[t|</literal>,
1728 <literal>$(</literal>,
1729 <literal>$<replaceable>varid</replaceable></literal>
1730 <indexterm><primary>Template Haskell</primary></indexterm>
1733 Stolen by: <option>-XTemplateHaskell</option>,
1739 <literal>[:<replaceable>varid</replaceable>|</literal>
1740 <indexterm><primary>quasi-quotation</primary></indexterm>
1743 Stolen by: <option>-XQuasiQuotes</option>,
1749 <replaceable>varid</replaceable>{<literal>#</literal>},
1750 <replaceable>char</replaceable><literal>#</literal>,
1751 <replaceable>string</replaceable><literal>#</literal>,
1752 <replaceable>integer</replaceable><literal>#</literal>,
1753 <replaceable>float</replaceable><literal>#</literal>,
1754 <replaceable>float</replaceable><literal>##</literal>,
1755 <literal>(#</literal>, <literal>#)</literal>,
1758 Stolen by: <option>-XMagicHash</option>,
1767 <!-- TYPE SYSTEM EXTENSIONS -->
1768 <sect1 id="data-type-extensions">
1769 <title>Extensions to data types and type synonyms</title>
1771 <sect2 id="nullary-types">
1772 <title>Data types with no constructors</title>
1774 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1775 a data type with no constructors. For example:</para>
1779 data T a -- T :: * -> *
1782 <para>Syntactically, the declaration lacks the "= constrs" part. The
1783 type can be parameterised over types of any kind, but if the kind is
1784 not <literal>*</literal> then an explicit kind annotation must be used
1785 (see <xref linkend="kinding"/>).</para>
1787 <para>Such data types have only one value, namely bottom.
1788 Nevertheless, they can be useful when defining "phantom types".</para>
1791 <sect2 id="infix-tycons">
1792 <title>Infix type constructors, classes, and type variables</title>
1795 GHC allows type constructors, classes, and type variables to be operators, and
1796 to be written infix, very much like expressions. More specifically:
1799 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1800 The lexical syntax is the same as that for data constructors.
1803 Data type and type-synonym declarations can be written infix, parenthesised
1804 if you want further arguments. E.g.
1806 data a :*: b = Foo a b
1807 type a :+: b = Either a b
1808 class a :=: b where ...
1810 data (a :**: b) x = Baz a b x
1811 type (a :++: b) y = Either (a,b) y
1815 Types, and class constraints, can be written infix. For example
1818 f :: (a :=: b) => a -> b
1822 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1823 The lexical syntax is the same as that for variable operators, excluding "(.)",
1824 "(!)", and "(*)". In a binding position, the operator must be
1825 parenthesised. For example:
1827 type T (+) = Int + Int
1831 liftA2 :: Arrow (~>)
1832 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1838 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1839 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1842 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1843 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1844 sets the fixity for a data constructor and the corresponding type constructor. For example:
1848 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1849 and similarly for <literal>:*:</literal>.
1850 <literal>Int `a` Bool</literal>.
1853 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1860 <sect2 id="type-synonyms">
1861 <title>Liberalised type synonyms</title>
1864 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1865 on individual synonym declarations.
1866 With the <option>-XLiberalTypeSynonyms</option> extension,
1867 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1868 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1871 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1872 in a type synonym, thus:
1874 type Discard a = forall b. Show b => a -> b -> (a, String)
1879 g :: Discard Int -> (Int,String) -- A rank-2 type
1886 If you also use <option>-XUnboxedTuples</option>,
1887 you can write an unboxed tuple in a type synonym:
1889 type Pr = (# Int, Int #)
1897 You can apply a type synonym to a forall type:
1899 type Foo a = a -> a -> Bool
1901 f :: Foo (forall b. b->b)
1903 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1905 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1910 You can apply a type synonym to a partially applied type synonym:
1912 type Generic i o = forall x. i x -> o x
1915 foo :: Generic Id []
1917 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1919 foo :: forall x. x -> [x]
1927 GHC currently does kind checking before expanding synonyms (though even that
1931 After expanding type synonyms, GHC does validity checking on types, looking for
1932 the following mal-formedness which isn't detected simply by kind checking:
1935 Type constructor applied to a type involving for-alls.
1938 Unboxed tuple on left of an arrow.
1941 Partially-applied type synonym.
1945 this will be rejected:
1947 type Pr = (# Int, Int #)
1952 because GHC does not allow unboxed tuples on the left of a function arrow.
1957 <sect2 id="existential-quantification">
1958 <title>Existentially quantified data constructors
1962 The idea of using existential quantification in data type declarations
1963 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1964 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1965 London, 1991). It was later formalised by Laufer and Odersky
1966 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1967 TOPLAS, 16(5), pp1411-1430, 1994).
1968 It's been in Lennart
1969 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1970 proved very useful. Here's the idea. Consider the declaration:
1976 data Foo = forall a. MkFoo a (a -> Bool)
1983 The data type <literal>Foo</literal> has two constructors with types:
1989 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1996 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1997 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1998 For example, the following expression is fine:
2004 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2010 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2011 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2012 isUpper</function> packages a character with a compatible function. These
2013 two things are each of type <literal>Foo</literal> and can be put in a list.
2017 What can we do with a value of type <literal>Foo</literal>?. In particular,
2018 what happens when we pattern-match on <function>MkFoo</function>?
2024 f (MkFoo val fn) = ???
2030 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2031 are compatible, the only (useful) thing we can do with them is to
2032 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2039 f (MkFoo val fn) = fn val
2045 What this allows us to do is to package heterogeneous values
2046 together with a bunch of functions that manipulate them, and then treat
2047 that collection of packages in a uniform manner. You can express
2048 quite a bit of object-oriented-like programming this way.
2051 <sect3 id="existential">
2052 <title>Why existential?
2056 What has this to do with <emphasis>existential</emphasis> quantification?
2057 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2063 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2069 But Haskell programmers can safely think of the ordinary
2070 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2071 adding a new existential quantification construct.
2076 <sect3 id="existential-with-context">
2077 <title>Existentials and type classes</title>
2080 An easy extension is to allow
2081 arbitrary contexts before the constructor. For example:
2087 data Baz = forall a. Eq a => Baz1 a a
2088 | forall b. Show b => Baz2 b (b -> b)
2094 The two constructors have the types you'd expect:
2100 Baz1 :: forall a. Eq a => a -> a -> Baz
2101 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2107 But when pattern matching on <function>Baz1</function> the matched values can be compared
2108 for equality, and when pattern matching on <function>Baz2</function> the first matched
2109 value can be converted to a string (as well as applying the function to it).
2110 So this program is legal:
2117 f (Baz1 p q) | p == q = "Yes"
2119 f (Baz2 v fn) = show (fn v)
2125 Operationally, in a dictionary-passing implementation, the
2126 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2127 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2128 extract it on pattern matching.
2133 <sect3 id="existential-records">
2134 <title>Record Constructors</title>
2137 GHC allows existentials to be used with records syntax as well. For example:
2140 data Counter a = forall self. NewCounter
2142 , _inc :: self -> self
2143 , _display :: self -> IO ()
2147 Here <literal>tag</literal> is a public field, with a well-typed selector
2148 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2149 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2150 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2151 compile-time error. In other words, <emphasis>GHC defines a record selector function
2152 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2153 (This example used an underscore in the fields for which record selectors
2154 will not be defined, but that is only programming style; GHC ignores them.)
2158 To make use of these hidden fields, we need to create some helper functions:
2161 inc :: Counter a -> Counter a
2162 inc (NewCounter x i d t) = NewCounter
2163 { _this = i x, _inc = i, _display = d, tag = t }
2165 display :: Counter a -> IO ()
2166 display NewCounter{ _this = x, _display = d } = d x
2169 Now we can define counters with different underlying implementations:
2172 counterA :: Counter String
2173 counterA = NewCounter
2174 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2176 counterB :: Counter String
2177 counterB = NewCounter
2178 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2181 display (inc counterA) -- prints "1"
2182 display (inc (inc counterB)) -- prints "##"
2185 Record update syntax is supported for existentials (and GADTs):
2187 setTag :: Counter a -> a -> Counter a
2188 setTag obj t = obj{ tag = t }
2190 The rule for record update is this: <emphasis>
2191 the types of the updated fields may
2192 mention only the universally-quantified type variables
2193 of the data constructor. For GADTs, the field may mention only types
2194 that appear as a simple type-variable argument in the constructor's result
2195 type</emphasis>. For example:
2197 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2198 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2199 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2200 -- existentially quantified)
2202 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2203 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2204 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2205 -- type-variable argument in G1's result type)
2213 <title>Restrictions</title>
2216 There are several restrictions on the ways in which existentially-quantified
2217 constructors can be use.
2226 When pattern matching, each pattern match introduces a new,
2227 distinct, type for each existential type variable. These types cannot
2228 be unified with any other type, nor can they escape from the scope of
2229 the pattern match. For example, these fragments are incorrect:
2237 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2238 is the result of <function>f1</function>. One way to see why this is wrong is to
2239 ask what type <function>f1</function> has:
2243 f1 :: Foo -> a -- Weird!
2247 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2252 f1 :: forall a. Foo -> a -- Wrong!
2256 The original program is just plain wrong. Here's another sort of error
2260 f2 (Baz1 a b) (Baz1 p q) = a==q
2264 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2265 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2266 from the two <function>Baz1</function> constructors.
2274 You can't pattern-match on an existentially quantified
2275 constructor in a <literal>let</literal> or <literal>where</literal> group of
2276 bindings. So this is illegal:
2280 f3 x = a==b where { Baz1 a b = x }
2283 Instead, use a <literal>case</literal> expression:
2286 f3 x = case x of Baz1 a b -> a==b
2289 In general, you can only pattern-match
2290 on an existentially-quantified constructor in a <literal>case</literal> expression or
2291 in the patterns of a function definition.
2293 The reason for this restriction is really an implementation one.
2294 Type-checking binding groups is already a nightmare without
2295 existentials complicating the picture. Also an existential pattern
2296 binding at the top level of a module doesn't make sense, because it's
2297 not clear how to prevent the existentially-quantified type "escaping".
2298 So for now, there's a simple-to-state restriction. We'll see how
2306 You can't use existential quantification for <literal>newtype</literal>
2307 declarations. So this is illegal:
2311 newtype T = forall a. Ord a => MkT a
2315 Reason: a value of type <literal>T</literal> must be represented as a
2316 pair of a dictionary for <literal>Ord t</literal> and a value of type
2317 <literal>t</literal>. That contradicts the idea that
2318 <literal>newtype</literal> should have no concrete representation.
2319 You can get just the same efficiency and effect by using
2320 <literal>data</literal> instead of <literal>newtype</literal>. If
2321 there is no overloading involved, then there is more of a case for
2322 allowing an existentially-quantified <literal>newtype</literal>,
2323 because the <literal>data</literal> version does carry an
2324 implementation cost, but single-field existentially quantified
2325 constructors aren't much use. So the simple restriction (no
2326 existential stuff on <literal>newtype</literal>) stands, unless there
2327 are convincing reasons to change it.
2335 You can't use <literal>deriving</literal> to define instances of a
2336 data type with existentially quantified data constructors.
2338 Reason: in most cases it would not make sense. For example:;
2341 data T = forall a. MkT [a] deriving( Eq )
2344 To derive <literal>Eq</literal> in the standard way we would need to have equality
2345 between the single component of two <function>MkT</function> constructors:
2349 (MkT a) == (MkT b) = ???
2352 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2353 It's just about possible to imagine examples in which the derived instance
2354 would make sense, but it seems altogether simpler simply to prohibit such
2355 declarations. Define your own instances!
2366 <!-- ====================== Generalised algebraic data types ======================= -->
2368 <sect2 id="gadt-style">
2369 <title>Declaring data types with explicit constructor signatures</title>
2371 <para>GHC allows you to declare an algebraic data type by
2372 giving the type signatures of constructors explicitly. For example:
2376 Just :: a -> Maybe a
2378 The form is called a "GADT-style declaration"
2379 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2380 can only be declared using this form.</para>
2381 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2382 For example, these two declarations are equivalent:
2384 data Foo = forall a. MkFoo a (a -> Bool)
2385 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2388 <para>Any data type that can be declared in standard Haskell-98 syntax
2389 can also be declared using GADT-style syntax.
2390 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2391 they treat class constraints on the data constructors differently.
2392 Specifically, if the constructor is given a type-class context, that
2393 context is made available by pattern matching. For example:
2396 MkSet :: Eq a => [a] -> Set a
2398 makeSet :: Eq a => [a] -> Set a
2399 makeSet xs = MkSet (nub xs)
2401 insert :: a -> Set a -> Set a
2402 insert a (MkSet as) | a `elem` as = MkSet as
2403 | otherwise = MkSet (a:as)
2405 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2406 gives rise to a <literal>(Eq a)</literal>
2407 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2408 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2409 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2410 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2411 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2412 In the example, the equality dictionary is used to satisfy the equality constraint
2413 generated by the call to <literal>elem</literal>, so that the type of
2414 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2417 For example, one possible application is to reify dictionaries:
2419 data NumInst a where
2420 MkNumInst :: Num a => NumInst a
2422 intInst :: NumInst Int
2425 plus :: NumInst a -> a -> a -> a
2426 plus MkNumInst p q = p + q
2428 Here, a value of type <literal>NumInst a</literal> is equivalent
2429 to an explicit <literal>(Num a)</literal> dictionary.
2432 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2433 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2437 = Num a => MkNumInst (NumInst a)
2439 Notice that, unlike the situation when declaring an existential, there is
2440 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2441 data type's universally quantified type variable <literal>a</literal>.
2442 A constructor may have both universal and existential type variables: for example,
2443 the following two declarations are equivalent:
2446 = forall b. (Num a, Eq b) => MkT1 a b
2448 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2451 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2452 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2453 In Haskell 98 the definition
2455 data Eq a => Set' a = MkSet' [a]
2457 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2458 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2459 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2460 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2461 GHC's behaviour is much more useful, as well as much more intuitive.
2465 The rest of this section gives further details about GADT-style data
2470 The result type of each data constructor must begin with the type constructor being defined.
2471 If the result type of all constructors
2472 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2473 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2474 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2478 As with other type signatures, you can give a single signature for several data constructors.
2479 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2488 The type signature of
2489 each constructor is independent, and is implicitly universally quantified as usual.
2490 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2491 have no scope, and different constructors may have different universally-quantified type variables:
2493 data T a where -- The 'a' has no scope
2494 T1,T2 :: b -> T b -- Means forall b. b -> T b
2495 T3 :: T a -- Means forall a. T a
2500 A constructor signature may mention type class constraints, which can differ for
2501 different constructors. For example, this is fine:
2504 T1 :: Eq b => b -> b -> T b
2505 T2 :: (Show c, Ix c) => c -> [c] -> T c
2507 When patten matching, these constraints are made available to discharge constraints
2508 in the body of the match. For example:
2511 f (T1 x y) | x==y = "yes"
2515 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2516 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2517 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2521 Unlike a Haskell-98-style
2522 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2523 have no scope. Indeed, one can write a kind signature instead:
2525 data Set :: * -> * where ...
2527 or even a mixture of the two:
2529 data Bar a :: (* -> *) -> * where ...
2531 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2534 data Bar a (b :: * -> *) where ...
2540 You can use strictness annotations, in the obvious places
2541 in the constructor type:
2544 Lit :: !Int -> Term Int
2545 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2546 Pair :: Term a -> Term b -> Term (a,b)
2551 You can use a <literal>deriving</literal> clause on a GADT-style data type
2552 declaration. For example, these two declarations are equivalent
2554 data Maybe1 a where {
2555 Nothing1 :: Maybe1 a ;
2556 Just1 :: a -> Maybe1 a
2557 } deriving( Eq, Ord )
2559 data Maybe2 a = Nothing2 | Just2 a
2565 The type signature may have quantified type variables that do not appear
2569 MkFoo :: a -> (a->Bool) -> Foo
2572 Here the type variable <literal>a</literal> does not appear in the result type
2573 of either constructor.
2574 Although it is universally quantified in the type of the constructor, such
2575 a type variable is often called "existential".
2576 Indeed, the above declaration declares precisely the same type as
2577 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2579 The type may contain a class context too, of course:
2582 MkShowable :: Show a => a -> Showable
2587 You can use record syntax on a GADT-style data type declaration:
2591 Adult :: { name :: String, children :: [Person] } -> Person
2592 Child :: Show a => { name :: !String, funny :: a } -> Person
2594 As usual, for every constructor that has a field <literal>f</literal>, the type of
2595 field <literal>f</literal> must be the same (modulo alpha conversion).
2596 The <literal>Child</literal> constructor above shows that the signature
2597 may have a context, existentially-quantified variables, and strictness annotations,
2598 just as in the non-record case. (NB: the "type" that follows the double-colon
2599 is not really a type, because of the record syntax and strictness annotations.
2600 A "type" of this form can appear only in a constructor signature.)
2604 Record updates are allowed with GADT-style declarations,
2605 only fields that have the following property: the type of the field
2606 mentions no existential type variables.
2610 As in the case of existentials declared using the Haskell-98-like record syntax
2611 (<xref linkend="existential-records"/>),
2612 record-selector functions are generated only for those fields that have well-typed
2614 Here is the example of that section, in GADT-style syntax:
2616 data Counter a where
2617 NewCounter { _this :: self
2618 , _inc :: self -> self
2619 , _display :: self -> IO ()
2624 As before, only one selector function is generated here, that for <literal>tag</literal>.
2625 Nevertheless, you can still use all the field names in pattern matching and record construction.
2627 </itemizedlist></para>
2631 <title>Generalised Algebraic Data Types (GADTs)</title>
2633 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2634 by allowing constructors to have richer return types. Here is an example:
2637 Lit :: Int -> Term Int
2638 Succ :: Term Int -> Term Int
2639 IsZero :: Term Int -> Term Bool
2640 If :: Term Bool -> Term a -> Term a -> Term a
2641 Pair :: Term a -> Term b -> Term (a,b)
2643 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2644 case with ordinary data types. This generality allows us to
2645 write a well-typed <literal>eval</literal> function
2646 for these <literal>Terms</literal>:
2650 eval (Succ t) = 1 + eval t
2651 eval (IsZero t) = eval t == 0
2652 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2653 eval (Pair e1 e2) = (eval e1, eval e2)
2655 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2656 For example, in the right hand side of the equation
2661 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2662 A precise specification of the type rules is beyond what this user manual aspires to,
2663 but the design closely follows that described in
2665 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2666 unification-based type inference for GADTs</ulink>,
2668 The general principle is this: <emphasis>type refinement is only carried out
2669 based on user-supplied type annotations</emphasis>.
2670 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2671 and lots of obscure error messages will
2672 occur. However, the refinement is quite general. For example, if we had:
2674 eval :: Term a -> a -> a
2675 eval (Lit i) j = i+j
2677 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2678 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2679 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2682 These and many other examples are given in papers by Hongwei Xi, and
2683 Tim Sheard. There is a longer introduction
2684 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2686 <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
2687 may use different notation to that implemented in GHC.
2690 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2691 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2694 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2695 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2696 The result type of each constructor must begin with the type constructor being defined,
2697 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2698 For example, in the <literal>Term</literal> data
2699 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2700 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2705 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2706 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2707 whose result type is not just <literal>T a b</literal>.
2711 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2712 an ordinary data type.
2716 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2720 Lit { val :: Int } :: Term Int
2721 Succ { num :: Term Int } :: Term Int
2722 Pred { num :: Term Int } :: Term Int
2723 IsZero { arg :: Term Int } :: Term Bool
2724 Pair { arg1 :: Term a
2727 If { cnd :: Term Bool
2732 However, for GADTs there is the following additional constraint:
2733 every constructor that has a field <literal>f</literal> must have
2734 the same result type (modulo alpha conversion)
2735 Hence, in the above example, we cannot merge the <literal>num</literal>
2736 and <literal>arg</literal> fields above into a
2737 single name. Although their field types are both <literal>Term Int</literal>,
2738 their selector functions actually have different types:
2741 num :: Term Int -> Term Int
2742 arg :: Term Bool -> Term Int
2747 When pattern-matching against data constructors drawn from a GADT,
2748 for example in a <literal>case</literal> expression, the following rules apply:
2750 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2751 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2752 <listitem><para>The type of any free variable mentioned in any of
2753 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2755 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2756 way to ensure that a variable a rigid type is to give it a type signature.
2757 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2758 Simple unification-based type inference for GADTs
2759 </ulink>. The criteria implemented by GHC are given in the Appendix.
2769 <!-- ====================== End of Generalised algebraic data types ======================= -->
2771 <sect1 id="deriving">
2772 <title>Extensions to the "deriving" mechanism</title>
2774 <sect2 id="deriving-inferred">
2775 <title>Inferred context for deriving clauses</title>
2778 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2781 data T0 f a = MkT0 a deriving( Eq )
2782 data T1 f a = MkT1 (f a) deriving( Eq )
2783 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2785 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2787 instance Eq a => Eq (T0 f a) where ...
2788 instance Eq (f a) => Eq (T1 f a) where ...
2789 instance Eq (f (f a)) => Eq (T2 f a) where ...
2791 The first of these is obviously fine. The second is still fine, although less obviously.
2792 The third is not Haskell 98, and risks losing termination of instances.
2795 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2796 each constraint in the inferred instance context must consist only of type variables,
2797 with no repetitions.
2800 This rule is applied regardless of flags. If you want a more exotic context, you can write
2801 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2805 <sect2 id="stand-alone-deriving">
2806 <title>Stand-alone deriving declarations</title>
2809 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2811 data Foo a = Bar a | Baz String
2813 deriving instance Eq a => Eq (Foo a)
2815 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2816 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2817 Note the following points:
2820 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2821 exactly as you would in an ordinary instance declaration.
2822 (In contrast, in a <literal>deriving</literal> clause
2823 attached to a data type declaration, the context is inferred.)
2827 A <literal>deriving instance</literal> declaration
2828 must obey the same rules concerning form and termination as ordinary instance declarations,
2829 controlled by the same flags; see <xref linkend="instance-decls"/>.
2833 Unlike a <literal>deriving</literal>
2834 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2835 than the data type (assuming you also use
2836 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2839 data Foo a = Bar a | Baz String
2841 deriving instance Eq a => Eq (Foo [a])
2842 deriving instance Eq a => Eq (Foo (Maybe a))
2844 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2845 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2849 Unlike a <literal>deriving</literal>
2850 declaration attached to a <literal>data</literal> declaration,
2851 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2852 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2853 your problem. (GHC will show you the offending code if it has a type error.)
2854 The merit of this is that you can derive instances for GADTs and other exotic
2855 data types, providing only that the boilerplate code does indeed typecheck. For example:
2861 deriving instance Show (T a)
2863 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2864 data type declaration for <literal>T</literal>,
2865 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2866 the instance declaration using stand-alone deriving.
2871 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2872 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2875 newtype Foo a = MkFoo (State Int a)
2877 deriving instance MonadState Int Foo
2879 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2880 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2882 </itemizedlist></para>
2887 <sect2 id="deriving-typeable">
2888 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2891 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2892 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2893 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2894 classes <literal>Eq</literal>, <literal>Ord</literal>,
2895 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2898 GHC extends this list with several more classes that may be automatically derived:
2900 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2901 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2902 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2904 <para>An instance of <literal>Typeable</literal> can only be derived if the
2905 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2906 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2908 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2909 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2911 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2912 are used, and only <literal>Typeable1</literal> up to
2913 <literal>Typeable7</literal> are provided in the library.)
2914 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2915 class, whose kind suits that of the data type constructor, and
2916 then writing the data type instance by hand.
2920 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2921 the class <literal>Functor</literal>,
2922 defined in <literal>GHC.Base</literal>.
2925 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2926 the class <literal>Foldable</literal>,
2927 defined in <literal>Data.Foldable</literal>.
2930 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2931 the class <literal>Traversable</literal>,
2932 defined in <literal>Data.Traversable</literal>.
2935 In each case the appropriate class must be in scope before it
2936 can be mentioned in the <literal>deriving</literal> clause.
2940 <sect2 id="newtype-deriving">
2941 <title>Generalised derived instances for newtypes</title>
2944 When you define an abstract type using <literal>newtype</literal>, you may want
2945 the new type to inherit some instances from its representation. In
2946 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2947 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2948 other classes you have to write an explicit instance declaration. For
2949 example, if you define
2952 newtype Dollars = Dollars Int
2955 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2956 explicitly define an instance of <literal>Num</literal>:
2959 instance Num Dollars where
2960 Dollars a + Dollars b = Dollars (a+b)
2963 All the instance does is apply and remove the <literal>newtype</literal>
2964 constructor. It is particularly galling that, since the constructor
2965 doesn't appear at run-time, this instance declaration defines a
2966 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2967 dictionary, only slower!
2971 <sect3> <title> Generalising the deriving clause </title>
2973 GHC now permits such instances to be derived instead,
2974 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2977 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2980 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2981 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2982 derives an instance declaration of the form
2985 instance Num Int => Num Dollars
2988 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2992 We can also derive instances of constructor classes in a similar
2993 way. For example, suppose we have implemented state and failure monad
2994 transformers, such that
2997 instance Monad m => Monad (State s m)
2998 instance Monad m => Monad (Failure m)
3000 In Haskell 98, we can define a parsing monad by
3002 type Parser tok m a = State [tok] (Failure m) a
3005 which is automatically a monad thanks to the instance declarations
3006 above. With the extension, we can make the parser type abstract,
3007 without needing to write an instance of class <literal>Monad</literal>, via
3010 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3013 In this case the derived instance declaration is of the form
3015 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3018 Notice that, since <literal>Monad</literal> is a constructor class, the
3019 instance is a <emphasis>partial application</emphasis> of the new type, not the
3020 entire left hand side. We can imagine that the type declaration is
3021 "eta-converted" to generate the context of the instance
3026 We can even derive instances of multi-parameter classes, provided the
3027 newtype is the last class parameter. In this case, a ``partial
3028 application'' of the class appears in the <literal>deriving</literal>
3029 clause. For example, given the class
3032 class StateMonad s m | m -> s where ...
3033 instance Monad m => StateMonad s (State s m) where ...
3035 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3037 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3038 deriving (Monad, StateMonad [tok])
3041 The derived instance is obtained by completing the application of the
3042 class to the new type:
3045 instance StateMonad [tok] (State [tok] (Failure m)) =>
3046 StateMonad [tok] (Parser tok m)
3051 As a result of this extension, all derived instances in newtype
3052 declarations are treated uniformly (and implemented just by reusing
3053 the dictionary for the representation type), <emphasis>except</emphasis>
3054 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3055 the newtype and its representation.
3059 <sect3> <title> A more precise specification </title>
3061 Derived instance declarations are constructed as follows. Consider the
3062 declaration (after expansion of any type synonyms)
3065 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3071 The <literal>ci</literal> are partial applications of
3072 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3073 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3076 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3079 The type <literal>t</literal> is an arbitrary type.
3082 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3083 nor in the <literal>ci</literal>, and
3086 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3087 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3088 should not "look through" the type or its constructor. You can still
3089 derive these classes for a newtype, but it happens in the usual way, not
3090 via this new mechanism.
3093 Then, for each <literal>ci</literal>, the derived instance
3096 instance ci t => ci (T v1...vk)
3098 As an example which does <emphasis>not</emphasis> work, consider
3100 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3102 Here we cannot derive the instance
3104 instance Monad (State s m) => Monad (NonMonad m)
3107 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3108 and so cannot be "eta-converted" away. It is a good thing that this
3109 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3110 not, in fact, a monad --- for the same reason. Try defining
3111 <literal>>>=</literal> with the correct type: you won't be able to.
3115 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3116 important, since we can only derive instances for the last one. If the
3117 <literal>StateMonad</literal> class above were instead defined as
3120 class StateMonad m s | m -> s where ...
3123 then we would not have been able to derive an instance for the
3124 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3125 classes usually have one "main" parameter for which deriving new
3126 instances is most interesting.
3128 <para>Lastly, all of this applies only for classes other than
3129 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3130 and <literal>Data</literal>, for which the built-in derivation applies (section
3131 4.3.3. of the Haskell Report).
3132 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3133 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3134 the standard method is used or the one described here.)
3141 <!-- TYPE SYSTEM EXTENSIONS -->
3142 <sect1 id="type-class-extensions">
3143 <title>Class and instances declarations</title>
3145 <sect2 id="multi-param-type-classes">
3146 <title>Class declarations</title>
3149 This section, and the next one, documents GHC's type-class extensions.
3150 There's lots of background in the paper <ulink
3151 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3152 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3153 Jones, Erik Meijer).
3156 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3160 <title>Multi-parameter type classes</title>
3162 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3167 class Collection c a where
3168 union :: c a -> c a -> c a
3175 <sect3 id="superclass-rules">
3176 <title>The superclasses of a class declaration</title>
3179 In Haskell 98 the context of a class declaration (which introduces superclasses)
3180 must be simple; that is, each predicate must consist of a class applied to
3181 type variables. The flag <option>-XFlexibleContexts</option>
3182 (<xref linkend="flexible-contexts"/>)
3183 lifts this restriction,
3184 so that the only restriction on the context in a class declaration is
3185 that the class hierarchy must be acyclic. So these class declarations are OK:
3189 class Functor (m k) => FiniteMap m k where
3192 class (Monad m, Monad (t m)) => Transform t m where
3193 lift :: m a -> (t m) a
3199 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3200 of "acyclic" involves only the superclass relationships. For example,
3206 op :: D b => a -> b -> b
3209 class C a => D a where { ... }
3213 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3214 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3215 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3222 <sect3 id="class-method-types">
3223 <title>Class method types</title>
3226 Haskell 98 prohibits class method types to mention constraints on the
3227 class type variable, thus:
3230 fromList :: [a] -> s a
3231 elem :: Eq a => a -> s a -> Bool
3233 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3234 contains the constraint <literal>Eq a</literal>, constrains only the
3235 class type variable (in this case <literal>a</literal>).
3236 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3243 <sect2 id="functional-dependencies">
3244 <title>Functional dependencies
3247 <para> Functional dependencies are implemented as described by Mark Jones
3248 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3249 In Proceedings of the 9th European Symposium on Programming,
3250 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3254 Functional dependencies are introduced by a vertical bar in the syntax of a
3255 class declaration; e.g.
3257 class (Monad m) => MonadState s m | m -> s where ...
3259 class Foo a b c | a b -> c where ...
3261 There should be more documentation, but there isn't (yet). Yell if you need it.
3264 <sect3><title>Rules for functional dependencies </title>
3266 In a class declaration, all of the class type variables must be reachable (in the sense
3267 mentioned in <xref linkend="type-restrictions"/>)
3268 from the free variables of each method type.
3272 class Coll s a where
3274 insert :: s -> a -> s
3277 is not OK, because the type of <literal>empty</literal> doesn't mention
3278 <literal>a</literal>. Functional dependencies can make the type variable
3281 class Coll s a | s -> a where
3283 insert :: s -> a -> s
3286 Alternatively <literal>Coll</literal> might be rewritten
3289 class Coll s a where
3291 insert :: s a -> a -> s a
3295 which makes the connection between the type of a collection of
3296 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3297 Occasionally this really doesn't work, in which case you can split the
3305 class CollE s => Coll s a where
3306 insert :: s -> a -> s
3313 <title>Background on functional dependencies</title>
3315 <para>The following description of the motivation and use of functional dependencies is taken
3316 from the Hugs user manual, reproduced here (with minor changes) by kind
3317 permission of Mark Jones.
3320 Consider the following class, intended as part of a
3321 library for collection types:
3323 class Collects e ce where
3325 insert :: e -> ce -> ce
3326 member :: e -> ce -> Bool
3328 The type variable e used here represents the element type, while ce is the type
3329 of the container itself. Within this framework, we might want to define
3330 instances of this class for lists or characteristic functions (both of which
3331 can be used to represent collections of any equality type), bit sets (which can
3332 be used to represent collections of characters), or hash tables (which can be
3333 used to represent any collection whose elements have a hash function). Omitting
3334 standard implementation details, this would lead to the following declarations:
3336 instance Eq e => Collects e [e] where ...
3337 instance Eq e => Collects e (e -> Bool) where ...
3338 instance Collects Char BitSet where ...
3339 instance (Hashable e, Collects a ce)
3340 => Collects e (Array Int ce) where ...
3342 All this looks quite promising; we have a class and a range of interesting
3343 implementations. Unfortunately, there are some serious problems with the class
3344 declaration. First, the empty function has an ambiguous type:
3346 empty :: Collects e ce => ce
3348 By "ambiguous" we mean that there is a type variable e that appears on the left
3349 of the <literal>=></literal> symbol, but not on the right. The problem with
3350 this is that, according to the theoretical foundations of Haskell overloading,
3351 we cannot guarantee a well-defined semantics for any term with an ambiguous
3355 We can sidestep this specific problem by removing the empty member from the
3356 class declaration. However, although the remaining members, insert and member,
3357 do not have ambiguous types, we still run into problems when we try to use
3358 them. For example, consider the following two functions:
3360 f x y = insert x . insert y
3363 for which GHC infers the following types:
3365 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3366 g :: (Collects Bool c, Collects Char c) => c -> c
3368 Notice that the type for f allows the two parameters x and y to be assigned
3369 different types, even though it attempts to insert each of the two values, one
3370 after the other, into the same collection. If we're trying to model collections
3371 that contain only one type of value, then this is clearly an inaccurate
3372 type. Worse still, the definition for g is accepted, without causing a type
3373 error. As a result, the error in this code will not be flagged at the point
3374 where it appears. Instead, it will show up only when we try to use g, which
3375 might even be in a different module.
3378 <sect4><title>An attempt to use constructor classes</title>
3381 Faced with the problems described above, some Haskell programmers might be
3382 tempted to use something like the following version of the class declaration:
3384 class Collects e c where
3386 insert :: e -> c e -> c e
3387 member :: e -> c e -> Bool
3389 The key difference here is that we abstract over the type constructor c that is
3390 used to form the collection type c e, and not over that collection type itself,
3391 represented by ce in the original class declaration. This avoids the immediate
3392 problems that we mentioned above: empty has type <literal>Collects e c => c
3393 e</literal>, which is not ambiguous.
3396 The function f from the previous section has a more accurate type:
3398 f :: (Collects e c) => e -> e -> c e -> c e
3400 The function g from the previous section is now rejected with a type error as
3401 we would hope because the type of f does not allow the two arguments to have
3403 This, then, is an example of a multiple parameter class that does actually work
3404 quite well in practice, without ambiguity problems.
3405 There is, however, a catch. This version of the Collects class is nowhere near
3406 as general as the original class seemed to be: only one of the four instances
3407 for <literal>Collects</literal>
3408 given above can be used with this version of Collects because only one of
3409 them---the instance for lists---has a collection type that can be written in
3410 the form c e, for some type constructor c, and element type e.
3414 <sect4><title>Adding functional dependencies</title>
3417 To get a more useful version of the Collects class, Hugs provides a mechanism
3418 that allows programmers to specify dependencies between the parameters of a
3419 multiple parameter class (For readers with an interest in theoretical
3420 foundations and previous work: The use of dependency information can be seen
3421 both as a generalization of the proposal for `parametric type classes' that was
3422 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3423 later framework for "improvement" of qualified types. The
3424 underlying ideas are also discussed in a more theoretical and abstract setting
3425 in a manuscript [implparam], where they are identified as one point in a
3426 general design space for systems of implicit parameterization.).
3428 To start with an abstract example, consider a declaration such as:
3430 class C a b where ...
3432 which tells us simply that C can be thought of as a binary relation on types
3433 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3434 included in the definition of classes to add information about dependencies
3435 between parameters, as in the following examples:
3437 class D a b | a -> b where ...
3438 class E a b | a -> b, b -> a where ...
3440 The notation <literal>a -> b</literal> used here between the | and where
3441 symbols --- not to be
3442 confused with a function type --- indicates that the a parameter uniquely
3443 determines the b parameter, and might be read as "a determines b." Thus D is
3444 not just a relation, but actually a (partial) function. Similarly, from the two
3445 dependencies that are included in the definition of E, we can see that E
3446 represents a (partial) one-one mapping between types.
3449 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3450 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3451 m>=0, meaning that the y parameters are uniquely determined by the x
3452 parameters. Spaces can be used as separators if more than one variable appears
3453 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3454 annotated with multiple dependencies using commas as separators, as in the
3455 definition of E above. Some dependencies that we can write in this notation are
3456 redundant, and will be rejected because they don't serve any useful
3457 purpose, and may instead indicate an error in the program. Examples of
3458 dependencies like this include <literal>a -> a </literal>,
3459 <literal>a -> a a </literal>,
3460 <literal>a -> </literal>, etc. There can also be
3461 some redundancy if multiple dependencies are given, as in
3462 <literal>a->b</literal>,
3463 <literal>b->c </literal>, <literal>a->c </literal>, and
3464 in which some subset implies the remaining dependencies. Examples like this are
3465 not treated as errors. Note that dependencies appear only in class
3466 declarations, and not in any other part of the language. In particular, the
3467 syntax for instance declarations, class constraints, and types is completely
3471 By including dependencies in a class declaration, we provide a mechanism for
3472 the programmer to specify each multiple parameter class more precisely. The
3473 compiler, on the other hand, is responsible for ensuring that the set of
3474 instances that are in scope at any given point in the program is consistent
3475 with any declared dependencies. For example, the following pair of instance
3476 declarations cannot appear together in the same scope because they violate the
3477 dependency for D, even though either one on its own would be acceptable:
3479 instance D Bool Int where ...
3480 instance D Bool Char where ...
3482 Note also that the following declaration is not allowed, even by itself:
3484 instance D [a] b where ...
3486 The problem here is that this instance would allow one particular choice of [a]
3487 to be associated with more than one choice for b, which contradicts the
3488 dependency specified in the definition of D. More generally, this means that,
3489 in any instance of the form:
3491 instance D t s where ...
3493 for some particular types t and s, the only variables that can appear in s are
3494 the ones that appear in t, and hence, if the type t is known, then s will be
3495 uniquely determined.
3498 The benefit of including dependency information is that it allows us to define
3499 more general multiple parameter classes, without ambiguity problems, and with
3500 the benefit of more accurate types. To illustrate this, we return to the
3501 collection class example, and annotate the original definition of <literal>Collects</literal>
3502 with a simple dependency:
3504 class Collects e ce | ce -> e where
3506 insert :: e -> ce -> ce
3507 member :: e -> ce -> Bool
3509 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3510 determined by the type of the collection ce. Note that both parameters of
3511 Collects are of kind *; there are no constructor classes here. Note too that
3512 all of the instances of Collects that we gave earlier can be used
3513 together with this new definition.
3516 What about the ambiguity problems that we encountered with the original
3517 definition? The empty function still has type Collects e ce => ce, but it is no
3518 longer necessary to regard that as an ambiguous type: Although the variable e
3519 does not appear on the right of the => symbol, the dependency for class
3520 Collects tells us that it is uniquely determined by ce, which does appear on
3521 the right of the => symbol. Hence the context in which empty is used can still
3522 give enough information to determine types for both ce and e, without
3523 ambiguity. More generally, we need only regard a type as ambiguous if it
3524 contains a variable on the left of the => that is not uniquely determined
3525 (either directly or indirectly) by the variables on the right.
3528 Dependencies also help to produce more accurate types for user defined
3529 functions, and hence to provide earlier detection of errors, and less cluttered
3530 types for programmers to work with. Recall the previous definition for a
3533 f x y = insert x y = insert x . insert y
3535 for which we originally obtained a type:
3537 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3539 Given the dependency information that we have for Collects, however, we can
3540 deduce that a and b must be equal because they both appear as the second
3541 parameter in a Collects constraint with the same first parameter c. Hence we
3542 can infer a shorter and more accurate type for f:
3544 f :: (Collects a c) => a -> a -> c -> c
3546 In a similar way, the earlier definition of g will now be flagged as a type error.
3549 Although we have given only a few examples here, it should be clear that the
3550 addition of dependency information can help to make multiple parameter classes
3551 more useful in practice, avoiding ambiguity problems, and allowing more general
3552 sets of instance declarations.
3558 <sect2 id="instance-decls">
3559 <title>Instance declarations</title>
3561 <para>An instance declaration has the form
3563 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 ...
3565 The part before the "<literal>=></literal>" is the
3566 <emphasis>context</emphasis>, while the part after the
3567 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3570 <sect3 id="flexible-instance-head">
3571 <title>Relaxed rules for the instance head</title>
3574 In Haskell 98 the head of an instance declaration
3575 must be of the form <literal>C (T a1 ... an)</literal>, where
3576 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3577 and the <literal>a1 ... an</literal> are distinct type variables.
3578 GHC relaxes these rules in two ways.
3582 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3583 declaration to mention arbitrary nested types.
3584 For example, this becomes a legal instance declaration
3586 instance C (Maybe Int) where ...
3588 See also the <link linkend="instance-overlap">rules on overlap</link>.
3591 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3592 synonyms. As always, using a type synonym is just shorthand for
3593 writing the RHS of the type synonym definition. For example:
3597 type Point = (Int,Int)
3598 instance C Point where ...
3599 instance C [Point] where ...
3603 is legal. However, if you added
3607 instance C (Int,Int) where ...
3611 as well, then the compiler will complain about the overlapping
3612 (actually, identical) instance declarations. As always, type synonyms
3613 must be fully applied. You cannot, for example, write:
3617 instance Monad P where ...
3625 <sect3 id="instance-rules">
3626 <title>Relaxed rules for instance contexts</title>
3628 <para>In Haskell 98, the assertions in the context of the instance declaration
3629 must be of the form <literal>C a</literal> where <literal>a</literal>
3630 is a type variable that occurs in the head.
3634 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3635 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3636 With this flag the context of the instance declaration can each consist of arbitrary
3637 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3641 The Paterson Conditions: for each assertion in the context
3643 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3644 <listitem><para>The assertion has fewer constructors and variables (taken together
3645 and counting repetitions) than the head</para></listitem>
3649 <listitem><para>The Coverage Condition. For each functional dependency,
3650 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3651 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3652 every type variable in
3653 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3654 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3655 substitution mapping each type variable in the class declaration to the
3656 corresponding type in the instance declaration.
3659 These restrictions ensure that context reduction terminates: each reduction
3660 step makes the problem smaller by at least one
3661 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3662 if you give the <option>-XUndecidableInstances</option>
3663 flag (<xref linkend="undecidable-instances"/>).
3664 You can find lots of background material about the reason for these
3665 restrictions in the paper <ulink
3666 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3667 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3670 For example, these are OK:
3672 instance C Int [a] -- Multiple parameters
3673 instance Eq (S [a]) -- Structured type in head
3675 -- Repeated type variable in head
3676 instance C4 a a => C4 [a] [a]
3677 instance Stateful (ST s) (MutVar s)
3679 -- Head can consist of type variables only
3681 instance (Eq a, Show b) => C2 a b
3683 -- Non-type variables in context
3684 instance Show (s a) => Show (Sized s a)
3685 instance C2 Int a => C3 Bool [a]
3686 instance C2 Int a => C3 [a] b
3690 -- Context assertion no smaller than head
3691 instance C a => C a where ...
3692 -- (C b b) has more more occurrences of b than the head
3693 instance C b b => Foo [b] where ...
3698 The same restrictions apply to instances generated by
3699 <literal>deriving</literal> clauses. Thus the following is accepted:
3701 data MinHeap h a = H a (h a)
3704 because the derived instance
3706 instance (Show a, Show (h a)) => Show (MinHeap h a)
3708 conforms to the above rules.
3712 A useful idiom permitted by the above rules is as follows.
3713 If one allows overlapping instance declarations then it's quite
3714 convenient to have a "default instance" declaration that applies if
3715 something more specific does not:
3723 <sect3 id="undecidable-instances">
3724 <title>Undecidable instances</title>
3727 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3728 For example, sometimes you might want to use the following to get the
3729 effect of a "class synonym":
3731 class (C1 a, C2 a, C3 a) => C a where { }
3733 instance (C1 a, C2 a, C3 a) => C a where { }
3735 This allows you to write shorter signatures:
3741 f :: (C1 a, C2 a, C3 a) => ...
3743 The restrictions on functional dependencies (<xref
3744 linkend="functional-dependencies"/>) are particularly troublesome.
3745 It is tempting to introduce type variables in the context that do not appear in
3746 the head, something that is excluded by the normal rules. For example:
3748 class HasConverter a b | a -> b where
3751 data Foo a = MkFoo a
3753 instance (HasConverter a b,Show b) => Show (Foo a) where
3754 show (MkFoo value) = show (convert value)
3756 This is dangerous territory, however. Here, for example, is a program that would make the
3761 instance F [a] [[a]]
3762 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3764 Similarly, it can be tempting to lift the coverage condition:
3766 class Mul a b c | a b -> c where
3767 (.*.) :: a -> b -> c
3769 instance Mul Int Int Int where (.*.) = (*)
3770 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3771 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3773 The third instance declaration does not obey the coverage condition;
3774 and indeed the (somewhat strange) definition:
3776 f = \ b x y -> if b then x .*. [y] else y
3778 makes instance inference go into a loop, because it requires the constraint
3779 <literal>(Mul a [b] b)</literal>.
3782 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3783 the experimental flag <option>-XUndecidableInstances</option>
3784 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3785 both the Paterson Conditions and the Coverage Condition
3786 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3787 fixed-depth recursion stack. If you exceed the stack depth you get a
3788 sort of backtrace, and the opportunity to increase the stack depth
3789 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3795 <sect3 id="instance-overlap">
3796 <title>Overlapping instances</title>
3798 In general, <emphasis>GHC requires that that it be unambiguous which instance
3800 should be used to resolve a type-class constraint</emphasis>. This behaviour
3801 can be modified by two flags: <option>-XOverlappingInstances</option>
3802 <indexterm><primary>-XOverlappingInstances
3803 </primary></indexterm>
3804 and <option>-XIncoherentInstances</option>
3805 <indexterm><primary>-XIncoherentInstances
3806 </primary></indexterm>, as this section discusses. Both these
3807 flags are dynamic flags, and can be set on a per-module basis, using
3808 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3810 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3811 it tries to match every instance declaration against the
3813 by instantiating the head of the instance declaration. For example, consider
3816 instance context1 => C Int a where ... -- (A)
3817 instance context2 => C a Bool where ... -- (B)
3818 instance context3 => C Int [a] where ... -- (C)
3819 instance context4 => C Int [Int] where ... -- (D)
3821 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3822 but (C) and (D) do not. When matching, GHC takes
3823 no account of the context of the instance declaration
3824 (<literal>context1</literal> etc).
3825 GHC's default behaviour is that <emphasis>exactly one instance must match the
3826 constraint it is trying to resolve</emphasis>.
3827 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3828 including both declarations (A) and (B), say); an error is only reported if a
3829 particular constraint matches more than one.
3833 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3834 more than one instance to match, provided there is a most specific one. For
3835 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3836 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3837 most-specific match, the program is rejected.
3840 However, GHC is conservative about committing to an overlapping instance. For example:
3845 Suppose that from the RHS of <literal>f</literal> we get the constraint
3846 <literal>C Int [b]</literal>. But
3847 GHC does not commit to instance (C), because in a particular
3848 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3849 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3850 So GHC rejects the program.
3851 (If you add the flag <option>-XIncoherentInstances</option>,
3852 GHC will instead pick (C), without complaining about
3853 the problem of subsequent instantiations.)
3856 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3857 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3858 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3859 it instead. In this case, GHC will refrain from
3860 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3861 as before) but, rather than rejecting the program, it will infer the type
3863 f :: C Int [b] => [b] -> [b]
3865 That postpones the question of which instance to pick to the
3866 call site for <literal>f</literal>
3867 by which time more is known about the type <literal>b</literal>.
3868 You can write this type signature yourself if you use the
3869 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3873 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3877 instance Foo [b] where
3880 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3881 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3882 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3883 declaration. The solution is to postpone the choice by adding the constraint to the context
3884 of the instance declaration, thus:
3886 instance C Int [b] => Foo [b] where
3889 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3892 The willingness to be overlapped or incoherent is a property of
3893 the <emphasis>instance declaration</emphasis> itself, controlled by the
3894 presence or otherwise of the <option>-XOverlappingInstances</option>
3895 and <option>-XIncoherentInstances</option> flags when that module is
3896 being defined. Neither flag is required in a module that imports and uses the
3897 instance declaration. Specifically, during the lookup process:
3900 An instance declaration is ignored during the lookup process if (a) a more specific
3901 match is found, and (b) the instance declaration was compiled with
3902 <option>-XOverlappingInstances</option>. The flag setting for the
3903 more-specific instance does not matter.
3906 Suppose an instance declaration does not match the constraint being looked up, but
3907 does unify with it, so that it might match when the constraint is further
3908 instantiated. Usually GHC will regard this as a reason for not committing to
3909 some other constraint. But if the instance declaration was compiled with
3910 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3911 check for that declaration.
3914 These rules make it possible for a library author to design a library that relies on
3915 overlapping instances without the library client having to know.
3918 If an instance declaration is compiled without
3919 <option>-XOverlappingInstances</option>,
3920 then that instance can never be overlapped. This could perhaps be
3921 inconvenient. Perhaps the rule should instead say that the
3922 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3923 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3924 at a usage site should be permitted regardless of how the instance declarations
3925 are compiled, if the <option>-XOverlappingInstances</option> flag is
3926 used at the usage site. (Mind you, the exact usage site can occasionally be
3927 hard to pin down.) We are interested to receive feedback on these points.
3929 <para>The <option>-XIncoherentInstances</option> flag implies the
3930 <option>-XOverlappingInstances</option> flag, but not vice versa.
3938 <sect2 id="overloaded-strings">
3939 <title>Overloaded string literals
3943 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3944 string literal has type <literal>String</literal>, but with overloaded string
3945 literals enabled (with <literal>-XOverloadedStrings</literal>)
3946 a string literal has type <literal>(IsString a) => a</literal>.
3949 This means that the usual string syntax can be used, e.g., for packed strings
3950 and other variations of string like types. String literals behave very much
3951 like integer literals, i.e., they can be used in both expressions and patterns.
3952 If used in a pattern the literal with be replaced by an equality test, in the same
3953 way as an integer literal is.
3956 The class <literal>IsString</literal> is defined as:
3958 class IsString a where
3959 fromString :: String -> a
3961 The only predefined instance is the obvious one to make strings work as usual:
3963 instance IsString [Char] where
3966 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3967 it explicitly (for example, to give an instance declaration for it), you can import it
3968 from module <literal>GHC.Exts</literal>.
3971 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3975 Each type in a default declaration must be an
3976 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3980 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3981 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3982 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3983 <emphasis>or</emphasis> <literal>IsString</literal>.
3992 import GHC.Exts( IsString(..) )
3994 newtype MyString = MyString String deriving (Eq, Show)
3995 instance IsString MyString where
3996 fromString = MyString
3998 greet :: MyString -> MyString
3999 greet "hello" = "world"
4003 print $ greet "hello"
4004 print $ greet "fool"
4008 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4009 to work since it gets translated into an equality comparison.
4015 <sect1 id="type-families">
4016 <title>Type families</title>
4019 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4020 facilitate type-level
4021 programming. Type families are a generalisation of <firstterm>associated
4022 data types</firstterm>
4023 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4024 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4025 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4026 Symposium on Principles of Programming Languages (POPL'05)”, pages
4027 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4028 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4029 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4031 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4032 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4033 themselves are described in the paper “<ulink
4034 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4035 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4037 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4038 13th ACM SIGPLAN International Conference on Functional
4039 Programming”, ACM Press, pages 51-62, 2008. Type families
4040 essentially provide type-indexed data types and named functions on types,
4041 which are useful for generic programming and highly parameterised library
4042 interfaces as well as interfaces with enhanced static information, much like
4043 dependent types. They might also be regarded as an alternative to functional
4044 dependencies, but provide a more functional style of type-level programming
4045 than the relational style of functional dependencies.
4048 Indexed type families, or type families for short, are type constructors that
4049 represent sets of types. Set members are denoted by supplying the type family
4050 constructor with type parameters, which are called <firstterm>type
4051 indices</firstterm>. The
4052 difference between vanilla parametrised type constructors and family
4053 constructors is much like between parametrically polymorphic functions and
4054 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4055 behave the same at all type instances, whereas class methods can change their
4056 behaviour in dependence on the class type parameters. Similarly, vanilla type
4057 constructors imply the same data representation for all type instances, but
4058 family constructors can have varying representation types for varying type
4062 Indexed type families come in two flavours: <firstterm>data
4063 families</firstterm> and <firstterm>type synonym
4064 families</firstterm>. They are the indexed family variants of algebraic
4065 data types and type synonyms, respectively. The instances of data families
4066 can be data types and newtypes.
4069 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4070 Additional information on the use of type families in GHC is available on
4071 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4072 Haskell wiki page on type families</ulink>.
4075 <sect2 id="data-families">
4076 <title>Data families</title>
4079 Data families appear in two flavours: (1) they can be defined on the
4081 or (2) they can appear inside type classes (in which case they are known as
4082 associated types). The former is the more general variant, as it lacks the
4083 requirement for the type-indexes to coincide with the class
4084 parameters. However, the latter can lead to more clearly structured code and
4085 compiler warnings if some type instances were - possibly accidentally -
4086 omitted. In the following, we always discuss the general toplevel form first
4087 and then cover the additional constraints placed on associated types.
4090 <sect3 id="data-family-declarations">
4091 <title>Data family declarations</title>
4094 Indexed data families are introduced by a signature, such as
4096 data family GMap k :: * -> *
4098 The special <literal>family</literal> distinguishes family from standard
4099 data declarations. The result kind annotation is optional and, as
4100 usual, defaults to <literal>*</literal> if omitted. An example is
4104 Named arguments can also be given explicit kind signatures if needed.
4106 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4107 declarations] named arguments are entirely optional, so that we can
4108 declare <literal>Array</literal> alternatively with
4110 data family Array :: * -> *
4114 <sect4 id="assoc-data-family-decl">
4115 <title>Associated data family declarations</title>
4117 When a data family is declared as part of a type class, we drop
4118 the <literal>family</literal> special. The <literal>GMap</literal>
4119 declaration takes the following form
4121 class GMapKey k where
4122 data GMap k :: * -> *
4125 In contrast to toplevel declarations, named arguments must be used for
4126 all type parameters that are to be used as type-indexes. Moreover,
4127 the argument names must be class parameters. Each class parameter may
4128 only be used at most once per associated type, but some may be omitted
4129 and they may be in an order other than in the class head. Hence, the
4130 following contrived example is admissible:
4139 <sect3 id="data-instance-declarations">
4140 <title>Data instance declarations</title>
4143 Instance declarations of data and newtype families are very similar to
4144 standard data and newtype declarations. The only two differences are
4145 that the keyword <literal>data</literal> or <literal>newtype</literal>
4146 is followed by <literal>instance</literal> and that some or all of the
4147 type arguments can be non-variable types, but may not contain forall
4148 types or type synonym families. However, data families are generally
4149 allowed in type parameters, and type synonyms are allowed as long as
4150 they are fully applied and expand to a type that is itself admissible -
4151 exactly as this is required for occurrences of type synonyms in class
4152 instance parameters. For example, the <literal>Either</literal>
4153 instance for <literal>GMap</literal> is
4155 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4157 In this example, the declaration has only one variant. In general, it
4161 Data and newtype instance declarations are only permitted when an
4162 appropriate family declaration is in scope - just as a class instance declaratoin
4163 requires the class declaration to be visible. Moreover, each instance
4164 declaration has to conform to the kind determined by its family
4165 declaration. This implies that the number of parameters of an instance
4166 declaration matches the arity determined by the kind of the family.
4169 A data family instance declaration can use the full exprssiveness of
4170 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4172 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4173 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4174 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4177 data instance T Int = T1 Int | T2 Bool
4178 newtype instance T Char = TC Bool
4181 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4182 and indeed can define a GADT. For example:
4185 data instance G [a] b where
4186 G1 :: c -> G [Int] b
4190 <listitem><para> You can use a <literal>deriving</literal> clause on a
4191 <literal>data instance</literal> or <literal>newtype instance</literal>
4198 Even if type families are defined as toplevel declarations, functions
4199 that perform different computations for different family instances may still
4200 need to be defined as methods of type classes. In particular, the
4201 following is not possible:
4204 data instance T Int = A
4205 data instance T Char = B
4207 foo A = 1 -- WRONG: These two equations together...
4208 foo B = 2 -- ...will produce a type error.
4210 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4214 instance Foo Int where
4216 instance Foo Char where
4219 (Given the functionality provided by GADTs (Generalised Algebraic Data
4220 Types), it might seem as if a definition, such as the above, should be
4221 feasible. However, type families are - in contrast to GADTs - are
4222 <emphasis>open;</emphasis> i.e., new instances can always be added,
4224 modules. Supporting pattern matching across different data instances
4225 would require a form of extensible case construct.)
4228 <sect4 id="assoc-data-inst">
4229 <title>Associated data instances</title>
4231 When an associated data family instance is declared within a type
4232 class instance, we drop the <literal>instance</literal> keyword in the
4233 family instance. So, the <literal>Either</literal> instance
4234 for <literal>GMap</literal> becomes:
4236 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4237 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4240 The most important point about associated family instances is that the
4241 type indexes corresponding to class parameters must be identical to
4242 the type given in the instance head; here this is the first argument
4243 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4244 which coincides with the only class parameter. Any parameters to the
4245 family constructor that do not correspond to class parameters, need to
4246 be variables in every instance; here this is the
4247 variable <literal>v</literal>.
4250 Instances for an associated family can only appear as part of
4251 instances declarations of the class in which the family was declared -
4252 just as with the equations of the methods of a class. Also in
4253 correspondence to how methods are handled, declarations of associated
4254 types can be omitted in class instances. If an associated family
4255 instance is omitted, the corresponding instance type is not inhabited;
4256 i.e., only diverging expressions, such
4257 as <literal>undefined</literal>, can assume the type.
4261 <sect4 id="scoping-class-params">
4262 <title>Scoping of class parameters</title>
4264 In the case of multi-parameter type classes, the visibility of class
4265 parameters in the right-hand side of associated family instances
4266 depends <emphasis>solely</emphasis> on the parameters of the data
4267 family. As an example, consider the simple class declaration
4272 Only one of the two class parameters is a parameter to the data
4273 family. Hence, the following instance declaration is invalid:
4275 instance C [c] d where
4276 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4278 Here, the right-hand side of the data instance mentions the type
4279 variable <literal>d</literal> that does not occur in its left-hand
4280 side. We cannot admit such data instances as they would compromise
4285 <sect4 id="family-class-inst">
4286 <title>Type class instances of family instances</title>
4288 Type class instances of instances of data families can be defined as
4289 usual, and in particular data instance declarations can
4290 have <literal>deriving</literal> clauses. For example, we can write
4292 data GMap () v = GMapUnit (Maybe v)
4295 which implicitly defines an instance of the form
4297 instance Show v => Show (GMap () v) where ...
4301 Note that class instances are always for
4302 particular <emphasis>instances</emphasis> of a data family and never
4303 for an entire family as a whole. This is for essentially the same
4304 reasons that we cannot define a toplevel function that performs
4305 pattern matching on the data constructors
4306 of <emphasis>different</emphasis> instances of a single type family.
4307 It would require a form of extensible case construct.
4311 <sect4 id="data-family-overlap">
4312 <title>Overlap of data instances</title>
4314 The instance declarations of a data family used in a single program
4315 may not overlap at all, independent of whether they are associated or
4316 not. In contrast to type class instances, this is not only a matter
4317 of consistency, but one of type safety.
4323 <sect3 id="data-family-import-export">
4324 <title>Import and export</title>
4327 The association of data constructors with type families is more dynamic
4328 than that is the case with standard data and newtype declarations. In
4329 the standard case, the notation <literal>T(..)</literal> in an import or
4330 export list denotes the type constructor and all the data constructors
4331 introduced in its declaration. However, a family declaration never
4332 introduces any data constructors; instead, data constructors are
4333 introduced by family instances. As a result, which data constructors
4334 are associated with a type family depends on the currently visible
4335 instance declarations for that family. Consequently, an import or
4336 export item of the form <literal>T(..)</literal> denotes the family
4337 constructor and all currently visible data constructors - in the case of
4338 an export item, these may be either imported or defined in the current
4339 module. The treatment of import and export items that explicitly list
4340 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4344 <sect4 id="data-family-impexp-assoc">
4345 <title>Associated families</title>
4347 As expected, an import or export item of the
4348 form <literal>C(..)</literal> denotes all of the class' methods and
4349 associated types. However, when associated types are explicitly
4350 listed as subitems of a class, we need some new syntax, as uppercase
4351 identifiers as subitems are usually data constructors, not type
4352 constructors. To clarify that we denote types here, each associated
4353 type name needs to be prefixed by the keyword <literal>type</literal>.
4354 So for example, when explicitly listing the components of
4355 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4356 GMap, empty, lookup, insert)</literal>.
4360 <sect4 id="data-family-impexp-examples">
4361 <title>Examples</title>
4363 Assuming our running <literal>GMapKey</literal> class example, let us
4364 look at some export lists and their meaning:
4367 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4368 just the class name.</para>
4371 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4372 Exports the class, the associated type <literal>GMap</literal>
4374 functions <literal>empty</literal>, <literal>lookup</literal>,
4375 and <literal>insert</literal>. None of the data constructors is
4379 <para><literal>module GMap (GMapKey(..), GMap(..))
4380 where...</literal>: As before, but also exports all the data
4381 constructors <literal>GMapInt</literal>,
4382 <literal>GMapChar</literal>,
4383 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4384 and <literal>GMapUnit</literal>.</para>
4387 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4388 GMap(..)) where...</literal>: As before.</para>
4391 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4392 where...</literal>: As before.</para>
4397 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4398 both the class <literal>GMapKey</literal> as well as its associated
4399 type <literal>GMap</literal>. However, you cannot
4400 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4401 sub-component specifications cannot be nested. To
4402 specify <literal>GMap</literal>'s data constructors, you have to list
4407 <sect4 id="data-family-impexp-instances">
4408 <title>Instances</title>
4410 Family instances are implicitly exported, just like class instances.
4411 However, this applies only to the heads of instances, not to the data
4412 constructors an instance defines.
4420 <sect2 id="synonym-families">
4421 <title>Synonym families</title>
4424 Type families appear in two flavours: (1) they can be defined on the
4425 toplevel or (2) they can appear inside type classes (in which case they
4426 are known as associated type synonyms). The former is the more general
4427 variant, as it lacks the requirement for the type-indexes to coincide with
4428 the class parameters. However, the latter can lead to more clearly
4429 structured code and compiler warnings if some type instances were -
4430 possibly accidentally - omitted. In the following, we always discuss the
4431 general toplevel form first and then cover the additional constraints
4432 placed on associated types.
4435 <sect3 id="type-family-declarations">
4436 <title>Type family declarations</title>
4439 Indexed type families are introduced by a signature, such as
4441 type family Elem c :: *
4443 The special <literal>family</literal> distinguishes family from standard
4444 type declarations. The result kind annotation is optional and, as
4445 usual, defaults to <literal>*</literal> if omitted. An example is
4449 Parameters can also be given explicit kind signatures if needed. We
4450 call the number of parameters in a type family declaration, the family's
4451 arity, and all applications of a type family must be fully saturated
4452 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4453 and it implies that the kind of a type family is not sufficient to
4454 determine a family's arity, and hence in general, also insufficient to
4455 determine whether a type family application is well formed. As an
4456 example, consider the following declaration:
4458 type family F a b :: * -> * -- F's arity is 2,
4459 -- although its overall kind is * -> * -> * -> *
4461 Given this declaration the following are examples of well-formed and
4464 F Char [Int] -- OK! Kind: * -> *
4465 F Char [Int] Bool -- OK! Kind: *
4466 F IO Bool -- WRONG: kind mismatch in the first argument
4467 F Bool -- WRONG: unsaturated application
4471 <sect4 id="assoc-type-family-decl">
4472 <title>Associated type family declarations</title>
4474 When a type family is declared as part of a type class, we drop
4475 the <literal>family</literal> special. The <literal>Elem</literal>
4476 declaration takes the following form
4478 class Collects ce where
4482 The argument names of the type family must be class parameters. Each
4483 class parameter may only be used at most once per associated type, but
4484 some may be omitted and they may be in an order other than in the
4485 class head. Hence, the following contrived example is admissible:
4490 These rules are exactly as for associated data families.
4495 <sect3 id="type-instance-declarations">
4496 <title>Type instance declarations</title>
4498 Instance declarations of type families are very similar to standard type
4499 synonym declarations. The only two differences are that the
4500 keyword <literal>type</literal> is followed
4501 by <literal>instance</literal> and that some or all of the type
4502 arguments can be non-variable types, but may not contain forall types or
4503 type synonym families. However, data families are generally allowed, and
4504 type synonyms are allowed as long as they are fully applied and expand
4505 to a type that is admissible - these are the exact same requirements as
4506 for data instances. For example, the <literal>[e]</literal> instance
4507 for <literal>Elem</literal> is
4509 type instance Elem [e] = e
4513 Type family instance declarations are only legitimate when an
4514 appropriate family declaration is in scope - just like class instances
4515 require the class declaration to be visible. Moreover, each instance
4516 declaration has to conform to the kind determined by its family
4517 declaration, and the number of type parameters in an instance
4518 declaration must match the number of type parameters in the family
4519 declaration. Finally, the right-hand side of a type instance must be a
4520 monotype (i.e., it may not include foralls) and after the expansion of
4521 all saturated vanilla type synonyms, no synonyms, except family synonyms
4522 may remain. Here are some examples of admissible and illegal type
4525 type family F a :: *
4526 type instance F [Int] = Int -- OK!
4527 type instance F String = Char -- OK!
4528 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4529 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4530 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4532 type family G a b :: * -> *
4533 type instance G Int = (,) -- WRONG: must be two type parameters
4534 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4538 <sect4 id="assoc-type-instance">
4539 <title>Associated type instance declarations</title>
4541 When an associated family instance is declared within a type class
4542 instance, we drop the <literal>instance</literal> keyword in the family
4543 instance. So, the <literal>[e]</literal> instance
4544 for <literal>Elem</literal> becomes:
4546 instance (Eq (Elem [e])) => Collects ([e]) where
4550 The most important point about associated family instances is that the
4551 type indexes corresponding to class parameters must be identical to the
4552 type given in the instance head; here this is <literal>[e]</literal>,
4553 which coincides with the only class parameter.
4556 Instances for an associated family can only appear as part of instances
4557 declarations of the class in which the family was declared - just as
4558 with the equations of the methods of a class. Also in correspondence to
4559 how methods are handled, declarations of associated types can be omitted
4560 in class instances. If an associated family instance is omitted, the
4561 corresponding instance type is not inhabited; i.e., only diverging
4562 expressions, such as <literal>undefined</literal>, can assume the type.
4566 <sect4 id="type-family-overlap">
4567 <title>Overlap of type synonym instances</title>
4569 The instance declarations of a type family used in a single program
4570 may only overlap if the right-hand sides of the overlapping instances
4571 coincide for the overlapping types. More formally, two instance
4572 declarations overlap if there is a substitution that makes the
4573 left-hand sides of the instances syntactically the same. Whenever
4574 that is the case, the right-hand sides of the instances must also be
4575 syntactically equal under the same substitution. This condition is
4576 independent of whether the type family is associated or not, and it is
4577 not only a matter of consistency, but one of type safety.
4580 Here are two example to illustrate the condition under which overlap
4583 type instance F (a, Int) = [a]
4584 type instance F (Int, b) = [b] -- overlap permitted
4586 type instance G (a, Int) = [a]
4587 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4592 <sect4 id="type-family-decidability">
4593 <title>Decidability of type synonym instances</title>
4595 In order to guarantee that type inference in the presence of type
4596 families decidable, we need to place a number of additional
4597 restrictions on the formation of type instance declarations (c.f.,
4598 Definition 5 (Relaxed Conditions) of “<ulink
4599 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4600 Checking with Open Type Functions</ulink>”). Instance
4601 declarations have the general form
4603 type instance F t1 .. tn = t
4605 where we require that for every type family application <literal>(G s1
4606 .. sm)</literal> in <literal>t</literal>,
4609 <para><literal>s1 .. sm</literal> do not contain any type family
4610 constructors,</para>
4613 <para>the total number of symbols (data type constructors and type
4614 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4615 in <literal>t1 .. tn</literal>, and</para>
4618 <para>for every type
4619 variable <literal>a</literal>, <literal>a</literal> occurs
4620 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4621 .. tn</literal>.</para>
4624 These restrictions are easily verified and ensure termination of type
4625 inference. However, they are not sufficient to guarantee completeness
4626 of type inference in the presence of, so called, ''loopy equalities'',
4627 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4628 a type variable is underneath a family application and data
4629 constructor application - see the above mentioned paper for details.
4632 If the option <option>-XUndecidableInstances</option> is passed to the
4633 compiler, the above restrictions are not enforced and it is on the
4634 programmer to ensure termination of the normalisation of type families
4635 during type inference.
4640 <sect3 id-="equality-constraints">
4641 <title>Equality constraints</title>
4643 Type context can include equality constraints of the form <literal>t1 ~
4644 t2</literal>, which denote that the types <literal>t1</literal>
4645 and <literal>t2</literal> need to be the same. In the presence of type
4646 families, whether two types are equal cannot generally be decided
4647 locally. Hence, the contexts of function signatures may include
4648 equality constraints, as in the following example:
4650 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4652 where we require that the element type of <literal>c1</literal>
4653 and <literal>c2</literal> are the same. In general, the
4654 types <literal>t1</literal> and <literal>t2</literal> of an equality
4655 constraint may be arbitrary monotypes; i.e., they may not contain any
4656 quantifiers, independent of whether higher-rank types are otherwise
4660 Equality constraints can also appear in class and instance contexts.
4661 The former enable a simple translation of programs using functional
4662 dependencies into programs using family synonyms instead. The general
4663 idea is to rewrite a class declaration of the form
4665 class C a b | a -> b
4669 class (F a ~ b) => C a b where
4672 That is, we represent every functional dependency (FD) <literal>a1 .. an
4673 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4674 superclass context equality <literal>F a1 .. an ~ b</literal>,
4675 essentially giving a name to the functional dependency. In class
4676 instances, we define the type instances of FD families in accordance
4677 with the class head. Method signatures are not affected by that
4681 NB: Equalities in superclass contexts are not fully implemented in
4686 <sect3 id-="ty-fams-in-instances">
4687 <title>Type families and instance declarations</title>
4688 <para>Type families require us to extend the rules for
4689 the form of instance heads, which are given
4690 in <xref linkend="flexible-instance-head"/>.
4693 <listitem><para>Data type families may appear in an instance head</para></listitem>
4694 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4696 The reason for the latter restriction is that there is no way to check for. Consider
4699 type instance F Bool = Int
4706 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4707 The situation is especially bad because the type instance for <literal>F Bool</literal>
4708 might be in another module, or even in a module that is not yet written.
4715 <sect1 id="other-type-extensions">
4716 <title>Other type system extensions</title>
4718 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4720 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4721 is used, the keyword <literal>forall</literal>
4722 allows us to say exactly what this means. For example:
4730 g :: forall b. (b -> b)
4732 The two are treated identically.
4735 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4736 a type variable any more!
4741 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4743 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4744 that the type-class constraints in a type signature must have the
4745 form <emphasis>(class type-variable)</emphasis> or
4746 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4747 With <option>-XFlexibleContexts</option>
4748 these type signatures are perfectly OK
4751 g :: Ord (T a ()) => ...
4753 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4754 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4755 (<xref linkend="instance-rules"/>).
4759 GHC imposes the following restrictions on the constraints in a type signature.
4763 forall tv1..tvn (c1, ...,cn) => type
4766 (Here, we write the "foralls" explicitly, although the Haskell source
4767 language omits them; in Haskell 98, all the free type variables of an
4768 explicit source-language type signature are universally quantified,
4769 except for the class type variables in a class declaration. However,
4770 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4779 <emphasis>Each universally quantified type variable
4780 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4782 A type variable <literal>a</literal> is "reachable" if it appears
4783 in the same constraint as either a type variable free in
4784 <literal>type</literal>, or another reachable type variable.
4785 A value with a type that does not obey
4786 this reachability restriction cannot be used without introducing
4787 ambiguity; that is why the type is rejected.
4788 Here, for example, is an illegal type:
4792 forall a. Eq a => Int
4796 When a value with this type was used, the constraint <literal>Eq tv</literal>
4797 would be introduced where <literal>tv</literal> is a fresh type variable, and
4798 (in the dictionary-translation implementation) the value would be
4799 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4800 can never know which instance of <literal>Eq</literal> to use because we never
4801 get any more information about <literal>tv</literal>.
4805 that the reachability condition is weaker than saying that <literal>a</literal> is
4806 functionally dependent on a type variable free in
4807 <literal>type</literal> (see <xref
4808 linkend="functional-dependencies"/>). The reason for this is there
4809 might be a "hidden" dependency, in a superclass perhaps. So
4810 "reachable" is a conservative approximation to "functionally dependent".
4811 For example, consider:
4813 class C a b | a -> b where ...
4814 class C a b => D a b where ...
4815 f :: forall a b. D a b => a -> a
4817 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4818 but that is not immediately apparent from <literal>f</literal>'s type.
4824 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4825 universally quantified type variables <literal>tvi</literal></emphasis>.
4827 For example, this type is OK because <literal>C a b</literal> mentions the
4828 universally quantified type variable <literal>b</literal>:
4832 forall a. C a b => burble
4836 The next type is illegal because the constraint <literal>Eq b</literal> does not
4837 mention <literal>a</literal>:
4841 forall a. Eq b => burble
4845 The reason for this restriction is milder than the other one. The
4846 excluded types are never useful or necessary (because the offending
4847 context doesn't need to be witnessed at this point; it can be floated
4848 out). Furthermore, floating them out increases sharing. Lastly,
4849 excluding them is a conservative choice; it leaves a patch of
4850 territory free in case we need it later.
4861 <sect2 id="implicit-parameters">
4862 <title>Implicit parameters</title>
4864 <para> Implicit parameters are implemented as described in
4865 "Implicit parameters: dynamic scoping with static types",
4866 J Lewis, MB Shields, E Meijer, J Launchbury,
4867 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4871 <para>(Most of the following, still rather incomplete, documentation is
4872 due to Jeff Lewis.)</para>
4874 <para>Implicit parameter support is enabled with the option
4875 <option>-XImplicitParams</option>.</para>
4878 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4879 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4880 context. In Haskell, all variables are statically bound. Dynamic
4881 binding of variables is a notion that goes back to Lisp, but was later
4882 discarded in more modern incarnations, such as Scheme. Dynamic binding
4883 can be very confusing in an untyped language, and unfortunately, typed
4884 languages, in particular Hindley-Milner typed languages like Haskell,
4885 only support static scoping of variables.
4888 However, by a simple extension to the type class system of Haskell, we
4889 can support dynamic binding. Basically, we express the use of a
4890 dynamically bound variable as a constraint on the type. These
4891 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4892 function uses a dynamically-bound variable <literal>?x</literal>
4893 of type <literal>t'</literal>". For
4894 example, the following expresses the type of a sort function,
4895 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4897 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4899 The dynamic binding constraints are just a new form of predicate in the type class system.
4902 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4903 where <literal>x</literal> is
4904 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4905 Use of this construct also introduces a new
4906 dynamic-binding constraint in the type of the expression.
4907 For example, the following definition
4908 shows how we can define an implicitly parameterized sort function in
4909 terms of an explicitly parameterized <literal>sortBy</literal> function:
4911 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4913 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4919 <title>Implicit-parameter type constraints</title>
4921 Dynamic binding constraints behave just like other type class
4922 constraints in that they are automatically propagated. Thus, when a
4923 function is used, its implicit parameters are inherited by the
4924 function that called it. For example, our <literal>sort</literal> function might be used
4925 to pick out the least value in a list:
4927 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4928 least xs = head (sort xs)
4930 Without lifting a finger, the <literal>?cmp</literal> parameter is
4931 propagated to become a parameter of <literal>least</literal> as well. With explicit
4932 parameters, the default is that parameters must always be explicit
4933 propagated. With implicit parameters, the default is to always
4937 An implicit-parameter type constraint differs from other type class constraints in the
4938 following way: All uses of a particular implicit parameter must have
4939 the same type. This means that the type of <literal>(?x, ?x)</literal>
4940 is <literal>(?x::a) => (a,a)</literal>, and not
4941 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4945 <para> You can't have an implicit parameter in the context of a class or instance
4946 declaration. For example, both these declarations are illegal:
4948 class (?x::Int) => C a where ...
4949 instance (?x::a) => Foo [a] where ...
4951 Reason: exactly which implicit parameter you pick up depends on exactly where
4952 you invoke a function. But the ``invocation'' of instance declarations is done
4953 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4954 Easiest thing is to outlaw the offending types.</para>
4956 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4958 f :: (?x :: [a]) => Int -> Int
4961 g :: (Read a, Show a) => String -> String
4964 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4965 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4966 quite unambiguous, and fixes the type <literal>a</literal>.
4971 <title>Implicit-parameter bindings</title>
4974 An implicit parameter is <emphasis>bound</emphasis> using the standard
4975 <literal>let</literal> or <literal>where</literal> binding forms.
4976 For example, we define the <literal>min</literal> function by binding
4977 <literal>cmp</literal>.
4980 min = let ?cmp = (<=) in least
4984 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4985 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4986 (including in a list comprehension, or do-notation, or pattern guards),
4987 or a <literal>where</literal> clause.
4988 Note the following points:
4991 An implicit-parameter binding group must be a
4992 collection of simple bindings to implicit-style variables (no
4993 function-style bindings, and no type signatures); these bindings are
4994 neither polymorphic or recursive.
4997 You may not mix implicit-parameter bindings with ordinary bindings in a
4998 single <literal>let</literal>
4999 expression; use two nested <literal>let</literal>s instead.
5000 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5004 You may put multiple implicit-parameter bindings in a
5005 single binding group; but they are <emphasis>not</emphasis> treated
5006 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5007 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5008 parameter. The bindings are not nested, and may be re-ordered without changing
5009 the meaning of the program.
5010 For example, consider:
5012 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5014 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5015 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5017 f :: (?x::Int) => Int -> Int
5025 <sect3><title>Implicit parameters and polymorphic recursion</title>
5028 Consider these two definitions:
5031 len1 xs = let ?acc = 0 in len_acc1 xs
5034 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5039 len2 xs = let ?acc = 0 in len_acc2 xs
5041 len_acc2 :: (?acc :: Int) => [a] -> Int
5043 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5045 The only difference between the two groups is that in the second group
5046 <literal>len_acc</literal> is given a type signature.
5047 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5048 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5049 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5050 has a type signature, the recursive call is made to the
5051 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5052 as an implicit parameter. So we get the following results in GHCi:
5059 Adding a type signature dramatically changes the result! This is a rather
5060 counter-intuitive phenomenon, worth watching out for.
5064 <sect3><title>Implicit parameters and monomorphism</title>
5066 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5067 Haskell Report) to implicit parameters. For example, consider:
5075 Since the binding for <literal>y</literal> falls under the Monomorphism
5076 Restriction it is not generalised, so the type of <literal>y</literal> is
5077 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5078 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5079 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5080 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5081 <literal>y</literal> in the body of the <literal>let</literal> will see the
5082 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5083 <literal>14</literal>.
5088 <!-- ======================= COMMENTED OUT ========================
5090 We intend to remove linear implicit parameters, so I'm at least removing
5091 them from the 6.6 user manual
5093 <sect2 id="linear-implicit-parameters">
5094 <title>Linear implicit parameters</title>
5096 Linear implicit parameters are an idea developed by Koen Claessen,
5097 Mark Shields, and Simon PJ. They address the long-standing
5098 problem that monads seem over-kill for certain sorts of problem, notably:
5101 <listitem> <para> distributing a supply of unique names </para> </listitem>
5102 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5103 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5107 Linear implicit parameters are just like ordinary implicit parameters,
5108 except that they are "linear"; that is, they cannot be copied, and
5109 must be explicitly "split" instead. Linear implicit parameters are
5110 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5111 (The '/' in the '%' suggests the split!)
5116 import GHC.Exts( Splittable )
5118 data NameSupply = ...
5120 splitNS :: NameSupply -> (NameSupply, NameSupply)
5121 newName :: NameSupply -> Name
5123 instance Splittable NameSupply where
5127 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5128 f env (Lam x e) = Lam x' (f env e)
5131 env' = extend env x x'
5132 ...more equations for f...
5134 Notice that the implicit parameter %ns is consumed
5136 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5137 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5141 So the translation done by the type checker makes
5142 the parameter explicit:
5144 f :: NameSupply -> Env -> Expr -> Expr
5145 f ns env (Lam x e) = Lam x' (f ns1 env e)
5147 (ns1,ns2) = splitNS ns
5149 env = extend env x x'
5151 Notice the call to 'split' introduced by the type checker.
5152 How did it know to use 'splitNS'? Because what it really did
5153 was to introduce a call to the overloaded function 'split',
5154 defined by the class <literal>Splittable</literal>:
5156 class Splittable a where
5159 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5160 split for name supplies. But we can simply write
5166 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5168 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5169 <literal>GHC.Exts</literal>.
5174 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5175 are entirely distinct implicit parameters: you
5176 can use them together and they won't interfere with each other. </para>
5179 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5181 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5182 in the context of a class or instance declaration. </para></listitem>
5186 <sect3><title>Warnings</title>
5189 The monomorphism restriction is even more important than usual.
5190 Consider the example above:
5192 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5193 f env (Lam x e) = Lam x' (f env e)
5196 env' = extend env x x'
5198 If we replaced the two occurrences of x' by (newName %ns), which is
5199 usually a harmless thing to do, we get:
5201 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5202 f env (Lam x e) = Lam (newName %ns) (f env e)
5204 env' = extend env x (newName %ns)
5206 But now the name supply is consumed in <emphasis>three</emphasis> places
5207 (the two calls to newName,and the recursive call to f), so
5208 the result is utterly different. Urk! We don't even have
5212 Well, this is an experimental change. With implicit
5213 parameters we have already lost beta reduction anyway, and
5214 (as John Launchbury puts it) we can't sensibly reason about
5215 Haskell programs without knowing their typing.
5220 <sect3><title>Recursive functions</title>
5221 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5224 foo :: %x::T => Int -> [Int]
5226 foo n = %x : foo (n-1)
5228 where T is some type in class Splittable.</para>
5230 Do you get a list of all the same T's or all different T's
5231 (assuming that split gives two distinct T's back)?
5233 If you supply the type signature, taking advantage of polymorphic
5234 recursion, you get what you'd probably expect. Here's the
5235 translated term, where the implicit param is made explicit:
5238 foo x n = let (x1,x2) = split x
5239 in x1 : foo x2 (n-1)
5241 But if you don't supply a type signature, GHC uses the Hindley
5242 Milner trick of using a single monomorphic instance of the function
5243 for the recursive calls. That is what makes Hindley Milner type inference
5244 work. So the translation becomes
5248 foom n = x : foom (n-1)
5252 Result: 'x' is not split, and you get a list of identical T's. So the
5253 semantics of the program depends on whether or not foo has a type signature.
5256 You may say that this is a good reason to dislike linear implicit parameters
5257 and you'd be right. That is why they are an experimental feature.
5263 ================ END OF Linear Implicit Parameters commented out -->
5265 <sect2 id="kinding">
5266 <title>Explicitly-kinded quantification</title>
5269 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5270 to give the kind explicitly as (machine-checked) documentation,
5271 just as it is nice to give a type signature for a function. On some occasions,
5272 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5273 John Hughes had to define the data type:
5275 data Set cxt a = Set [a]
5276 | Unused (cxt a -> ())
5278 The only use for the <literal>Unused</literal> constructor was to force the correct
5279 kind for the type variable <literal>cxt</literal>.
5282 GHC now instead allows you to specify the kind of a type variable directly, wherever
5283 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5286 This flag enables kind signatures in the following places:
5288 <listitem><para><literal>data</literal> declarations:
5290 data Set (cxt :: * -> *) a = Set [a]
5291 </screen></para></listitem>
5292 <listitem><para><literal>type</literal> declarations:
5294 type T (f :: * -> *) = f Int
5295 </screen></para></listitem>
5296 <listitem><para><literal>class</literal> declarations:
5298 class (Eq a) => C (f :: * -> *) a where ...
5299 </screen></para></listitem>
5300 <listitem><para><literal>forall</literal>'s in type signatures:
5302 f :: forall (cxt :: * -> *). Set cxt Int
5303 </screen></para></listitem>
5308 The parentheses are required. Some of the spaces are required too, to
5309 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5310 will get a parse error, because "<literal>::*->*</literal>" is a
5311 single lexeme in Haskell.
5315 As part of the same extension, you can put kind annotations in types
5318 f :: (Int :: *) -> Int
5319 g :: forall a. a -> (a :: *)
5323 atype ::= '(' ctype '::' kind ')
5325 The parentheses are required.
5330 <sect2 id="universal-quantification">
5331 <title>Arbitrary-rank polymorphism
5335 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5336 explicit universal quantification in
5338 For example, all the following types are legal:
5340 f1 :: forall a b. a -> b -> a
5341 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5343 f2 :: (forall a. a->a) -> Int -> Int
5344 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5346 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5348 f4 :: Int -> (forall a. a -> a)
5350 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5351 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5352 The <literal>forall</literal> makes explicit the universal quantification that
5353 is implicitly added by Haskell.
5356 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5357 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5358 shows, the polymorphic type on the left of the function arrow can be overloaded.
5361 The function <literal>f3</literal> has a rank-3 type;
5362 it has rank-2 types on the left of a function arrow.
5365 GHC has three flags to control higher-rank types:
5368 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5371 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5374 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5375 That is, you can nest <literal>forall</literal>s
5376 arbitrarily deep in function arrows.
5377 In particular, a forall-type (also called a "type scheme"),
5378 including an operational type class context, is legal:
5380 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5381 of a function arrow </para> </listitem>
5382 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5383 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5384 field type signatures.</para> </listitem>
5385 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5386 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5398 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5399 the types of the constructor arguments. Here are several examples:
5405 data T a = T1 (forall b. b -> b -> b) a
5407 data MonadT m = MkMonad { return :: forall a. a -> m a,
5408 bind :: forall a b. m a -> (a -> m b) -> m b
5411 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5417 The constructors have rank-2 types:
5423 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5424 MkMonad :: forall m. (forall a. a -> m a)
5425 -> (forall a b. m a -> (a -> m b) -> m b)
5427 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5433 Notice that you don't need to use a <literal>forall</literal> if there's an
5434 explicit context. For example in the first argument of the
5435 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5436 prefixed to the argument type. The implicit <literal>forall</literal>
5437 quantifies all type variables that are not already in scope, and are
5438 mentioned in the type quantified over.
5442 As for type signatures, implicit quantification happens for non-overloaded
5443 types too. So if you write this:
5446 data T a = MkT (Either a b) (b -> b)
5449 it's just as if you had written this:
5452 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5455 That is, since the type variable <literal>b</literal> isn't in scope, it's
5456 implicitly universally quantified. (Arguably, it would be better
5457 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5458 where that is what is wanted. Feedback welcomed.)
5462 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5463 the constructor to suitable values, just as usual. For example,
5474 a3 = MkSwizzle reverse
5477 a4 = let r x = Just x
5484 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5485 mkTs f x y = [T1 f x, T1 f y]
5491 The type of the argument can, as usual, be more general than the type
5492 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5493 does not need the <literal>Ord</literal> constraint.)
5497 When you use pattern matching, the bound variables may now have
5498 polymorphic types. For example:
5504 f :: T a -> a -> (a, Char)
5505 f (T1 w k) x = (w k x, w 'c' 'd')
5507 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5508 g (MkSwizzle s) xs f = s (map f (s xs))
5510 h :: MonadT m -> [m a] -> m [a]
5511 h m [] = return m []
5512 h m (x:xs) = bind m x $ \y ->
5513 bind m (h m xs) $ \ys ->
5520 In the function <function>h</function> we use the record selectors <literal>return</literal>
5521 and <literal>bind</literal> to extract the polymorphic bind and return functions
5522 from the <literal>MonadT</literal> data structure, rather than using pattern
5528 <title>Type inference</title>
5531 In general, type inference for arbitrary-rank types is undecidable.
5532 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5533 to get a decidable algorithm by requiring some help from the programmer.
5534 We do not yet have a formal specification of "some help" but the rule is this:
5537 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5538 provides an explicit polymorphic type for x, or GHC's type inference will assume
5539 that x's type has no foralls in it</emphasis>.
5542 What does it mean to "provide" an explicit type for x? You can do that by
5543 giving a type signature for x directly, using a pattern type signature
5544 (<xref linkend="scoped-type-variables"/>), thus:
5546 \ f :: (forall a. a->a) -> (f True, f 'c')
5548 Alternatively, you can give a type signature to the enclosing
5549 context, which GHC can "push down" to find the type for the variable:
5551 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5553 Here the type signature on the expression can be pushed inwards
5554 to give a type signature for f. Similarly, and more commonly,
5555 one can give a type signature for the function itself:
5557 h :: (forall a. a->a) -> (Bool,Char)
5558 h f = (f True, f 'c')
5560 You don't need to give a type signature if the lambda bound variable
5561 is a constructor argument. Here is an example we saw earlier:
5563 f :: T a -> a -> (a, Char)
5564 f (T1 w k) x = (w k x, w 'c' 'd')
5566 Here we do not need to give a type signature to <literal>w</literal>, because
5567 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5574 <sect3 id="implicit-quant">
5575 <title>Implicit quantification</title>
5578 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5579 user-written types, if and only if there is no explicit <literal>forall</literal>,
5580 GHC finds all the type variables mentioned in the type that are not already
5581 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5585 f :: forall a. a -> a
5592 h :: forall b. a -> b -> b
5598 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5601 f :: (a -> a) -> Int
5603 f :: forall a. (a -> a) -> Int
5605 f :: (forall a. a -> a) -> Int
5608 g :: (Ord a => a -> a) -> Int
5609 -- MEANS the illegal type
5610 g :: forall a. (Ord a => a -> a) -> Int
5612 g :: (forall a. Ord a => a -> a) -> Int
5614 The latter produces an illegal type, which you might think is silly,
5615 but at least the rule is simple. If you want the latter type, you
5616 can write your for-alls explicitly. Indeed, doing so is strongly advised
5623 <sect2 id="impredicative-polymorphism">
5624 <title>Impredicative polymorphism
5626 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5627 enabled with <option>-XImpredicativeTypes</option>.
5629 that you can call a polymorphic function at a polymorphic type, and
5630 parameterise data structures over polymorphic types. For example:
5632 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5633 f (Just g) = Just (g [3], g "hello")
5636 Notice here that the <literal>Maybe</literal> type is parameterised by the
5637 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5640 <para>The technical details of this extension are described in the paper
5641 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5642 type inference for higher-rank types and impredicativity</ulink>,
5643 which appeared at ICFP 2006.
5647 <sect2 id="scoped-type-variables">
5648 <title>Lexically scoped type variables
5652 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5653 which some type signatures are simply impossible to write. For example:
5655 f :: forall a. [a] -> [a]
5661 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5662 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5663 The type variables bound by a <literal>forall</literal> scope over
5664 the entire definition of the accompanying value declaration.
5665 In this example, the type variable <literal>a</literal> scopes over the whole
5666 definition of <literal>f</literal>, including over
5667 the type signature for <varname>ys</varname>.
5668 In Haskell 98 it is not possible to declare
5669 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5670 it becomes possible to do so.
5672 <para>Lexically-scoped type variables are enabled by
5673 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5675 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5676 variables work, compared to earlier releases. Read this section
5680 <title>Overview</title>
5682 <para>The design follows the following principles
5684 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5685 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5686 design.)</para></listitem>
5687 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5688 type variables. This means that every programmer-written type signature
5689 (including one that contains free scoped type variables) denotes a
5690 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5691 checker, and no inference is involved.</para></listitem>
5692 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5693 changing the program.</para></listitem>
5697 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5699 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5700 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5701 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5702 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5706 In Haskell, a programmer-written type signature is implicitly quantified over
5707 its free type variables (<ulink
5708 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5710 of the Haskell Report).
5711 Lexically scoped type variables affect this implicit quantification rules
5712 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5713 quantified. For example, if type variable <literal>a</literal> is in scope,
5716 (e :: a -> a) means (e :: a -> a)
5717 (e :: b -> b) means (e :: forall b. b->b)
5718 (e :: a -> b) means (e :: forall b. a->b)
5726 <sect3 id="decl-type-sigs">
5727 <title>Declaration type signatures</title>
5728 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5729 quantification (using <literal>forall</literal>) brings into scope the
5730 explicitly-quantified
5731 type variables, in the definition of the named function. For example:
5733 f :: forall a. [a] -> [a]
5734 f (x:xs) = xs ++ [ x :: a ]
5736 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5737 the definition of "<literal>f</literal>".
5739 <para>This only happens if:
5741 <listitem><para> The quantification in <literal>f</literal>'s type
5742 signature is explicit. For example:
5745 g (x:xs) = xs ++ [ x :: a ]
5747 This program will be rejected, because "<literal>a</literal>" does not scope
5748 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5749 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5750 quantification rules.
5752 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5753 not a pattern binding.
5756 f1 :: forall a. [a] -> [a]
5757 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5759 f2 :: forall a. [a] -> [a]
5760 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5762 f3 :: forall a. [a] -> [a]
5763 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5765 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5766 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5767 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5768 the type signature brings <literal>a</literal> into scope.
5774 <sect3 id="exp-type-sigs">
5775 <title>Expression type signatures</title>
5777 <para>An expression type signature that has <emphasis>explicit</emphasis>
5778 quantification (using <literal>forall</literal>) brings into scope the
5779 explicitly-quantified
5780 type variables, in the annotated expression. For example:
5782 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5784 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5785 type variable <literal>s</literal> into scope, in the annotated expression
5786 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5791 <sect3 id="pattern-type-sigs">
5792 <title>Pattern type signatures</title>
5794 A type signature may occur in any pattern; this is a <emphasis>pattern type
5795 signature</emphasis>.
5798 -- f and g assume that 'a' is already in scope
5799 f = \(x::Int, y::a) -> x
5801 h ((x,y) :: (Int,Bool)) = (y,x)
5803 In the case where all the type variables in the pattern type signature are
5804 already in scope (i.e. bound by the enclosing context), matters are simple: the
5805 signature simply constrains the type of the pattern in the obvious way.
5808 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5809 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5810 that are already in scope. For example:
5812 f :: forall a. [a] -> (Int, [a])
5815 (ys::[a], n) = (reverse xs, length xs) -- OK
5816 zs::[a] = xs ++ ys -- OK
5818 Just (v::b) = ... -- Not OK; b is not in scope
5820 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5821 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5825 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5826 type signature may mention a type variable that is not in scope; in this case,
5827 <emphasis>the signature brings that type variable into scope</emphasis>.
5828 This is particularly important for existential data constructors. For example:
5830 data T = forall a. MkT [a]
5833 k (MkT [t::a]) = MkT t3
5837 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5838 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5839 because it is bound by the pattern match. GHC's rule is that in this situation
5840 (and only then), a pattern type signature can mention a type variable that is
5841 not already in scope; the effect is to bring it into scope, standing for the
5842 existentially-bound type variable.
5845 When a pattern type signature binds a type variable in this way, GHC insists that the
5846 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5847 This means that any user-written type signature always stands for a completely known type.
5850 If all this seems a little odd, we think so too. But we must have
5851 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5852 could not name existentially-bound type variables in subsequent type signatures.
5855 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5856 signature is allowed to mention a lexical variable that is not already in
5858 For example, both <literal>f</literal> and <literal>g</literal> would be
5859 illegal if <literal>a</literal> was not already in scope.
5865 <!-- ==================== Commented out part about result type signatures
5867 <sect3 id="result-type-sigs">
5868 <title>Result type signatures</title>
5871 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5874 {- f assumes that 'a' is already in scope -}
5875 f x y :: [a] = [x,y,x]
5877 g = \ x :: [Int] -> [3,4]
5879 h :: forall a. [a] -> a
5883 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5884 the result of the function. Similarly, the body of the lambda in the RHS of
5885 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5886 alternative in <literal>h</literal> is <literal>a</literal>.
5888 <para> A result type signature never brings new type variables into scope.</para>
5890 There are a couple of syntactic wrinkles. First, notice that all three
5891 examples would parse quite differently with parentheses:
5893 {- f assumes that 'a' is already in scope -}
5894 f x (y :: [a]) = [x,y,x]
5896 g = \ (x :: [Int]) -> [3,4]
5898 h :: forall a. [a] -> a
5902 Now the signature is on the <emphasis>pattern</emphasis>; and
5903 <literal>h</literal> would certainly be ill-typed (since the pattern
5904 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5906 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5907 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5908 token or a parenthesised type of some sort). To see why,
5909 consider how one would parse this:
5918 <sect3 id="cls-inst-scoped-tyvars">
5919 <title>Class and instance declarations</title>
5922 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5923 scope over the methods defined in the <literal>where</literal> part. For example:
5941 <sect2 id="typing-binds">
5942 <title>Generalised typing of mutually recursive bindings</title>
5945 The Haskell Report specifies that a group of bindings (at top level, or in a
5946 <literal>let</literal> or <literal>where</literal>) should be sorted into
5947 strongly-connected components, and then type-checked in dependency order
5948 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5949 Report, Section 4.5.1</ulink>).
5950 As each group is type-checked, any binders of the group that
5952 an explicit type signature are put in the type environment with the specified
5954 and all others are monomorphic until the group is generalised
5955 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5958 <para>Following a suggestion of Mark Jones, in his paper
5959 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5961 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5963 <emphasis>the dependency analysis ignores references to variables that have an explicit
5964 type signature</emphasis>.
5965 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5966 typecheck. For example, consider:
5968 f :: Eq a => a -> Bool
5969 f x = (x == x) || g True || g "Yes"
5971 g y = (y <= y) || f True
5973 This is rejected by Haskell 98, but under Jones's scheme the definition for
5974 <literal>g</literal> is typechecked first, separately from that for
5975 <literal>f</literal>,
5976 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5977 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5978 type is generalised, to get
5980 g :: Ord a => a -> Bool
5982 Now, the definition for <literal>f</literal> is typechecked, with this type for
5983 <literal>g</literal> in the type environment.
5987 The same refined dependency analysis also allows the type signatures of
5988 mutually-recursive functions to have different contexts, something that is illegal in
5989 Haskell 98 (Section 4.5.2, last sentence). With
5990 <option>-XRelaxedPolyRec</option>
5991 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5992 type signatures; in practice this means that only variables bound by the same
5993 pattern binding must have the same context. For example, this is fine:
5995 f :: Eq a => a -> Bool
5996 f x = (x == x) || g True
5998 g :: Ord a => a -> Bool
5999 g y = (y <= y) || f True
6004 <sect2 id="mono-local-binds">
6005 <title>Monomorphic local bindings</title>
6007 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6008 The rationale is described in the paper
6009 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6012 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6013 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6014 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6015 If you supply a type signature, then the flag has no effect.
6020 <!-- ==================== End of type system extensions ================= -->
6022 <!-- ====================== TEMPLATE HASKELL ======================= -->
6024 <sect1 id="template-haskell">
6025 <title>Template Haskell</title>
6027 <para>Template Haskell allows you to do compile-time meta-programming in
6030 the main technical innovations is discussed in "<ulink
6031 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6032 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6035 There is a Wiki page about
6036 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6037 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6041 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6042 Haskell library reference material</ulink>
6043 (look for module <literal>Language.Haskell.TH</literal>).
6044 Many changes to the original design are described in
6045 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6046 Notes on Template Haskell version 2</ulink>.
6047 Not all of these changes are in GHC, however.
6050 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6051 as a worked example to help get you started.
6055 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6056 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6061 <title>Syntax</title>
6063 <para> Template Haskell has the following new syntactic
6064 constructions. You need to use the flag
6065 <option>-XTemplateHaskell</option>
6066 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6067 </indexterm>to switch these syntactic extensions on
6068 (<option>-XTemplateHaskell</option> is no longer implied by
6069 <option>-fglasgow-exts</option>).</para>
6073 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6074 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6075 There must be no space between the "$" and the identifier or parenthesis. This use
6076 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6077 of "." as an infix operator. If you want the infix operator, put spaces around it.
6079 <para> A splice can occur in place of
6081 <listitem><para> an expression; the spliced expression must
6082 have type <literal>Q Exp</literal></para></listitem>
6083 <listitem><para> an type; the spliced expression must
6084 have type <literal>Q Typ</literal></para></listitem>
6085 <listitem><para> a list of top-level declarations; the spliced expression
6086 must have type <literal>Q [Dec]</literal></para></listitem>
6088 Inside a splice you can can only call functions defined in imported modules,
6089 not functions defined elsewhere in the same module.</para></listitem>
6092 A expression quotation is written in Oxford brackets, thus:
6094 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
6095 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6096 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6097 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6098 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6099 the quotation has type <literal>Q Typ</literal>.</para></listitem>
6100 </itemizedlist></para></listitem>
6103 A quasi-quotation can appear in either a pattern context or an
6104 expression context and is also written in Oxford brackets:
6106 <listitem><para> <literal>[$<replaceable>varid</replaceable>| ... |]</literal>,
6107 where the "..." is an arbitrary string; a full description of the
6108 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6109 </itemizedlist></para></listitem>
6112 A name can be quoted with either one or two prefix single quotes:
6114 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6115 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6116 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6118 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6119 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6122 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6123 may also be given as an argument to the <literal>reify</literal> function.
6127 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6128 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6135 $(deriveStuff 'f) -- Uses the $(...) notation
6139 deriveStuff 'g -- Omits the $(...)
6143 This abbreviation makes top-level declaration slices quieter and less intimidating.
6148 (Compared to the original paper, there are many differences of detail.
6149 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6150 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6151 Pattern splices and quotations are not implemented.)
6155 <sect2> <title> Using Template Haskell </title>
6159 The data types and monadic constructor functions for Template Haskell are in the library
6160 <literal>Language.Haskell.THSyntax</literal>.
6164 You can only run a function at compile time if it is imported from another module. That is,
6165 you can't define a function in a module, and call it from within a splice in the same module.
6166 (It would make sense to do so, but it's hard to implement.)
6170 You can only run a function at compile time if it is imported
6171 from another module <emphasis>that is not part of a mutually-recursive group of modules
6172 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6173 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6174 splice is to be run.</para>
6176 For example, when compiling module A,
6177 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6178 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6182 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6185 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6186 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6187 compiles and runs a program, and then looks at the result. So it's important that
6188 the program it compiles produces results whose representations are identical to
6189 those of the compiler itself.
6193 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6194 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6199 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6200 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6201 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6208 -- Import our template "pr"
6209 import Printf ( pr )
6211 -- The splice operator $ takes the Haskell source code
6212 -- generated at compile time by "pr" and splices it into
6213 -- the argument of "putStrLn".
6214 main = putStrLn ( $(pr "Hello") )
6220 -- Skeletal printf from the paper.
6221 -- It needs to be in a separate module to the one where
6222 -- you intend to use it.
6224 -- Import some Template Haskell syntax
6225 import Language.Haskell.TH
6227 -- Describe a format string
6228 data Format = D | S | L String
6230 -- Parse a format string. This is left largely to you
6231 -- as we are here interested in building our first ever
6232 -- Template Haskell program and not in building printf.
6233 parse :: String -> [Format]
6236 -- Generate Haskell source code from a parsed representation
6237 -- of the format string. This code will be spliced into
6238 -- the module which calls "pr", at compile time.
6239 gen :: [Format] -> Q Exp
6240 gen [D] = [| \n -> show n |]
6241 gen [S] = [| \s -> s |]
6242 gen [L s] = stringE s
6244 -- Here we generate the Haskell code for the splice
6245 -- from an input format string.
6246 pr :: String -> Q Exp
6247 pr s = gen (parse s)
6250 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6253 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6256 <para>Run "main.exe" and here is your output:</para>
6266 <title>Using Template Haskell with Profiling</title>
6267 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6269 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6270 interpreter to run the splice expressions. The bytecode interpreter
6271 runs the compiled expression on top of the same runtime on which GHC
6272 itself is running; this means that the compiled code referred to by
6273 the interpreted expression must be compatible with this runtime, and
6274 in particular this means that object code that is compiled for
6275 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6276 expression, because profiled object code is only compatible with the
6277 profiling version of the runtime.</para>
6279 <para>This causes difficulties if you have a multi-module program
6280 containing Template Haskell code and you need to compile it for
6281 profiling, because GHC cannot load the profiled object code and use it
6282 when executing the splices. Fortunately GHC provides a workaround.
6283 The basic idea is to compile the program twice:</para>
6287 <para>Compile the program or library first the normal way, without
6288 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6291 <para>Then compile it again with <option>-prof</option>, and
6292 additionally use <option>-osuf
6293 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6294 to name the object files differently (you can choose any suffix
6295 that isn't the normal object suffix here). GHC will automatically
6296 load the object files built in the first step when executing splice
6297 expressions. If you omit the <option>-osuf</option> flag when
6298 building with <option>-prof</option> and Template Haskell is used,
6299 GHC will emit an error message. </para>
6304 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6305 <para>Quasi-quotation allows patterns and expressions to be written using
6306 programmer-defined concrete syntax; the motivation behind the extension and
6307 several examples are documented in
6308 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6309 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6310 2007). The example below shows how to write a quasiquoter for a simple
6311 expression language.</para>
6314 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6315 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6316 functions for quoting expressions and patterns, respectively. The first argument
6317 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6318 context of the quasi-quotation statement determines which of the two parsers is
6319 called: if the quasi-quotation occurs in an expression context, the expression
6320 parser is called, and if it occurs in a pattern context, the pattern parser is
6324 Note that in the example we make use of an antiquoted
6325 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6326 (this syntax for anti-quotation was defined by the parser's
6327 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6328 integer value argument of the constructor <literal>IntExpr</literal> when
6329 pattern matching. Please see the referenced paper for further details regarding
6330 anti-quotation as well as the description of a technique that uses SYB to
6331 leverage a single parser of type <literal>String -> a</literal> to generate both
6332 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6333 pattern parser that returns a value of type <literal>Q Pat</literal>.
6336 <para>In general, a quasi-quote has the form
6337 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6338 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6339 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6340 can be arbitrary, and may contain newlines.
6343 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6344 the example, <literal>expr</literal> cannot be defined
6345 in <literal>Main.hs</literal> where it is used, but must be imported.
6356 main = do { print $ eval [$expr|1 + 2|]
6358 { [$expr|'int:n|] -> print n
6367 import qualified Language.Haskell.TH as TH
6368 import Language.Haskell.TH.Quote
6370 data Expr = IntExpr Integer
6371 | AntiIntExpr String
6372 | BinopExpr BinOp Expr Expr
6374 deriving(Show, Typeable, Data)
6380 deriving(Show, Typeable, Data)
6382 eval :: Expr -> Integer
6383 eval (IntExpr n) = n
6384 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6391 expr = QuasiQuoter parseExprExp parseExprPat
6393 -- Parse an Expr, returning its representation as
6394 -- either a Q Exp or a Q Pat. See the referenced paper
6395 -- for how to use SYB to do this by writing a single
6396 -- parser of type String -> Expr instead of two
6397 -- separate parsers.
6399 parseExprExp :: String -> Q Exp
6402 parseExprPat :: String -> Q Pat
6406 <para>Now run the compiler:
6409 $ ghc --make -XQuasiQuotes Main.hs -o main
6412 <para>Run "main" and here is your output:</para>
6424 <!-- ===================== Arrow notation =================== -->
6426 <sect1 id="arrow-notation">
6427 <title>Arrow notation
6430 <para>Arrows are a generalization of monads introduced by John Hughes.
6431 For more details, see
6436 “Generalising Monads to Arrows”,
6437 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6438 pp67–111, May 2000.
6439 The paper that introduced arrows: a friendly introduction, motivated with
6440 programming examples.
6446 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6447 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6448 Introduced the notation described here.
6454 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6455 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6462 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6463 John Hughes, in <citetitle>5th International Summer School on
6464 Advanced Functional Programming</citetitle>,
6465 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6467 This paper includes another introduction to the notation,
6468 with practical examples.
6474 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6475 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6476 A terse enumeration of the formal rules used
6477 (extracted from comments in the source code).
6483 The arrows web page at
6484 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6489 With the <option>-XArrows</option> flag, GHC supports the arrow
6490 notation described in the second of these papers,
6491 translating it using combinators from the
6492 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6494 What follows is a brief introduction to the notation;
6495 it won't make much sense unless you've read Hughes's paper.
6498 <para>The extension adds a new kind of expression for defining arrows:
6500 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6501 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6503 where <literal>proc</literal> is a new keyword.
6504 The variables of the pattern are bound in the body of the
6505 <literal>proc</literal>-expression,
6506 which is a new sort of thing called a <firstterm>command</firstterm>.
6507 The syntax of commands is as follows:
6509 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6510 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6511 | <replaceable>cmd</replaceable><superscript>0</superscript>
6513 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6514 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6515 infix operators as for expressions, and
6517 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6518 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6519 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6520 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6521 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6522 | <replaceable>fcmd</replaceable>
6524 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6525 | ( <replaceable>cmd</replaceable> )
6526 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6528 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6529 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6530 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6531 | <replaceable>cmd</replaceable>
6533 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6534 except that the bodies are commands instead of expressions.
6538 Commands produce values, but (like monadic computations)
6539 may yield more than one value,
6540 or none, and may do other things as well.
6541 For the most part, familiarity with monadic notation is a good guide to
6543 However the values of expressions, even monadic ones,
6544 are determined by the values of the variables they contain;
6545 this is not necessarily the case for commands.
6549 A simple example of the new notation is the expression
6551 proc x -> f -< x+1
6553 We call this a <firstterm>procedure</firstterm> or
6554 <firstterm>arrow abstraction</firstterm>.
6555 As with a lambda expression, the variable <literal>x</literal>
6556 is a new variable bound within the <literal>proc</literal>-expression.
6557 It refers to the input to the arrow.
6558 In the above example, <literal>-<</literal> is not an identifier but an
6559 new reserved symbol used for building commands from an expression of arrow
6560 type and an expression to be fed as input to that arrow.
6561 (The weird look will make more sense later.)
6562 It may be read as analogue of application for arrows.
6563 The above example is equivalent to the Haskell expression
6565 arr (\ x -> x+1) >>> f
6567 That would make no sense if the expression to the left of
6568 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6569 More generally, the expression to the left of <literal>-<</literal>
6570 may not involve any <firstterm>local variable</firstterm>,
6571 i.e. a variable bound in the current arrow abstraction.
6572 For such a situation there is a variant <literal>-<<</literal>, as in
6574 proc x -> f x -<< x+1
6576 which is equivalent to
6578 arr (\ x -> (f x, x+1)) >>> app
6580 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6582 Such an arrow is equivalent to a monad, so if you're using this form
6583 you may find a monadic formulation more convenient.
6587 <title>do-notation for commands</title>
6590 Another form of command is a form of <literal>do</literal>-notation.
6591 For example, you can write
6600 You can read this much like ordinary <literal>do</literal>-notation,
6601 but with commands in place of monadic expressions.
6602 The first line sends the value of <literal>x+1</literal> as an input to
6603 the arrow <literal>f</literal>, and matches its output against
6604 <literal>y</literal>.
6605 In the next line, the output is discarded.
6606 The arrow <function>returnA</function> is defined in the
6607 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6608 module as <literal>arr id</literal>.
6609 The above example is treated as an abbreviation for
6611 arr (\ x -> (x, x)) >>>
6612 first (arr (\ x -> x+1) >>> f) >>>
6613 arr (\ (y, x) -> (y, (x, y))) >>>
6614 first (arr (\ y -> 2*y) >>> g) >>>
6616 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6617 first (arr (\ (x, z) -> x*z) >>> h) >>>
6618 arr (\ (t, z) -> t+z) >>>
6621 Note that variables not used later in the composition are projected out.
6622 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6624 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6625 module, this reduces to
6627 arr (\ x -> (x+1, x)) >>>
6629 arr (\ (y, x) -> (2*y, (x, y))) >>>
6631 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6633 arr (\ (t, z) -> t+z)
6635 which is what you might have written by hand.
6636 With arrow notation, GHC keeps track of all those tuples of variables for you.
6640 Note that although the above translation suggests that
6641 <literal>let</literal>-bound variables like <literal>z</literal> must be
6642 monomorphic, the actual translation produces Core,
6643 so polymorphic variables are allowed.
6647 It's also possible to have mutually recursive bindings,
6648 using the new <literal>rec</literal> keyword, as in the following example:
6650 counter :: ArrowCircuit a => a Bool Int
6651 counter = proc reset -> do
6652 rec output <- returnA -< if reset then 0 else next
6653 next <- delay 0 -< output+1
6654 returnA -< output
6656 The translation of such forms uses the <function>loop</function> combinator,
6657 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6663 <title>Conditional commands</title>
6666 In the previous example, we used a conditional expression to construct the
6668 Sometimes we want to conditionally execute different commands, as in
6675 which is translated to
6677 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6678 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6680 Since the translation uses <function>|||</function>,
6681 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6685 There are also <literal>case</literal> commands, like
6691 y <- h -< (x1, x2)
6695 The syntax is the same as for <literal>case</literal> expressions,
6696 except that the bodies of the alternatives are commands rather than expressions.
6697 The translation is similar to that of <literal>if</literal> commands.
6703 <title>Defining your own control structures</title>
6706 As we're seen, arrow notation provides constructs,
6707 modelled on those for expressions,
6708 for sequencing, value recursion and conditionals.
6709 But suitable combinators,
6710 which you can define in ordinary Haskell,
6711 may also be used to build new commands out of existing ones.
6712 The basic idea is that a command defines an arrow from environments to values.
6713 These environments assign values to the free local variables of the command.
6714 Thus combinators that produce arrows from arrows
6715 may also be used to build commands from commands.
6716 For example, the <literal>ArrowChoice</literal> class includes a combinator
6718 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6720 so we can use it to build commands:
6722 expr' = proc x -> do
6725 symbol Plus -< ()
6726 y <- term -< ()
6729 symbol Minus -< ()
6730 y <- term -< ()
6733 (The <literal>do</literal> on the first line is needed to prevent the first
6734 <literal><+> ...</literal> from being interpreted as part of the
6735 expression on the previous line.)
6736 This is equivalent to
6738 expr' = (proc x -> returnA -< x)
6739 <+> (proc x -> do
6740 symbol Plus -< ()
6741 y <- term -< ()
6743 <+> (proc x -> do
6744 symbol Minus -< ()
6745 y <- term -< ()
6748 It is essential that this operator be polymorphic in <literal>e</literal>
6749 (representing the environment input to the command
6750 and thence to its subcommands)
6751 and satisfy the corresponding naturality property
6753 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6755 at least for strict <literal>k</literal>.
6756 (This should be automatic if you're not using <function>seq</function>.)
6757 This ensures that environments seen by the subcommands are environments
6758 of the whole command,
6759 and also allows the translation to safely trim these environments.
6760 The operator must also not use any variable defined within the current
6765 We could define our own operator
6767 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6768 untilA body cond = proc x ->
6769 b <- cond -< x
6770 if b then returnA -< ()
6773 untilA body cond -< x
6775 and use it in the same way.
6776 Of course this infix syntax only makes sense for binary operators;
6777 there is also a more general syntax involving special brackets:
6781 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6788 <title>Primitive constructs</title>
6791 Some operators will need to pass additional inputs to their subcommands.
6792 For example, in an arrow type supporting exceptions,
6793 the operator that attaches an exception handler will wish to pass the
6794 exception that occurred to the handler.
6795 Such an operator might have a type
6797 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6799 where <literal>Ex</literal> is the type of exceptions handled.
6800 You could then use this with arrow notation by writing a command
6802 body `handleA` \ ex -> handler
6804 so that if an exception is raised in the command <literal>body</literal>,
6805 the variable <literal>ex</literal> is bound to the value of the exception
6806 and the command <literal>handler</literal>,
6807 which typically refers to <literal>ex</literal>, is entered.
6808 Though the syntax here looks like a functional lambda,
6809 we are talking about commands, and something different is going on.
6810 The input to the arrow represented by a command consists of values for
6811 the free local variables in the command, plus a stack of anonymous values.
6812 In all the prior examples, this stack was empty.
6813 In the second argument to <function>handleA</function>,
6814 this stack consists of one value, the value of the exception.
6815 The command form of lambda merely gives this value a name.
6820 the values on the stack are paired to the right of the environment.
6821 So operators like <function>handleA</function> that pass
6822 extra inputs to their subcommands can be designed for use with the notation
6823 by pairing the values with the environment in this way.
6824 More precisely, the type of each argument of the operator (and its result)
6825 should have the form
6827 a (...(e,t1), ... tn) t
6829 where <replaceable>e</replaceable> is a polymorphic variable
6830 (representing the environment)
6831 and <replaceable>ti</replaceable> are the types of the values on the stack,
6832 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6833 The polymorphic variable <replaceable>e</replaceable> must not occur in
6834 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6835 <replaceable>t</replaceable>.
6836 However the arrows involved need not be the same.
6837 Here are some more examples of suitable operators:
6839 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6840 runReader :: ... => a e c -> a' (e,State) c
6841 runState :: ... => a e c -> a' (e,State) (c,State)
6843 We can supply the extra input required by commands built with the last two
6844 by applying them to ordinary expressions, as in
6848 (|runReader (do { ... })|) s
6850 which adds <literal>s</literal> to the stack of inputs to the command
6851 built using <function>runReader</function>.
6855 The command versions of lambda abstraction and application are analogous to
6856 the expression versions.
6857 In particular, the beta and eta rules describe equivalences of commands.
6858 These three features (operators, lambda abstraction and application)
6859 are the core of the notation; everything else can be built using them,
6860 though the results would be somewhat clumsy.
6861 For example, we could simulate <literal>do</literal>-notation by defining
6863 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6864 u `bind` f = returnA &&& u >>> f
6866 bind_ :: Arrow a => a e b -> a e c -> a e c
6867 u `bind_` f = u `bind` (arr fst >>> f)
6869 We could simulate <literal>if</literal> by defining
6871 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6872 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6879 <title>Differences with the paper</title>
6884 <para>Instead of a single form of arrow application (arrow tail) with two
6885 translations, the implementation provides two forms
6886 <quote><literal>-<</literal></quote> (first-order)
6887 and <quote><literal>-<<</literal></quote> (higher-order).
6892 <para>User-defined operators are flagged with banana brackets instead of
6893 a new <literal>form</literal> keyword.
6902 <title>Portability</title>
6905 Although only GHC implements arrow notation directly,
6906 there is also a preprocessor
6908 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6909 that translates arrow notation into Haskell 98
6910 for use with other Haskell systems.
6911 You would still want to check arrow programs with GHC;
6912 tracing type errors in the preprocessor output is not easy.
6913 Modules intended for both GHC and the preprocessor must observe some
6914 additional restrictions:
6919 The module must import
6920 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6926 The preprocessor cannot cope with other Haskell extensions.
6927 These would have to go in separate modules.
6933 Because the preprocessor targets Haskell (rather than Core),
6934 <literal>let</literal>-bound variables are monomorphic.
6945 <!-- ==================== BANG PATTERNS ================= -->
6947 <sect1 id="bang-patterns">
6948 <title>Bang patterns
6949 <indexterm><primary>Bang patterns</primary></indexterm>
6951 <para>GHC supports an extension of pattern matching called <emphasis>bang
6952 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6953 Bang patterns are under consideration for Haskell Prime.
6955 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6956 prime feature description</ulink> contains more discussion and examples
6957 than the material below.
6960 The key change is the addition of a new rule to the
6961 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6962 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6963 against a value <replaceable>v</replaceable> behaves as follows:
6965 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6966 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6970 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6973 <sect2 id="bang-patterns-informal">
6974 <title>Informal description of bang patterns
6977 The main idea is to add a single new production to the syntax of patterns:
6981 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6982 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6987 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6988 whereas without the bang it would be lazy.
6989 Bang patterns can be nested of course:
6993 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6994 <literal>y</literal>.
6995 A bang only really has an effect if it precedes a variable or wild-card pattern:
7000 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7001 putting a bang before a pattern that
7002 forces evaluation anyway does nothing.
7005 There is one (apparent) exception to this general rule that a bang only
7006 makes a difference when it precedes a variable or wild-card: a bang at the
7007 top level of a <literal>let</literal> or <literal>where</literal>
7008 binding makes the binding strict, regardless of the pattern. For example:
7012 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
7013 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
7014 (We say "apparent" exception because the Right Way to think of it is that the bang
7015 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7016 is part of the syntax of the <emphasis>binding</emphasis>.)
7017 Nested bangs in a pattern binding behave uniformly with all other forms of
7018 pattern matching. For example
7020 let (!x,[y]) = e in b
7022 is equivalent to this:
7024 let { t = case e of (x,[y]) -> x `seq` (x,y)
7029 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7030 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7031 evaluation of <literal>x</literal>.
7034 Bang patterns work in <literal>case</literal> expressions too, of course:
7036 g5 x = let y = f x in body
7037 g6 x = case f x of { y -> body }
7038 g7 x = case f x of { !y -> body }
7040 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7041 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7042 result, and then evaluates <literal>body</literal>.
7047 <sect2 id="bang-patterns-sem">
7048 <title>Syntax and semantics
7052 We add a single new production to the syntax of patterns:
7056 There is one problem with syntactic ambiguity. Consider:
7060 Is this a definition of the infix function "<literal>(!)</literal>",
7061 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7062 ambiguity in favour of the latter. If you want to define
7063 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7068 The semantics of Haskell pattern matching is described in <ulink
7069 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7070 Section 3.17.2</ulink> of the Haskell Report. To this description add
7071 one extra item 10, saying:
7072 <itemizedlist><listitem><para>Matching
7073 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7074 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7075 <listitem><para>otherwise, <literal>pat</literal> is matched against
7076 <literal>v</literal></para></listitem>
7078 </para></listitem></itemizedlist>
7079 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7080 Section 3.17.3</ulink>, add a new case (t):
7082 case v of { !pat -> e; _ -> e' }
7083 = v `seq` case v of { pat -> e; _ -> e' }
7086 That leaves let expressions, whose translation is given in
7087 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7089 of the Haskell Report.
7090 In the translation box, first apply
7091 the following transformation: for each pattern <literal>pi</literal> that is of
7092 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7093 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7094 have a bang at the top, apply the rules in the existing box.
7096 <para>The effect of the let rule is to force complete matching of the pattern
7097 <literal>qi</literal> before evaluation of the body is begun. The bang is
7098 retained in the translated form in case <literal>qi</literal> is a variable,
7106 The let-binding can be recursive. However, it is much more common for
7107 the let-binding to be non-recursive, in which case the following law holds:
7108 <literal>(let !p = rhs in body)</literal>
7110 <literal>(case rhs of !p -> body)</literal>
7113 A pattern with a bang at the outermost level is not allowed at the top level of
7119 <!-- ==================== ASSERTIONS ================= -->
7121 <sect1 id="assertions">
7123 <indexterm><primary>Assertions</primary></indexterm>
7127 If you want to make use of assertions in your standard Haskell code, you
7128 could define a function like the following:
7134 assert :: Bool -> a -> a
7135 assert False x = error "assertion failed!"
7142 which works, but gives you back a less than useful error message --
7143 an assertion failed, but which and where?
7147 One way out is to define an extended <function>assert</function> function which also
7148 takes a descriptive string to include in the error message and
7149 perhaps combine this with the use of a pre-processor which inserts
7150 the source location where <function>assert</function> was used.
7154 Ghc offers a helping hand here, doing all of this for you. For every
7155 use of <function>assert</function> in the user's source:
7161 kelvinToC :: Double -> Double
7162 kelvinToC k = assert (k >= 0.0) (k+273.15)
7168 Ghc will rewrite this to also include the source location where the
7175 assert pred val ==> assertError "Main.hs|15" pred val
7181 The rewrite is only performed by the compiler when it spots
7182 applications of <function>Control.Exception.assert</function>, so you
7183 can still define and use your own versions of
7184 <function>assert</function>, should you so wish. If not, import
7185 <literal>Control.Exception</literal> to make use
7186 <function>assert</function> in your code.
7190 GHC ignores assertions when optimisation is turned on with the
7191 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7192 <literal>assert pred e</literal> will be rewritten to
7193 <literal>e</literal>. You can also disable assertions using the
7194 <option>-fignore-asserts</option>
7195 option<indexterm><primary><option>-fignore-asserts</option></primary>
7196 </indexterm>.</para>
7199 Assertion failures can be caught, see the documentation for the
7200 <literal>Control.Exception</literal> library for the details.
7206 <!-- =============================== PRAGMAS =========================== -->
7208 <sect1 id="pragmas">
7209 <title>Pragmas</title>
7211 <indexterm><primary>pragma</primary></indexterm>
7213 <para>GHC supports several pragmas, or instructions to the
7214 compiler placed in the source code. Pragmas don't normally affect
7215 the meaning of the program, but they might affect the efficiency
7216 of the generated code.</para>
7218 <para>Pragmas all take the form
7220 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7222 where <replaceable>word</replaceable> indicates the type of
7223 pragma, and is followed optionally by information specific to that
7224 type of pragma. Case is ignored in
7225 <replaceable>word</replaceable>. The various values for
7226 <replaceable>word</replaceable> that GHC understands are described
7227 in the following sections; any pragma encountered with an
7228 unrecognised <replaceable>word</replaceable> is
7229 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7230 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7232 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7236 pragma must precede the <literal>module</literal> keyword in the file.
7239 There can be as many file-header pragmas as you please, and they can be
7240 preceded or followed by comments.
7243 File-header pragmas are read once only, before
7244 pre-processing the file (e.g. with cpp).
7247 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7248 <literal>{-# OPTIONS_GHC #-}</literal>, and
7249 <literal>{-# INCLUDE #-}</literal>.
7254 <sect2 id="language-pragma">
7255 <title>LANGUAGE pragma</title>
7257 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7258 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7260 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7262 It is the intention that all Haskell compilers support the
7263 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7264 all extensions are supported by all compilers, of
7265 course. The <literal>LANGUAGE</literal> pragma should be used instead
7266 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7268 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7270 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7272 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7274 <para>Every language extension can also be turned into a command-line flag
7275 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7276 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7279 <para>A list of all supported language extensions can be obtained by invoking
7280 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7282 <para>Any extension from the <literal>Extension</literal> type defined in
7284 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7285 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7289 <sect2 id="options-pragma">
7290 <title>OPTIONS_GHC pragma</title>
7291 <indexterm><primary>OPTIONS_GHC</primary>
7293 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7296 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7297 additional options that are given to the compiler when compiling
7298 this source file. See <xref linkend="source-file-options"/> for
7301 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7302 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7305 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7307 <sect2 id="include-pragma">
7308 <title>INCLUDE pragma</title>
7310 <para>The <literal>INCLUDE</literal> used to be necessary for
7311 specifying header files to be included when using the FFI and
7312 compiling via C. It is no longer required for GHC, but is
7313 accepted (and ignored) for compatibility with other
7317 <sect2 id="warning-deprecated-pragma">
7318 <title>WARNING and DEPRECATED pragmas</title>
7319 <indexterm><primary>WARNING</primary></indexterm>
7320 <indexterm><primary>DEPRECATED</primary></indexterm>
7322 <para>The WARNING pragma allows you to attach an arbitrary warning
7323 to a particular function, class, or type.
7324 A DEPRECATED pragma lets you specify that
7325 a particular function, class, or type is deprecated.
7326 There are two ways of using these pragmas.
7330 <para>You can work on an entire module thus:</para>
7332 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7337 module Wibble {-# WARNING "This is an unstable interface." #-} where
7340 <para>When you compile any module that import
7341 <literal>Wibble</literal>, GHC will print the specified
7346 <para>You can attach a warning to a function, class, type, or data constructor, with the
7347 following top-level declarations:</para>
7349 {-# DEPRECATED f, C, T "Don't use these" #-}
7350 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7352 <para>When you compile any module that imports and uses any
7353 of the specified entities, GHC will print the specified
7355 <para> You can only attach to entities declared at top level in the module
7356 being compiled, and you can only use unqualified names in the list of
7357 entities. A capitalised name, such as <literal>T</literal>
7358 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7359 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7360 both are in scope. If both are in scope, there is currently no way to
7361 specify one without the other (c.f. fixities
7362 <xref linkend="infix-tycons"/>).</para>
7365 Warnings and deprecations are not reported for
7366 (a) uses within the defining module, and
7367 (b) uses in an export list.
7368 The latter reduces spurious complaints within a library
7369 in which one module gathers together and re-exports
7370 the exports of several others.
7372 <para>You can suppress the warnings with the flag
7373 <option>-fno-warn-warnings-deprecations</option>.</para>
7376 <sect2 id="inline-noinline-pragma">
7377 <title>INLINE and NOINLINE pragmas</title>
7379 <para>These pragmas control the inlining of function
7382 <sect3 id="inline-pragma">
7383 <title>INLINE pragma</title>
7384 <indexterm><primary>INLINE</primary></indexterm>
7386 <para>GHC (with <option>-O</option>, as always) tries to
7387 inline (or “unfold”) functions/values that are
7388 “small enough,” thus avoiding the call overhead
7389 and possibly exposing other more-wonderful optimisations.
7390 Normally, if GHC decides a function is “too
7391 expensive” to inline, it will not do so, nor will it
7392 export that unfolding for other modules to use.</para>
7394 <para>The sledgehammer you can bring to bear is the
7395 <literal>INLINE</literal><indexterm><primary>INLINE
7396 pragma</primary></indexterm> pragma, used thusly:</para>
7399 key_function :: Int -> String -> (Bool, Double)
7400 {-# INLINE key_function #-}
7403 <para>The major effect of an <literal>INLINE</literal> pragma
7404 is to declare a function's “cost” to be very low.
7405 The normal unfolding machinery will then be very keen to
7406 inline it. However, an <literal>INLINE</literal> pragma for a
7407 function "<literal>f</literal>" has a number of other effects:
7410 No functions are inlined into <literal>f</literal>. Otherwise
7411 GHC might inline a big function into <literal>f</literal>'s right hand side,
7412 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7415 The float-in, float-out, and common-sub-expression transformations are not
7416 applied to the body of <literal>f</literal>.
7419 An INLINE function is not worker/wrappered by strictness analysis.
7420 It's going to be inlined wholesale instead.
7423 All of these effects are aimed at ensuring that what gets inlined is
7424 exactly what you asked for, no more and no less.
7426 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7427 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7428 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7429 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7430 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7431 when there is no choice even an INLINE function can be selected, in which case
7432 the INLINE pragma is ignored.
7433 For example, for a self-recursive function, the loop breaker can only be the function
7434 itself, so an INLINE pragma is always ignored.</para>
7436 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7437 function can be put anywhere its type signature could be
7440 <para><literal>INLINE</literal> pragmas are a particularly
7442 <literal>then</literal>/<literal>return</literal> (or
7443 <literal>bind</literal>/<literal>unit</literal>) functions in
7444 a monad. For example, in GHC's own
7445 <literal>UniqueSupply</literal> monad code, we have:</para>
7448 {-# INLINE thenUs #-}
7449 {-# INLINE returnUs #-}
7452 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7453 linkend="noinline-pragma"/>).</para>
7455 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7456 so if you want your code to be HBC-compatible you'll have to surround
7457 the pragma with C pre-processor directives
7458 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7462 <sect3 id="noinline-pragma">
7463 <title>NOINLINE pragma</title>
7465 <indexterm><primary>NOINLINE</primary></indexterm>
7466 <indexterm><primary>NOTINLINE</primary></indexterm>
7468 <para>The <literal>NOINLINE</literal> pragma does exactly what
7469 you'd expect: it stops the named function from being inlined
7470 by the compiler. You shouldn't ever need to do this, unless
7471 you're very cautious about code size.</para>
7473 <para><literal>NOTINLINE</literal> is a synonym for
7474 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7475 specified by Haskell 98 as the standard way to disable
7476 inlining, so it should be used if you want your code to be
7480 <sect3 id="phase-control">
7481 <title>Phase control</title>
7483 <para> Sometimes you want to control exactly when in GHC's
7484 pipeline the INLINE pragma is switched on. Inlining happens
7485 only during runs of the <emphasis>simplifier</emphasis>. Each
7486 run of the simplifier has a different <emphasis>phase
7487 number</emphasis>; the phase number decreases towards zero.
7488 If you use <option>-dverbose-core2core</option> you'll see the
7489 sequence of phase numbers for successive runs of the
7490 simplifier. In an INLINE pragma you can optionally specify a
7494 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7495 <literal>f</literal>
7496 until phase <literal>k</literal>, but from phase
7497 <literal>k</literal> onwards be very keen to inline it.
7500 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7501 <literal>f</literal>
7502 until phase <literal>k</literal>, but from phase
7503 <literal>k</literal> onwards do not inline it.
7506 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7507 <literal>f</literal>
7508 until phase <literal>k</literal>, but from phase
7509 <literal>k</literal> onwards be willing to inline it (as if
7510 there was no pragma).
7513 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7514 <literal>f</literal>
7515 until phase <literal>k</literal>, but from phase
7516 <literal>k</literal> onwards do not inline it.
7519 The same information is summarised here:
7521 -- Before phase 2 Phase 2 and later
7522 {-# INLINE [2] f #-} -- No Yes
7523 {-# INLINE [~2] f #-} -- Yes No
7524 {-# NOINLINE [2] f #-} -- No Maybe
7525 {-# NOINLINE [~2] f #-} -- Maybe No
7527 {-# INLINE f #-} -- Yes Yes
7528 {-# NOINLINE f #-} -- No No
7530 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7531 function body is small, or it is applied to interesting-looking arguments etc).
7532 Another way to understand the semantics is this:
7534 <listitem><para>For both INLINE and NOINLINE, the phase number says
7535 when inlining is allowed at all.</para></listitem>
7536 <listitem><para>The INLINE pragma has the additional effect of making the
7537 function body look small, so that when inlining is allowed it is very likely to
7542 <para>The same phase-numbering control is available for RULES
7543 (<xref linkend="rewrite-rules"/>).</para>
7547 <sect2 id="annotation-pragmas">
7548 <title>ANN pragmas</title>
7550 <para>GHC offers the ability to annotate various code constructs with additional
7551 data by using three pragmas. This data can then be inspected at a later date by
7552 using GHC-as-a-library.</para>
7554 <sect3 id="ann-pragma">
7555 <title>Annotating values</title>
7557 <indexterm><primary>ANN</primary></indexterm>
7559 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7560 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7561 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7562 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7563 you would do this:</para>
7566 {-# ANN foo (Just "Hello") #-}
7571 A number of restrictions apply to use of annotations:
7573 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7574 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7575 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7576 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7577 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7579 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7580 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7583 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7584 please give the GHC team a shout</ulink>.
7587 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7588 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7591 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7596 <sect3 id="typeann-pragma">
7597 <title>Annotating types</title>
7599 <indexterm><primary>ANN type</primary></indexterm>
7600 <indexterm><primary>ANN</primary></indexterm>
7602 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7605 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7610 <sect3 id="modann-pragma">
7611 <title>Annotating modules</title>
7613 <indexterm><primary>ANN module</primary></indexterm>
7614 <indexterm><primary>ANN</primary></indexterm>
7616 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7619 {-# ANN module (Just "A `Maybe String' annotation") #-}
7624 <sect2 id="line-pragma">
7625 <title>LINE pragma</title>
7627 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7628 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7629 <para>This pragma is similar to C's <literal>#line</literal>
7630 pragma, and is mainly for use in automatically generated Haskell
7631 code. It lets you specify the line number and filename of the
7632 original code; for example</para>
7634 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7636 <para>if you'd generated the current file from something called
7637 <filename>Foo.vhs</filename> and this line corresponds to line
7638 42 in the original. GHC will adjust its error messages to refer
7639 to the line/file named in the <literal>LINE</literal>
7644 <title>RULES pragma</title>
7646 <para>The RULES pragma lets you specify rewrite rules. It is
7647 described in <xref linkend="rewrite-rules"/>.</para>
7650 <sect2 id="specialize-pragma">
7651 <title>SPECIALIZE pragma</title>
7653 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7654 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7655 <indexterm><primary>overloading, death to</primary></indexterm>
7657 <para>(UK spelling also accepted.) For key overloaded
7658 functions, you can create extra versions (NB: more code space)
7659 specialised to particular types. Thus, if you have an
7660 overloaded function:</para>
7663 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7666 <para>If it is heavily used on lists with
7667 <literal>Widget</literal> keys, you could specialise it as
7671 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7674 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7675 be put anywhere its type signature could be put.</para>
7677 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7678 (a) a specialised version of the function and (b) a rewrite rule
7679 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7680 un-specialised function into a call to the specialised one.</para>
7682 <para>The type in a SPECIALIZE pragma can be any type that is less
7683 polymorphic than the type of the original function. In concrete terms,
7684 if the original function is <literal>f</literal> then the pragma
7686 {-# SPECIALIZE f :: <type> #-}
7688 is valid if and only if the definition
7690 f_spec :: <type>
7693 is valid. Here are some examples (where we only give the type signature
7694 for the original function, not its code):
7696 f :: Eq a => a -> b -> b
7697 {-# SPECIALISE f :: Int -> b -> b #-}
7699 g :: (Eq a, Ix b) => a -> b -> b
7700 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7702 h :: Eq a => a -> a -> a
7703 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7705 The last of these examples will generate a
7706 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7707 well. If you use this kind of specialisation, let us know how well it works.
7710 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7711 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7712 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7713 The <literal>INLINE</literal> pragma affects the specialised version of the
7714 function (only), and applies even if the function is recursive. The motivating
7717 -- A GADT for arrays with type-indexed representation
7719 ArrInt :: !Int -> ByteArray# -> Arr Int
7720 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7722 (!:) :: Arr e -> Int -> e
7723 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7724 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7725 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7726 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7728 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7729 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7730 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7731 the specialised function will be inlined. It has two calls to
7732 <literal>(!:)</literal>,
7733 both at type <literal>Int</literal>. Both these calls fire the first
7734 specialisation, whose body is also inlined. The result is a type-based
7735 unrolling of the indexing function.</para>
7736 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7737 on an ordinarily-recursive function.</para>
7739 <para>Note: In earlier versions of GHC, it was possible to provide your own
7740 specialised function for a given type:
7743 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7746 This feature has been removed, as it is now subsumed by the
7747 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7751 <sect2 id="specialize-instance-pragma">
7752 <title>SPECIALIZE instance pragma
7756 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7757 <indexterm><primary>overloading, death to</primary></indexterm>
7758 Same idea, except for instance declarations. For example:
7761 instance (Eq a) => Eq (Foo a) where {
7762 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7766 The pragma must occur inside the <literal>where</literal> part
7767 of the instance declaration.
7770 Compatible with HBC, by the way, except perhaps in the placement
7776 <sect2 id="unpack-pragma">
7777 <title>UNPACK pragma</title>
7779 <indexterm><primary>UNPACK</primary></indexterm>
7781 <para>The <literal>UNPACK</literal> indicates to the compiler
7782 that it should unpack the contents of a constructor field into
7783 the constructor itself, removing a level of indirection. For
7787 data T = T {-# UNPACK #-} !Float
7788 {-# UNPACK #-} !Float
7791 <para>will create a constructor <literal>T</literal> containing
7792 two unboxed floats. This may not always be an optimisation: if
7793 the <function>T</function> constructor is scrutinised and the
7794 floats passed to a non-strict function for example, they will
7795 have to be reboxed (this is done automatically by the
7798 <para>Unpacking constructor fields should only be used in
7799 conjunction with <option>-O</option>, in order to expose
7800 unfoldings to the compiler so the reboxing can be removed as
7801 often as possible. For example:</para>
7805 f (T f1 f2) = f1 + f2
7808 <para>The compiler will avoid reboxing <function>f1</function>
7809 and <function>f2</function> by inlining <function>+</function>
7810 on floats, but only when <option>-O</option> is on.</para>
7812 <para>Any single-constructor data is eligible for unpacking; for
7816 data T = T {-# UNPACK #-} !(Int,Int)
7819 <para>will store the two <literal>Int</literal>s directly in the
7820 <function>T</function> constructor, by flattening the pair.
7821 Multi-level unpacking is also supported:
7824 data T = T {-# UNPACK #-} !S
7825 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7828 will store two unboxed <literal>Int#</literal>s
7829 directly in the <function>T</function> constructor. The
7830 unpacker can see through newtypes, too.</para>
7832 <para>If a field cannot be unpacked, you will not get a warning,
7833 so it might be an idea to check the generated code with
7834 <option>-ddump-simpl</option>.</para>
7836 <para>See also the <option>-funbox-strict-fields</option> flag,
7837 which essentially has the effect of adding
7838 <literal>{-# UNPACK #-}</literal> to every strict
7839 constructor field.</para>
7842 <sect2 id="source-pragma">
7843 <title>SOURCE pragma</title>
7845 <indexterm><primary>SOURCE</primary></indexterm>
7846 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7847 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7853 <!-- ======================= REWRITE RULES ======================== -->
7855 <sect1 id="rewrite-rules">
7856 <title>Rewrite rules
7858 <indexterm><primary>RULES pragma</primary></indexterm>
7859 <indexterm><primary>pragma, RULES</primary></indexterm>
7860 <indexterm><primary>rewrite rules</primary></indexterm></title>
7863 The programmer can specify rewrite rules as part of the source program
7869 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7874 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7875 If you need more information, then <option>-ddump-rule-firings</option> shows you
7876 each individual rule firing in detail.
7880 <title>Syntax</title>
7883 From a syntactic point of view:
7889 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7890 may be generated by the layout rule).
7896 The layout rule applies in a pragma.
7897 Currently no new indentation level
7898 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7899 you must lay out the starting in the same column as the enclosing definitions.
7902 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7903 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7906 Furthermore, the closing <literal>#-}</literal>
7907 should start in a column to the right of the opening <literal>{-#</literal>.
7913 Each rule has a name, enclosed in double quotes. The name itself has
7914 no significance at all. It is only used when reporting how many times the rule fired.
7920 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7921 immediately after the name of the rule. Thus:
7924 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7927 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7928 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7937 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7938 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7939 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7940 by spaces, just like in a type <literal>forall</literal>.
7946 A pattern variable may optionally have a type signature.
7947 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7948 For example, here is the <literal>foldr/build</literal> rule:
7951 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7952 foldr k z (build g) = g k z
7955 Since <function>g</function> has a polymorphic type, it must have a type signature.
7962 The left hand side of a rule must consist of a top-level variable applied
7963 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7966 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7967 "wrong2" forall f. f True = True
7970 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7977 A rule does not need to be in the same module as (any of) the
7978 variables it mentions, though of course they need to be in scope.
7984 All rules are implicitly exported from the module, and are therefore
7985 in force in any module that imports the module that defined the rule, directly
7986 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7987 in force when compiling A.) The situation is very similar to that for instance
7995 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7996 any other flag settings. Furthermore, inside a RULE, the language extension
7997 <option>-XScopedTypeVariables</option> is automatically enabled; see
7998 <xref linkend="scoped-type-variables"/>.
8004 Like other pragmas, RULE pragmas are always checked for scope errors, and
8005 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8006 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8007 if the <option>-fenable-rewrite-rules</option> flag is
8008 on (see <xref linkend="rule-semantics"/>).
8017 <sect2 id="rule-semantics">
8018 <title>Semantics</title>
8021 From a semantic point of view:
8026 Rules are enabled (that is, used during optimisation)
8027 by the <option>-fenable-rewrite-rules</option> flag.
8028 This flag is implied by <option>-O</option>, and may be switched
8029 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8030 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8031 may not do what you expect, though, because without <option>-O</option> GHC
8032 ignores all optimisation information in interface files;
8033 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8034 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8035 has no effect on parsing or typechecking.
8041 Rules are regarded as left-to-right rewrite rules.
8042 When GHC finds an expression that is a substitution instance of the LHS
8043 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8044 By "a substitution instance" we mean that the LHS can be made equal to the
8045 expression by substituting for the pattern variables.
8052 GHC makes absolutely no attempt to verify that the LHS and RHS
8053 of a rule have the same meaning. That is undecidable in general, and
8054 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8061 GHC makes no attempt to make sure that the rules are confluent or
8062 terminating. For example:
8065 "loop" forall x y. f x y = f y x
8068 This rule will cause the compiler to go into an infinite loop.
8075 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8081 GHC currently uses a very simple, syntactic, matching algorithm
8082 for matching a rule LHS with an expression. It seeks a substitution
8083 which makes the LHS and expression syntactically equal modulo alpha
8084 conversion. The pattern (rule), but not the expression, is eta-expanded if
8085 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8086 But not beta conversion (that's called higher-order matching).
8090 Matching is carried out on GHC's intermediate language, which includes
8091 type abstractions and applications. So a rule only matches if the
8092 types match too. See <xref linkend="rule-spec"/> below.
8098 GHC keeps trying to apply the rules as it optimises the program.
8099 For example, consider:
8108 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8109 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8110 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8111 not be substituted, and the rule would not fire.
8118 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8119 results. Consider this (artificial) example
8122 {-# RULES "f" f True = False #-}
8128 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8133 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8135 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8136 would have been a better chance that <literal>f</literal>'s RULE might fire.
8139 The way to get predictable behaviour is to use a NOINLINE
8140 pragma on <literal>f</literal>, to ensure
8141 that it is not inlined until its RULEs have had a chance to fire.
8151 <title>List fusion</title>
8154 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8155 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8156 intermediate list should be eliminated entirely.
8160 The following are good producers:
8172 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8178 Explicit lists (e.g. <literal>[True, False]</literal>)
8184 The cons constructor (e.g <literal>3:4:[]</literal>)
8190 <function>++</function>
8196 <function>map</function>
8202 <function>take</function>, <function>filter</function>
8208 <function>iterate</function>, <function>repeat</function>
8214 <function>zip</function>, <function>zipWith</function>
8223 The following are good consumers:
8235 <function>array</function> (on its second argument)
8241 <function>++</function> (on its first argument)
8247 <function>foldr</function>
8253 <function>map</function>
8259 <function>take</function>, <function>filter</function>
8265 <function>concat</function>
8271 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8277 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8278 will fuse with one but not the other)
8284 <function>partition</function>
8290 <function>head</function>
8296 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8302 <function>sequence_</function>
8308 <function>msum</function>
8314 <function>sortBy</function>
8323 So, for example, the following should generate no intermediate lists:
8326 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8332 This list could readily be extended; if there are Prelude functions that you use
8333 a lot which are not included, please tell us.
8337 If you want to write your own good consumers or producers, look at the
8338 Prelude definitions of the above functions to see how to do so.
8343 <sect2 id="rule-spec">
8344 <title>Specialisation
8348 Rewrite rules can be used to get the same effect as a feature
8349 present in earlier versions of GHC.
8350 For example, suppose that:
8353 genericLookup :: Ord a => Table a b -> a -> b
8354 intLookup :: Table Int b -> Int -> b
8357 where <function>intLookup</function> is an implementation of
8358 <function>genericLookup</function> that works very fast for
8359 keys of type <literal>Int</literal>. You might wish
8360 to tell GHC to use <function>intLookup</function> instead of
8361 <function>genericLookup</function> whenever the latter was called with
8362 type <literal>Table Int b -> Int -> b</literal>.
8363 It used to be possible to write
8366 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8369 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8372 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8375 This slightly odd-looking rule instructs GHC to replace
8376 <function>genericLookup</function> by <function>intLookup</function>
8377 <emphasis>whenever the types match</emphasis>.
8378 What is more, this rule does not need to be in the same
8379 file as <function>genericLookup</function>, unlike the
8380 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8381 have an original definition available to specialise).
8384 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8385 <function>intLookup</function> really behaves as a specialised version
8386 of <function>genericLookup</function>!!!</para>
8388 <para>An example in which using <literal>RULES</literal> for
8389 specialisation will Win Big:
8392 toDouble :: Real a => a -> Double
8393 toDouble = fromRational . toRational
8395 {-# RULES "toDouble/Int" toDouble = i2d #-}
8396 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8399 The <function>i2d</function> function is virtually one machine
8400 instruction; the default conversion—via an intermediate
8401 <literal>Rational</literal>—is obscenely expensive by
8408 <title>Controlling what's going on</title>
8416 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8422 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8423 If you add <option>-dppr-debug</option> you get a more detailed listing.
8429 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8432 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8433 {-# INLINE build #-}
8437 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8438 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8439 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8440 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8447 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8448 see how to write rules that will do fusion and yet give an efficient
8449 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8459 <sect2 id="core-pragma">
8460 <title>CORE pragma</title>
8462 <indexterm><primary>CORE pragma</primary></indexterm>
8463 <indexterm><primary>pragma, CORE</primary></indexterm>
8464 <indexterm><primary>core, annotation</primary></indexterm>
8467 The external core format supports <quote>Note</quote> annotations;
8468 the <literal>CORE</literal> pragma gives a way to specify what these
8469 should be in your Haskell source code. Syntactically, core
8470 annotations are attached to expressions and take a Haskell string
8471 literal as an argument. The following function definition shows an
8475 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8478 Semantically, this is equivalent to:
8486 However, when external core is generated (via
8487 <option>-fext-core</option>), there will be Notes attached to the
8488 expressions <function>show</function> and <varname>x</varname>.
8489 The core function declaration for <function>f</function> is:
8493 f :: %forall a . GHCziShow.ZCTShow a ->
8494 a -> GHCziBase.ZMZN GHCziBase.Char =
8495 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8497 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8499 (tpl1::GHCziBase.Int ->
8501 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8503 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8504 (tpl3::GHCziBase.ZMZN a ->
8505 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8513 Here, we can see that the function <function>show</function> (which
8514 has been expanded out to a case expression over the Show dictionary)
8515 has a <literal>%note</literal> attached to it, as does the
8516 expression <varname>eta</varname> (which used to be called
8517 <varname>x</varname>).
8524 <sect1 id="special-ids">
8525 <title>Special built-in functions</title>
8526 <para>GHC has a few built-in functions with special behaviour. These
8527 are now described in the module <ulink
8528 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8529 in the library documentation.</para>
8533 <sect1 id="generic-classes">
8534 <title>Generic classes</title>
8537 The ideas behind this extension are described in detail in "Derivable type classes",
8538 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8539 An example will give the idea:
8547 fromBin :: [Int] -> (a, [Int])
8549 toBin {| Unit |} Unit = []
8550 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8551 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8552 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8554 fromBin {| Unit |} bs = (Unit, bs)
8555 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8556 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8557 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8558 (y,bs'') = fromBin bs'
8561 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8562 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8563 which are defined thus in the library module <literal>Generics</literal>:
8567 data a :+: b = Inl a | Inr b
8568 data a :*: b = a :*: b
8571 Now you can make a data type into an instance of Bin like this:
8573 instance (Bin a, Bin b) => Bin (a,b)
8574 instance Bin a => Bin [a]
8576 That is, just leave off the "where" clause. Of course, you can put in the
8577 where clause and over-ride whichever methods you please.
8581 <title> Using generics </title>
8582 <para>To use generics you need to</para>
8585 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8586 <option>-XGenerics</option> (to generate extra per-data-type code),
8587 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8591 <para>Import the module <literal>Generics</literal> from the
8592 <literal>lang</literal> package. This import brings into
8593 scope the data types <literal>Unit</literal>,
8594 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8595 don't need this import if you don't mention these types
8596 explicitly; for example, if you are simply giving instance
8597 declarations.)</para>
8602 <sect2> <title> Changes wrt the paper </title>
8604 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8605 can be written infix (indeed, you can now use
8606 any operator starting in a colon as an infix type constructor). Also note that
8607 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8608 Finally, note that the syntax of the type patterns in the class declaration
8609 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8610 alone would ambiguous when they appear on right hand sides (an extension we
8611 anticipate wanting).
8615 <sect2> <title>Terminology and restrictions</title>
8617 Terminology. A "generic default method" in a class declaration
8618 is one that is defined using type patterns as above.
8619 A "polymorphic default method" is a default method defined as in Haskell 98.
8620 A "generic class declaration" is a class declaration with at least one
8621 generic default method.
8629 Alas, we do not yet implement the stuff about constructor names and
8636 A generic class can have only one parameter; you can't have a generic
8637 multi-parameter class.
8643 A default method must be defined entirely using type patterns, or entirely
8644 without. So this is illegal:
8647 op :: a -> (a, Bool)
8648 op {| Unit |} Unit = (Unit, True)
8651 However it is perfectly OK for some methods of a generic class to have
8652 generic default methods and others to have polymorphic default methods.
8658 The type variable(s) in the type pattern for a generic method declaration
8659 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:
8663 op {| p :*: q |} (x :*: y) = op (x :: p)
8671 The type patterns in a generic default method must take one of the forms:
8677 where "a" and "b" are type variables. Furthermore, all the type patterns for
8678 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8679 must use the same type variables. So this is illegal:
8683 op {| a :+: b |} (Inl x) = True
8684 op {| p :+: q |} (Inr y) = False
8686 The type patterns must be identical, even in equations for different methods of the class.
8687 So this too is illegal:
8691 op1 {| a :*: b |} (x :*: y) = True
8694 op2 {| p :*: q |} (x :*: y) = False
8696 (The reason for this restriction is that we gather all the equations for a particular type constructor
8697 into a single generic instance declaration.)
8703 A generic method declaration must give a case for each of the three type constructors.
8709 The type for a generic method can be built only from:
8711 <listitem> <para> Function arrows </para> </listitem>
8712 <listitem> <para> Type variables </para> </listitem>
8713 <listitem> <para> Tuples </para> </listitem>
8714 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8716 Here are some example type signatures for generic methods:
8719 op2 :: Bool -> (a,Bool)
8720 op3 :: [Int] -> a -> a
8723 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8727 This restriction is an implementation restriction: we just haven't got around to
8728 implementing the necessary bidirectional maps over arbitrary type constructors.
8729 It would be relatively easy to add specific type constructors, such as Maybe and list,
8730 to the ones that are allowed.</para>
8735 In an instance declaration for a generic class, the idea is that the compiler
8736 will fill in the methods for you, based on the generic templates. However it can only
8741 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8746 No constructor of the instance type has unboxed fields.
8750 (Of course, these things can only arise if you are already using GHC extensions.)
8751 However, you can still give an instance declarations for types which break these rules,
8752 provided you give explicit code to override any generic default methods.
8760 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8761 what the compiler does with generic declarations.
8766 <sect2> <title> Another example </title>
8768 Just to finish with, here's another example I rather like:
8772 nCons {| Unit |} _ = 1
8773 nCons {| a :*: b |} _ = 1
8774 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8777 tag {| Unit |} _ = 1
8778 tag {| a :*: b |} _ = 1
8779 tag {| a :+: b |} (Inl x) = tag x
8780 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8786 <sect1 id="monomorphism">
8787 <title>Control over monomorphism</title>
8789 <para>GHC supports two flags that control the way in which generalisation is
8790 carried out at let and where bindings.
8794 <title>Switching off the dreaded Monomorphism Restriction</title>
8795 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8797 <para>Haskell's monomorphism restriction (see
8798 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8800 of the Haskell Report)
8801 can be completely switched off by
8802 <option>-XNoMonomorphismRestriction</option>.
8807 <title>Monomorphic pattern bindings</title>
8808 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8809 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8811 <para> As an experimental change, we are exploring the possibility of
8812 making pattern bindings monomorphic; that is, not generalised at all.
8813 A pattern binding is a binding whose LHS has no function arguments,
8814 and is not a simple variable. For example:
8816 f x = x -- Not a pattern binding
8817 f = \x -> x -- Not a pattern binding
8818 f :: Int -> Int = \x -> x -- Not a pattern binding
8820 (g,h) = e -- A pattern binding
8821 (f) = e -- A pattern binding
8822 [x] = e -- A pattern binding
8824 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8825 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
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